Global uniqueness in an inverse problem for time fractional diffusion equations

NASA Astrophysics Data System (ADS)

Kian, Y.; Oksanen, L.; Soccorsi, E.; Yamamoto, M.

2018-01-01

Given (M , g), a compact connected Riemannian manifold of dimension d ⩾ 2, with boundary ∂M, we consider an initial boundary value problem for a fractional diffusion equation on (0 , T) × M, T > 0, with time-fractional Caputo derivative of order α ∈ (0 , 1) ∪ (1 , 2). We prove uniqueness in the inverse problem of determining the smooth manifold (M , g) (up to an isometry), and various time-independent smooth coefficients appearing in this equation, from measurements of the solutions on a subset of ∂M at fixed time. In the "flat" case where M is a compact subset of Rd, two out the three coefficients ρ (density), a (conductivity) and q (potential) appearing in the equation ρ ∂tα u - div (a∇u) + qu = 0 on (0 , T) × M are recovered simultaneously.

Absolute mass scale calibration in the inverse problem of the physical theory of fireballs.

NASA Astrophysics Data System (ADS)

Kalenichenko, V. V.

A method of the absolute mass scale calibration is suggested for solving the inverse problem of the physical theory of fireballs. The method is based on the data on the masses of the fallen meteorites whose fireballs have been photographed in their flight. The method may be applied to those fireballs whose bodies have not experienced considerable fragmentation during their destruction in the atmosphere and have kept their form well enough. Statistical analysis of the inverse problem solution for a sufficiently representative sample makes it possible to separate a subsample of such fireballs. The data on the Lost City and Innisfree meteorites are used to obtain calibration coefficients.

Combined inverse-forward artificial neural networks for fast and accurate estimation of the diffusion coefficients of cartilage based on multi-physics models.

PubMed

Arbabi, Vahid; Pouran, Behdad; Weinans, Harrie; Zadpoor, Amir A

2016-09-06

Analytical and numerical methods have been used to extract essential engineering parameters such as elastic modulus, Poisson׳s ratio, permeability and diffusion coefficient from experimental data in various types of biological tissues. The major limitation associated with analytical techniques is that they are often only applicable to problems with simplified assumptions. Numerical multi-physics methods, on the other hand, enable minimizing the simplified assumptions but require substantial computational expertise, which is not always available. In this paper, we propose a novel approach that combines inverse and forward artificial neural networks (ANNs) which enables fast and accurate estimation of the diffusion coefficient of cartilage without any need for computational modeling. In this approach, an inverse ANN is trained using our multi-zone biphasic-solute finite-bath computational model of diffusion in cartilage to estimate the diffusion coefficient of the various zones of cartilage given the concentration-time curves. Robust estimation of the diffusion coefficients, however, requires introducing certain levels of stochastic variations during the training process. Determining the required level of stochastic variation is performed by coupling the inverse ANN with a forward ANN that receives the diffusion coefficient as input and returns the concentration-time curve as output. Combined together, forward-inverse ANNs enable computationally inexperienced users to obtain accurate and fast estimation of the diffusion coefficients of cartilage zones. The diffusion coefficients estimated using the proposed approach are compared with those determined using direct scanning of the parameter space as the optimization approach. It has been shown that both approaches yield comparable results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Determination of Diffusion Coefficients in Cement-Based Materials: An Inverse Problem for the Nernst-Planck and Poisson Models

NASA Astrophysics Data System (ADS)

Szyszkiewicz-Warzecha, Krzysztof; Jasielec, Jerzy J.; Fausek, Janusz; Filipek, Robert

2016-08-01

Transport properties of ions have significant impact on the possibility of rebars corrosion thus the knowledge of a diffusion coefficient is important for reinforced concrete durability. Numerous tests for the determination of diffusion coefficients have been proposed but analysis of some of these tests show that they are too simplistic or even not valid. Hence, more rigorous models to calculate the coefficients should be employed. Here we propose the Nernst-Planck and Poisson equations, which take into account the concentration and electric potential field. Based on this model a special inverse method is presented for determination of a chloride diffusion coefficient. It requires the measurement of concentration profiles or flux on the boundary and solution of the NPP model to define the goal function. Finding the global minimum is equivalent to the determination of diffusion coefficients. Typical examples of the application of the presented method are given.

Numerical computations on one-dimensional inverse scattering problems

NASA Technical Reports Server (NTRS)

Dunn, M. H.; Hariharan, S. I.

1983-01-01

An approximate method to determine the index of refraction of a dielectric obstacle is presented. For simplicity one dimensional models of electromagnetic scattering are treated. The governing equations yield a second order boundary value problem, in which the index of refraction appears as a functional parameter. The availability of reflection coefficients yield two additional boundary conditions. The index of refraction by a k-th order spline which can be written as a linear combination of B-splines is approximated. For N distinct reflection coefficients, the resulting N boundary value problems yield a system of N nonlinear equations in N unknowns which are the coefficients of the B-splines.

An Efficient Spectral Method for Ordinary Differential Equations with Rational Function Coefficients

NASA Technical Reports Server (NTRS)

Coutsias, Evangelos A.; Torres, David; Hagstrom, Thomas

1994-01-01

We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, including all the classical orthogonal polynomials. These families obey a simple three-term recurrence relation for differentiation, which implies that on an appropriately restricted domain the differentiation operator has a unique banded inverse. The inverse is an integration operator for the family, and it is simply the tridiagonal coefficient matrix for the recurrence. Since in these families convolution operators (i.e. matrix representations of multiplication by a function) are banded for polynomials, we are able to obtain a banded representation for linear differential operators with rational coefficients. This leads to a method of solution of initial or boundary value problems that, besides having an operation count that scales linearly with the order of truncation N, is computationally well conditioned. Among the applications considered is the use of rational maps for the resolution of sharp interior layers.

Inverse transport problems in quantitative PAT for molecular imaging

NASA Astrophysics Data System (ADS)

Ren, Kui; Zhang, Rongting; Zhong, Yimin

2015-12-01

Fluorescence photoacoustic tomography (fPAT) is a molecular imaging modality that combines photoacoustic tomography with fluorescence imaging to obtain high-resolution imaging of fluorescence distributions inside heterogeneous media. The objective of this work is to study inverse problems in the quantitative step of fPAT where we intend to reconstruct physical coefficients in a coupled system of radiative transport equations using internal data recovered from ultrasound measurements. We derive uniqueness and stability results on the inverse problems and develop some efficient algorithms for image reconstructions. Numerical simulations based on synthetic data are presented to validate the theoretical analysis. The results we present here complement these in Ren K and Zhao H (2013 SIAM J. Imaging Sci. 6 2024-49) on the same problem but in the diffusive regime.

Exact solution for an optimal impermeable parachute problem

NASA Astrophysics Data System (ADS)

Lupu, Mircea; Scheiber, Ernest

2002-10-01

In the paper there are solved direct and inverse boundary problems and analytical solutions are obtained for optimization problems in the case of some nonlinear integral operators. It is modeled the plane potential flow of an inviscid, incompressible and nonlimited fluid jet, witch encounters a symmetrical, curvilinear obstacle--the deflector of maximal drag. There are derived integral singular equations, for direct and inverse problems and the movement in the auxiliary canonical half-plane is obtained. Next, the optimization problem is solved in an analytical manner. The design of the optimal airfoil is performed and finally, numerical computations concerning the drag coefficient and other geometrical and aerodynamical parameters are carried out. This model corresponds to the Helmholtz impermeable parachute problem.

Reconstruction of the spatial dependence of dielectric and geometrical properties of adhesively bonded structures

NASA Astrophysics Data System (ADS)

Mackay, C.; Hayward, D.; Mulholland, A. J.; McKee, S.; Pethrick, R. A.

2005-06-01

An inverse problem motivated by the nondestructive testing of adhesively bonded structures used in the aircraft industry is studied. Using transmission line theory, a model is developed which, when supplied with electrical and geometrical parameters, accurately predicts the reflection coefficient associated with such structures. Particular attention is paid to modelling the connection between the structures and the equipment used to measure the reflection coefficient. The inverse problem is then studied and an optimization approach employed to recover these electrical and geometrical parameters from experimentally obtained data. In particular the approach focuses on the recovery of spatially varying geometrical parameters as this is paramount to the successful reconstruction of electrical parameters. Reconstructions of structure geometry using this method are found to be in close agreement with experimental observations.

Geoacoustic inversion with two source-receiver arrays in shallow water.

PubMed

Sukhovich, Alexey; Roux, Philippe; Wathelet, Marc

2010-08-01

A geoacoustic inversion scheme based on a double beamforming algorithm in shallow water is proposed and tested. Double beamforming allows identification of multi-reverberated eigenrays propagating between two vertical transducer arrays according to their emission and reception angles and arrival times. Analysis of eigenray intensities yields the bottom reflection coefficient as a function of angle of incidence. By fitting the experimental reflection coefficient with a theoretical prediction, values of the acoustic parameters of the waveguide bottom can be extracted. The procedure was initially tested in a small-scale tank experiment for a waveguide with a Plexiglas bottom. Inversion results for the speed of shear waves in Plexiglas are in good agreement with the table values. A similar analysis was applied to data collected during an at-sea experiment in shallow coastal waters of the Mediterranean. Bottom reflection coefficient was fitted with the theory in which bottom sediments are modeled as a multi-layered system. Retrieved bottom parameters are in quantitative agreement with those determined from a prior inversion scheme performed in the same area. The present study confirms the interest in processing source-receiver array data through the double beamforming algorithm, and indicates the potential for application of eigenray intensity analysis to geoacoustic inversion problems.

Quantitative imaging technique using the layer-stripping algorithm

NASA Astrophysics Data System (ADS)

Beilina, L.

2017-07-01

We present the layer-stripping algorithm for the solution of the hyperbolic coefficient inverse problem (CIP). Our numerical examples show quantitative reconstruction of small tumor-like inclusions in two-dimensions.

The determination of solubility and diffusion coefficient for solids in liquids by an inverse measurement technique using cylinders of amorphous glucose as a model compound

NASA Astrophysics Data System (ADS)

Hu, Chengyao; Huang, Pei

2011-05-01

The importance of sugar and sugar-containing materials is well recognized nowadays, owing to their application in industrial processes, particularly in the food, pharmaceutical and cosmetic industries. Because of the large numbers of those compounds involved and the relatively small number of solubility and/or diffusion coefficient data for each compound available, it is highly desirable to measure the solubility and/or diffusion coefficient as efficiently as possible and to be able to improve the accuracy of the methods used. In this work, a new technique was developed for the measurement of the diffusion coefficient of a stationary solid solute in a stagnant solvent which simultaneously measures solubility based on an inverse measurement problem algorithm with the real-time dissolved amount profile as a function of time. This study differs from established techniques in both the experimental method and the data analysis. The experimental method was developed in which the dissolved amount of solid solute in quiescent solvent was investigated using a continuous weighing technique. In the data analysis, the hybrid genetic algorithm is used to minimize an objective function containing a calculated and a measured dissolved amount with time. This is measured on a cylindrical sample of amorphous glucose in methanol or ethanol. The calculated dissolved amount, that is a function of the unknown physical properties of the solid solute in the solvent, is calculated by the solution of the two-dimensional nonlinear inverse natural convection problem. The estimated values of the solubility of amorphous glucose in methanol and ethanol at 293 K were respectively 32.1 g/100 g methanol and 1.48 g/100 g ethanol, in agreement with the literature values, and support the validity of the simultaneously measured diffusion coefficient. These results show the efficiency and the stability of the developed technique to simultaneously estimate the solubility and diffusion coefficient. Also the influence of the solution density change and the initial concentration conditions on the dissolved amount was investigated by the numerical results using the estimated parameters. It is found that the theoretical assumption to simplify the inverse measurement problem algorithm is reasonable for low solubility.

Absolute calibration of the mass scale in the inverse problem of the physical theory of fireballs

NASA Astrophysics Data System (ADS)

Kalenichenko, V. V.

1992-08-01

A method of the absolute calibration of the mass scale is proposed for solving the inverse problem of the physical theory of fireballs. The method is based on data on the masses of fallen meteorites whose fireballs have been photographed in flight. The method can be applied to fireballs whose bodies have not experienced significant fragmentation during their flight in the atmosphere and have kept their shape relatively well. Data on the Lost City and Innisfree meteorites are used to calculate the calibration coefficients.

Inversion of solar extinction data from the Apollo-Soyuz Test Project Stratospheric Aerosol Measurement (ASTP/SAM) experiment

NASA Technical Reports Server (NTRS)

Pepin, T. J.

1977-01-01

The inversion methods are reported that have been used to determine the vertical profile of the extinction coefficient due to the stratospheric aerosols from data measured during the ASTP/SAM solar occultation experiment. Inversion methods include the onion skin peel technique and methods of solving the Fredholm equation for the problem subject to smoothing constraints. The latter of these approaches involves a double inversion scheme. Comparisons are made between the inverted results from the SAM experiment and near simultaneous measurements made by lidar and balloon born dustsonde. The results are used to demonstrate the assumptions required to perform the inversions for aerosols.

The heat transfer coefficient determination with the use of the Beck-Trefftz method in flow boiling in a minichannel

NASA Astrophysics Data System (ADS)

Strąk, Kinga; Maciejewska, Beata; Piasecka, Magdalena

2018-06-01

In this paper, the solution of the two-dimensional inverse heat transfer problem with the use of the Beck method coupled with the Trefftz method is proposed. This method was applied for solving an inverse heat conduction problem. The aim of the calculation was to determine the boiling heat transfer coefficient on the basis of temperature measurements taken by infrared thermography. The experimental data of flow boiling heat transfer in a single vertical minichannel of 1.7 mm depth, heated asymmetrically, were used in calculations. The heating element for two refrigerants (FC-72 and HFE-7100, 3M) flowing in the minichannel was the plate enhanced on the side contacting with the fluid. The analysis of the results was performed on the basis of experimental series obtained for the same heat flux and two different mass flow velocities. The results were presented as infrared thermographs, heated wall temperature and heat transfer coefficient as a function of the distance from the minichannel inlet. The results was discussed for the subcooled and saturated boiling regions separately.

Optimization method for an evolutional type inverse heat conduction problem

NASA Astrophysics Data System (ADS)

Deng, Zui-Cha; Yu, Jian-Ning; Yang, Liu

2008-01-01

This paper deals with the determination of a pair (q, u) in the heat conduction equation u_t-u_{xx}+q(x,t)u=0, with initial and boundary conditions u(x,0)=u_0(x),\\qquad u_x|_{x=0}=u_x|_{x=1}=0, from the overspecified data u(x, t) = g(x, t). By the time semi-discrete scheme, the problem is transformed into a sequence of inverse problems in which the unknown coefficients are purely space dependent. Based on the optimal control framework, the existence, uniqueness and stability of the solution (q, u) are proved. A necessary condition which is a couple system of a parabolic equation and parabolic variational inequality is deduced.

Inverse solutions for electrical impedance tomography based on conjugate gradients methods

NASA Astrophysics Data System (ADS)

Wang, M.

2002-01-01

A multistep inverse solution for two-dimensional electric field distribution is developed to deal with the nonlinear inverse problem of electric field distribution in relation to its boundary condition and the problem of divergence due to errors introduced by the ill-conditioned sensitivity matrix and the noise produced by electrode modelling and instruments. This solution is based on a normalized linear approximation method where the change in mutual impedance is derived from the sensitivity theorem and a method of error vector decomposition. This paper presents an algebraic solution of the linear equations at each inverse step, using a generalized conjugate gradients method. Limiting the number of iterations in the generalized conjugate gradients method controls the artificial errors introduced by the assumption of linearity and the ill-conditioned sensitivity matrix. The solution of the nonlinear problem is approached using a multistep inversion. This paper also reviews the mathematical and physical definitions of the sensitivity back-projection algorithm based on the sensitivity theorem. Simulations and discussion based on the multistep algorithm, the sensitivity coefficient back-projection method and the Newton-Raphson method are given. Examples of imaging gas-liquid mixing and a human hand in brine are presented.

Long-Range Adiabatic Corrections to the Ground Molecular State of Alkali-Metal Dimers.

NASA Astrophysics Data System (ADS)

Marinescu, M.; Dalgarno, A.

1997-04-01

The structure of the long-range limit of the diagonal adiabatic corrections to the ground molecular state of diatomic molecules, may be expressed as a series of inverse powers of internuclear distance, R. The coefficients of this expansion are proportional to the inverse of the nuclear mass. Thus, they may be interpreted as a nuclear mass-dependent corrections to the dispersion coefficients. Using perturbation theory we have calculated the long-range coefficients of the diagonal adiabatic corrections up to the order of R-10. The final expressions are in terms of integrals over imaginary frequencies of products of atomic matrix elements involving Green's functions of complex energy. Thus, in our approach the molecular problem is reduced to an atomic one. Numerical evaluations have been done for all alkali-metal dimers. We acknowledge the support of the U.S. Dept. of Energy.

A model reduction approach to numerical inversion for a parabolic partial differential equation

NASA Astrophysics Data System (ADS)

Borcea, Liliana; Druskin, Vladimir; Mamonov, Alexander V.; Zaslavsky, Mikhail

2014-12-01

We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss-Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments.

Fractional Gaussian model in global optimization

NASA Astrophysics Data System (ADS)

Dimri, V. P.; Srivastava, R. P.

2009-12-01

Earth system is inherently non-linear and it can be characterized well if we incorporate no-linearity in the formulation and solution of the problem. General tool often used for characterization of the earth system is inversion. Traditionally inverse problems are solved using least-square based inversion by linearizing the formulation. The initial model in such inversion schemes is often assumed to follow posterior Gaussian probability distribution. It is now well established that most of the physical properties of the earth follow power law (fractal distribution). Thus, the selection of initial model based on power law probability distribution will provide more realistic solution. We present a new method which can draw samples of posterior probability density function very efficiently using fractal based statistics. The application of the method has been demonstrated to invert band limited seismic data with well control. We used fractal based probability density function which uses mean, variance and Hurst coefficient of the model space to draw initial model. Further this initial model is used in global optimization inversion scheme. Inversion results using initial models generated by our method gives high resolution estimates of the model parameters than the hitherto used gradient based liner inversion method.

Improved real-time dynamics from imaginary frequency lattice simulations

NASA Astrophysics Data System (ADS)

Pawlowski, Jan M.; Rothkopf, Alexander

2018-03-01

The computation of real-time properties, such as transport coefficients or bound state spectra of strongly interacting quantum fields in thermal equilibrium is a pressing matter. Since the sign problem prevents a direct evaluation of these quantities, lattice data needs to be analytically continued from the Euclidean domain of the simulation to Minkowski time, in general an ill-posed inverse problem. Here we report on a novel approach to improve the determination of real-time information in the form of spectral functions by setting up a simulation prescription in imaginary frequencies. By carefully distinguishing between initial conditions and quantum dynamics one obtains access to correlation functions also outside the conventional Matsubara frequencies. In particular the range between ω0 and ω1 = 2πT, which is most relevant for the inverse problem may be more highly resolved. In combination with the fact that in imaginary frequencies the kernel of the inverse problem is not an exponential but only a rational function we observe significant improvements in the reconstruction of spectral functions, demonstrated in a simple 0+1 dimensional scalar field theory toy model.

Estimation of spatially varying heat transfer coefficient from a flat plate with flush mounted heat sources using Bayesian inference

NASA Astrophysics Data System (ADS)

Jakkareddy, Pradeep S.; Balaji, C.

2016-09-01

This paper employs the Bayesian based Metropolis Hasting - Markov Chain Monte Carlo algorithm to solve inverse heat transfer problem of determining the spatially varying heat transfer coefficient from a flat plate with flush mounted discrete heat sources with measured temperatures at the bottom of the plate. The Nusselt number is assumed to be of the form Nu = aReb(x/l)c . To input reasonable values of ’a’ and ‘b’ into the inverse problem, first limited two dimensional conjugate convection simulations were done with Comsol. Based on the guidance from this different values of ‘a’ and ‘b’ are input to a computationally less complex problem of conjugate conduction in the flat plate (15mm thickness) and temperature distributions at the bottom of the plate which is a more convenient location for measuring the temperatures without disturbing the flow were obtained. Since the goal of this work is to demonstrate the eficiacy of the Bayesian approach to accurately retrieve ‘a’ and ‘b’, numerically generated temperatures with known values of ‘a’ and ‘b’ are treated as ‘surrogate’ experimental data. The inverse problem is then solved by repeatedly using the forward solutions together with the MH-MCMC aprroach. To speed up the estimation, the forward model is replaced by an artificial neural network. The mean, maximum-a-posteriori and standard deviation of the estimated parameters ‘a’ and ‘b’ are reported. The robustness of the proposed method is examined, by synthetically adding noise to the temperatures.

Inverse Problems for Semilinear Wave Equations on Lorentzian Manifolds

NASA Astrophysics Data System (ADS)

Lassas, Matti; Uhlmann, Gunther; Wang, Yiran

2018-06-01

We consider inverse problems in space-time ( M, g), a 4-dimensional Lorentzian manifold. For semilinear wave equations {\\square_g u + H(x, u) = f}, where {\\square_g} denotes the usual Laplace-Beltrami operator, we prove that the source-to-solution map {L: f → u|_V}, where V is a neighborhood of a time-like geodesic {μ}, determines the topological, differentiable structure and the conformal class of the metric of the space-time in the maximal set, where waves can propagate from {μ} and return back. Moreover, on a given space-time ( M, g), the source-to-solution map determines some coefficients of the Taylor expansion of H in u.

Low frequency full waveform seismic inversion within a tree based Bayesian framework

NASA Astrophysics Data System (ADS)

Ray, Anandaroop; Kaplan, Sam; Washbourne, John; Albertin, Uwe

2018-01-01

Limited illumination, insufficient offset, noisy data and poor starting models can pose challenges for seismic full waveform inversion. We present an application of a tree based Bayesian inversion scheme which attempts to mitigate these problems by accounting for data uncertainty while using a mildly informative prior about subsurface structure. We sample the resulting posterior model distribution of compressional velocity using a trans-dimensional (trans-D) or Reversible Jump Markov chain Monte Carlo method in the wavelet transform domain of velocity. This allows us to attain rapid convergence to a stationary distribution of posterior models while requiring a limited number of wavelet coefficients to define a sampled model. Two synthetic, low frequency, noisy data examples are provided. The first example is a simple reflection + transmission inverse problem, and the second uses a scaled version of the Marmousi velocity model, dominated by reflections. Both examples are initially started from a semi-infinite half-space with incorrect background velocity. We find that the trans-D tree based approach together with parallel tempering for navigating rugged likelihood (i.e. misfit) topography provides a promising, easily generalized method for solving large-scale geophysical inverse problems which are difficult to optimize, but where the true model contains a hierarchy of features at multiple scales.

Efficient Storage Scheme of Covariance Matrix during Inverse Modeling

NASA Astrophysics Data System (ADS)

Mao, D.; Yeh, T. J.

2013-12-01

During stochastic inverse modeling, the covariance matrix of geostatistical based methods carries the information about the geologic structure. Its update during iterations reflects the decrease of uncertainty with the incorporation of observed data. For large scale problem, its storage and update cost too much memory and computational resources. In this study, we propose a new efficient storage scheme for storage and update. Compressed Sparse Column (CSC) format is utilized to storage the covariance matrix, and users can assign how many data they prefer to store based on correlation scales since the data beyond several correlation scales are usually not very informative for inverse modeling. After every iteration, only the diagonal terms of the covariance matrix are updated. The off diagonal terms are calculated and updated based on shortened correlation scales with a pre-assigned exponential model. The correlation scales are shortened by a coefficient, i.e. 0.95, every iteration to show the decrease of uncertainty. There is no universal coefficient for all the problems and users are encouraged to try several times. This new scheme is tested with 1D examples first. The estimated results and uncertainty are compared with the traditional full storage method. In the end, a large scale numerical model is utilized to validate this new scheme.

Cloud Tracking from Satellite Pictures.

DTIC Science & Technology

1981-07-01

sufficiently smooth contours, this information can be obtained from very few low-order coefficients. The inverse transform of the two lowest-order...obtained from very few low- order coefficients. The inverse transform of the two lowest-order coefficients is an ellipse approximating the original...coefficients obtained from the contour of Fig. 9. .. . ........ .. .. ... ..... 67 11. Inverse transform of truncated FD series .. .. . .. .... 67 12

Determination of Nerve Fiber Diameter Distribution From Compound Action Potential: A Continuous Approach.

PubMed

Un, M Kerem; Kaghazchi, Hamed

2018-01-01

When a signal is initiated in the nerve, it is transmitted along each nerve fiber via an action potential (called single fiber action potential (SFAP)) which travels with a velocity that is related with the diameter of the fiber. The additive superposition of SFAPs constitutes the compound action potential (CAP) of the nerve. The fiber diameter distribution (FDD) in the nerve can be computed from the CAP data by solving an inverse problem. This is usually achieved by dividing the fibers into a finite number of diameter groups and solve a corresponding linear system to optimize FDD. However, number of fibers in a nerve can be measured sometimes in thousands and it is possible to assume a continuous distribution for the fiber diameters which leads to a gradient optimization problem. In this paper, we have evaluated this continuous approach to the solution of the inverse problem. We have utilized an analytical function for SFAP and an assumed a polynomial form for FDD. The inverse problem involves the optimization of polynomial coefficients to obtain the best estimate for the FDD. We have observed that an eighth order polynomial for FDD can capture both unimodal and bimodal fiber distributions present in vivo, even in case of noisy CAP data. The assumed FDD distribution regularizes the ill-conditioned inverse problem and produces good results.

Inverse resonance scattering for Jacobi operators

NASA Astrophysics Data System (ADS)

Korotyaev, E. L.

2011-12-01

The Jacobi operator ( Jf) n = a n-1 f n-1 + a n f n+1 + b n f n on ℤ with real finitely supported sequences ( a n - 1) n∈ℤ and ( b n ) n∈ℤ is considered. The inverse problem for two mappings (including their characterization): ( a n , b n , n ∈ ℤ) → {the zeros of the reflection coefficient} and ( a n , b n , n ∈ ℤ) → {the eigenvalues and the resonances} is solved. All Jacobi operators with the same eigenvalues and resonances are also described.

Estimating surface acoustic impedance with the inverse method.

PubMed

Piechowicz, Janusz

2011-01-01

Sound field parameters are predicted with numerical methods in sound control systems, in acoustic designs of building and in sound field simulations. Those methods define the acoustic properties of surfaces, such as sound absorption coefficients or acoustic impedance, to determine boundary conditions. Several in situ measurement techniques were developed; one of them uses 2 microphones to measure direct and reflected sound over a planar test surface. Another approach is used in the inverse boundary elements method, in which estimating acoustic impedance of a surface is expressed as an inverse boundary problem. The boundary values can be found from multipoint sound pressure measurements in the interior of a room. This method can be applied to arbitrarily-shaped surfaces. This investigation is part of a research programme on using inverse methods in industrial room acoustics.

Computational methods for estimation of parameters in hyperbolic systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.; Murphy, K. A.

1983-01-01

Approximation techniques for estimating spatially varying coefficients and unknown boundary parameters in second order hyperbolic systems are discussed. Methods for state approximation (cubic splines, tau-Legendre) and approximation of function space parameters (interpolatory splines) are outlined and numerical findings for use of the resulting schemes in model "one dimensional seismic inversion' problems are summarized.

On determining important aspects of mathematical models: Application to problems in physics and chemistry

NASA Technical Reports Server (NTRS)

Rabitz, Herschel

1987-01-01

The use of parametric and functional gradient sensitivity analysis techniques is considered for models described by partial differential equations. By interchanging appropriate dependent and independent variables, questions of inverse sensitivity may be addressed to gain insight into the inversion of observational data for parameter and function identification in mathematical models. It may be argued that the presence of a subset of dominantly strong coupled dependent variables will result in the overall system sensitivity behavior collapsing into a simple set of scaling and self similarity relations amongst elements of the entire matrix of sensitivity coefficients. These general tools are generic in nature, but herein their application to problems arising in selected areas of physics and chemistry is presented.

A physiologically motivated sparse, compact, and smooth (SCS) approach to EEG source localization.

PubMed

Cao, Cheng; Akalin Acar, Zeynep; Kreutz-Delgado, Kenneth; Makeig, Scott

2012-01-01

Here, we introduce a novel approach to the EEG inverse problem based on the assumption that principal cortical sources of multi-channel EEG recordings may be assumed to be spatially sparse, compact, and smooth (SCS). To enforce these characteristics of solutions to the EEG inverse problem, we propose a correlation-variance model which factors a cortical source space covariance matrix into the multiplication of a pre-given correlation coefficient matrix and the square root of the diagonal variance matrix learned from the data under a Bayesian learning framework. We tested the SCS method using simulated EEG data with various SNR and applied it to a real ECOG data set. We compare the results of SCS to those of an established SBL algorithm.

Random noise attenuation of non-uniformly sampled 3D seismic data along two spatial coordinates using non-equispaced curvelet transform

NASA Astrophysics Data System (ADS)

Zhang, Hua; Yang, Hui; Li, Hongxing; Huang, Guangnan; Ding, Zheyi

2018-04-01

The attenuation of random noise is important for improving the signal to noise ratio (SNR). However, the precondition for most conventional denoising methods is that the noisy data must be sampled on a uniform grid, making the conventional methods unsuitable for non-uniformly sampled data. In this paper, a denoising method capable of regularizing the noisy data from a non-uniform grid to a specified uniform grid is proposed. Firstly, the denoising method is performed for every time slice extracted from the 3D noisy data along the source and receiver directions, then the 2D non-equispaced fast Fourier transform (NFFT) is introduced in the conventional fast discrete curvelet transform (FDCT). The non-equispaced fast discrete curvelet transform (NFDCT) can be achieved based on the regularized inversion of an operator that links the uniformly sampled curvelet coefficients to the non-uniformly sampled noisy data. The uniform curvelet coefficients can be calculated by using the inversion algorithm of the spectral projected-gradient for ℓ1-norm problems. Then local threshold factors are chosen for the uniform curvelet coefficients for each decomposition scale, and effective curvelet coefficients are obtained respectively for each scale. Finally, the conventional inverse FDCT is applied to the effective curvelet coefficients. This completes the proposed 3D denoising method using the non-equispaced curvelet transform in the source-receiver domain. The examples for synthetic data and real data reveal the effectiveness of the proposed approach in applications to noise attenuation for non-uniformly sampled data compared with the conventional FDCT method and wavelet transformation.

Retrieval of LAI and leaf chlorophyll content from remote sensing data by agronomy mechanism knowledge to solve the ill-posed inverse problem

NASA Astrophysics Data System (ADS)

Li, Zhenhai; Nie, Chenwei; Yang, Guijun; Xu, Xingang; Jin, Xiuliang; Gu, Xiaohe

2014-10-01

Leaf area index (LAI) and LCC, as the two most important crop growth variables, are major considerations in management decisions, agricultural planning and policy making. Estimation of canopy biophysical variables from remote sensing data was investigated using a radiative transfer model. However, the ill-posed problem is unavoidable for the unique solution of the inverse problem and the uncertainty of measurements and model assumptions. This study focused on the use of agronomy mechanism knowledge to restrict and remove the ill-posed inversion results. For this purpose, the inversion results obtained using the PROSAIL model alone (NAMK) and linked with agronomic mechanism knowledge (AMK) were compared. The results showed that AMK did not significantly improve the accuracy of LAI inversion. LAI was estimated with high accuracy, and there was no significant improvement after considering AMK. The validation results of the determination coefficient (R2) and the corresponding root mean square error (RMSE) between measured LAI and estimated LAI were 0.635 and 1.022 for NAMK, and 0.637 and 0.999 for AMK, respectively. LCC estimation was significantly improved with agronomy mechanism knowledge; the R2 and RMSE values were 0.377 and 14.495 μg cm-2 for NAMK, and 0.503 and 10.661 μg cm-2 for AMK, respectively. Results of the comparison demonstrated the need for agronomy mechanism knowledge in radiative transfer model inversion.

Identification of the heat transfer coefficient in the two-dimensional model of binary alloy solidification

NASA Astrophysics Data System (ADS)

Hetmaniok, Edyta; Hristov, Jordan; Słota, Damian; Zielonka, Adam

2017-05-01

The paper presents the procedure for solving the inverse problem for the binary alloy solidification in a two-dimensional space. This is a continuation of some previous works of the authors investigating a similar problem but in the one-dimensional domain. Goal of the problem consists in identification of the heat transfer coefficient on boundary of the region and in reconstruction of the temperature distribution inside the considered region in case when the temperature measurements in selected points of the alloy are known. Mathematical model of the problem is based on the heat conduction equation with the substitute thermal capacity and with the liquidus and solidus temperatures varying in dependance on the concentration of the alloy component. For describing this concentration the Scheil model is used. Investigated procedure involves also the parallelized Ant Colony Optimization algorithm applied for minimizing a functional expressing the error of approximate solution.

[Research on the measurement range of particle size with total light scattering method in vis-IR region].

PubMed

Sun, Xiao-gang; Tang, Hong; Dai, Jing-min

2008-12-01

The problem of determining the particle size range in the visible-infrared region was studied using the independent model algorithm in the total scattering technique. By the analysis and comparison of the accuracy of the inversion results for different R-R distributions, the measurement range of particle size was determined. Meanwhile, the corrected extinction coefficient was used instead of the original extinction coefficient, which could determine the measurement range of particle size with higher accuracy. Simulation experiments illustrate that the particle size distribution can be retrieved very well in the range from 0. 05 to 18 microm at relative refractive index m=1.235 in the visible-infrared spectral region, and the measurement range of particle size will vary with the varied wavelength range and relative refractive index. It is feasible to use the constrained least squares inversion method in the independent model to overcome the influence of the measurement error, and the inverse results are all still satisfactory when 1% stochastic noise is added to the value of the light extinction.

On the simultaneous inversion of micro-perforated panels' parameters: Application to single and double air-cavity backed systems.

PubMed

Tayong, Rostand B; Manyo Manyo, Jacques A; Siryabe, Emmanuel; Ntamack, Guy E

2018-04-01

This study deals with the deduction of parameters of Micro-Perforated Panel (MPP) systems from impedance tube data. It is shown that there is an ambiguity problem that exists between the MPP thickness and its open area ratio. This problem makes it difficult to invert the reflection coefficient data fitting and therefore to deduct the MPP parameters. A technique is proposed to reduce this ambiguity by using an equation that links the hole diameter to the open area ratio. Reflection coefficient data obtained for two specimens with different characteristics is employed for searching the MPP parameters using a simulated annealing algorithm. The results obtained demonstrate the effectiveness of this technique.

On a generalized Ablowitz-Kaup-Newell-Segur hierarchy in inhomogeneities of media: soliton solutions and wave propagation influenced from coefficient functions and scattering data

NASA Astrophysics Data System (ADS)

Zhang, Sheng; Hong, Siyu

2018-07-01

In this paper, a generalized Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy in inhomogeneities of media described by variable coefficients is investigated, which includes some important nonlinear evolution equations as special cases, for example, the celebrated Korteweg-de Vries equation modeling waves on shallow water surfaces. To be specific, the known AKNS spectral problem and its time evolution equation are first generalized by embedding a finite number of differentiable and time-dependent functions. Starting from the generalized AKNS spectral problem and its generalized time evolution equation, a generalized AKNS hierarchy with variable coefficients is then derived. Furthermore, based on a systematic analysis on the time dependence of related scattering data of the generalized AKNS spectral problem, exact solutions of the generalized AKNS hierarchy are formulated through the inverse scattering transform method. In the case of reflectionless potentials, the obtained exact solutions are reduced to n-soliton solutions. It is graphically shown that the dynamical evolutions of such soliton solutions are influenced by not only the time-dependent coefficients but also the related scattering data in the process of propagations.

Forward and inverse models of electromagnetic scattering from layered media with rough interfaces

NASA Astrophysics Data System (ADS)

Tabatabaeenejad, Seyed Alireza

This work addresses the problem of electromagnetic scattering from layered dielectric structures with rough boundaries and the associated inverse problem of retrieving the subsurface parameters of the structure using the scattered field. To this end, a forward scattering model based on the Small Perturbation Method (SPM) is developed to calculate the first-order spectral-domain bistatic scattering coefficients of a two-layer rough surface structure. SPM requires the boundaries to be slightly rough compared to the wavelength, but to understand the range of applicability of this method in scattering from two-layer rough surfaces, its region of validity is investigated by comparing its output with that of a first principle solver that does not impose roughness restrictions. The Method of Moments (MoM) is used for this purpose. Finally, for retrieval of the model parameters of the layered structure using scattered field, an inversion scheme based on the Simulated Annealing method is investigated and a strategy is proposed to address convergence to local minimum.

Approximate Global Convergence and Quasi-Reversibility for a Coefficient Inverse Problem with Backscattering Data

DTIC Science & Technology

2011-04-01

L1u. Assume that geodesic lines, generated by the eikonal equation corresponding to the function c (x) are regular, i.e. any two points in R3 can be...source x0 is located far from Ω, then similarly with (107) ∆l (x, x0) ≈ 0 in Ω. The function l (x, x0) satisfies the eikonal equation [38] |∇xl (x, x0...called “inverse kinematic problem” which aims to recover the function c (x) from the eikonal equation assuming that the function l (x, x0) is known for

Frequency-domain optical tomographic image reconstruction algorithm with the simplified spherical harmonics (SP3) light propagation model.

PubMed

Kim, Hyun Keol; Montejo, Ludguier D; Jia, Jingfei; Hielscher, Andreas H

2017-06-01

We introduce here the finite volume formulation of the frequency-domain simplified spherical harmonics model with n -th order absorption coefficients (FD-SP N ) that approximates the frequency-domain equation of radiative transfer (FD-ERT). We then present the FD-SP N based reconstruction algorithm that recovers absorption and scattering coefficients in biological tissue. The FD-SP N model with 3 rd order absorption coefficient (i.e., FD-SP 3 ) is used as a forward model to solve the inverse problem. The FD-SP 3 is discretized with a node-centered finite volume scheme and solved with a restarted generalized minimum residual (GMRES) algorithm. The absorption and scattering coefficients are retrieved using a limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. Finally, the forward and inverse algorithms are evaluated using numerical phantoms with optical properties and size that mimic small-volume tissue such as finger joints and small animals. The forward results show that the FD-SP 3 model approximates the FD-ERT (S 12 ) solution within relatively high accuracy; the average error in the phase (<3.7%) and the amplitude (<7.1%) of the partial current at the boundary are reported. From the inverse results we find that the absorption and scattering coefficient maps are more accurately reconstructed with the SP 3 model than those with the SP 1 model. Therefore, this work shows that the FD-SP 3 is an efficient model for optical tomographic imaging of small-volume media with non-diffuse properties both in terms of computational time and accuracy as it requires significantly lower CPU time than the FD-ERT (S 12 ) and also it is more accurate than the FD-SP 1 .

Using the Coefficient of Confidence to Make the Philosophical Switch from a Posteriori to a Priori Inferential Statistics

ERIC Educational Resources Information Center

Trafimow, David

2017-01-01

There has been much controversy over the null hypothesis significance testing procedure, with much of the criticism centered on the problem of inverse inference. Specifically, p gives the probability of the finding (or one more extreme) given the null hypothesis, whereas the null hypothesis significance testing procedure involves drawing a…

Inverse scattering for an exterior Dirichlet program

NASA Technical Reports Server (NTRS)

Hariharan, S. I.

1981-01-01

Scattering due to a metallic cylinder which is in the field of a wire carrying a periodic current is considered. The location and shape of the cylinder is obtained with a far field measurement in between the wire and the cylinder. The same analysis is applicable in acoustics in the situation that the cylinder is a soft wall body and the wire is a line source. The associated direct problem in this situation is an exterior Dirichlet problem for the Helmholtz equation in two dimensions. An improved low frequency estimate for the solution of this problem using integral equation methods is presented. The far field measurements are related to the solutions of boundary integral equations in the low frequency situation. These solutions are expressed in terms of mapping function which maps the exterior of the unknown curve onto the exterior of a unit disk. The coefficients of the Laurent expansion of the conformal transformations are related to the far field coefficients. The first far field coefficient leads to the calculation of the distance between the source and the cylinder.

Obtaining sparse distributions in 2D inverse problems.

PubMed

Reci, A; Sederman, A J; Gladden, L F

2017-08-01

The mathematics of inverse problems has relevance across numerous estimation problems in science and engineering. L 1 regularization has attracted recent attention in reconstructing the system properties in the case of sparse inverse problems; i.e., when the true property sought is not adequately described by a continuous distribution, in particular in Compressed Sensing image reconstruction. In this work, we focus on the application of L 1 regularization to a class of inverse problems; relaxation-relaxation, T 1 -T 2 , and diffusion-relaxation, D-T 2 , correlation experiments in NMR, which have found widespread applications in a number of areas including probing surface interactions in catalysis and characterizing fluid composition and pore structures in rocks. We introduce a robust algorithm for solving the L 1 regularization problem and provide a guide to implementing it, including the choice of the amount of regularization used and the assignment of error estimates. We then show experimentally that L 1 regularization has significant advantages over both the Non-Negative Least Squares (NNLS) algorithm and Tikhonov regularization. It is shown that the L 1 regularization algorithm stably recovers a distribution at a signal to noise ratio<20 and that it resolves relaxation time constants and diffusion coefficients differing by as little as 10%. The enhanced resolving capability is used to measure the inter and intra particle concentrations of a mixture of hexane and dodecane present within porous silica beads immersed within a bulk liquid phase; neither NNLS nor Tikhonov regularization are able to provide this resolution. This experimental study shows that the approach enables discrimination between different chemical species when direct spectroscopic discrimination is impossible, and hence measurement of chemical composition within porous media, such as catalysts or rocks, is possible while still being stable to high levels of noise. Copyright © 2017. Published by Elsevier Inc.

Obtaining sparse distributions in 2D inverse problems

NASA Astrophysics Data System (ADS)

Reci, A.; Sederman, A. J.; Gladden, L. F.

2017-08-01

The mathematics of inverse problems has relevance across numerous estimation problems in science and engineering. L1 regularization has attracted recent attention in reconstructing the system properties in the case of sparse inverse problems; i.e., when the true property sought is not adequately described by a continuous distribution, in particular in Compressed Sensing image reconstruction. In this work, we focus on the application of L1 regularization to a class of inverse problems; relaxation-relaxation, T1-T2, and diffusion-relaxation, D-T2, correlation experiments in NMR, which have found widespread applications in a number of areas including probing surface interactions in catalysis and characterizing fluid composition and pore structures in rocks. We introduce a robust algorithm for solving the L1 regularization problem and provide a guide to implementing it, including the choice of the amount of regularization used and the assignment of error estimates. We then show experimentally that L1 regularization has significant advantages over both the Non-Negative Least Squares (NNLS) algorithm and Tikhonov regularization. It is shown that the L1 regularization algorithm stably recovers a distribution at a signal to noise ratio < 20 and that it resolves relaxation time constants and diffusion coefficients differing by as little as 10%. The enhanced resolving capability is used to measure the inter and intra particle concentrations of a mixture of hexane and dodecane present within porous silica beads immersed within a bulk liquid phase; neither NNLS nor Tikhonov regularization are able to provide this resolution. This experimental study shows that the approach enables discrimination between different chemical species when direct spectroscopic discrimination is impossible, and hence measurement of chemical composition within porous media, such as catalysts or rocks, is possible while still being stable to high levels of noise.

Are two plasma equilibrium states possible when the emission coefficient exceeds unity?

NASA Astrophysics Data System (ADS)

Campanell, M. D.; Umansky, M. V.

2017-05-01

Two floating sheath solutions with strong electron emission in planar geometry have been proposed, a "space-charge limited" (SCL) sheath and an "inverse" sheath. SCL and inverse models contain different assumptions about conditions outside the sheath (e.g., the velocity of ions entering the sheath). So it is not yet clear whether both sheaths are possible in practice, or only one. Here we treat the global presheath-sheath problem for a plasma produced volumetrically between two planar walls. We show that all equilibrium requirements (a) floating condition, (b) plasma shielding, and (c) presheath force balance, can indeed be satisfied in two different ways when the emission coefficient γ > 1. There is one solution with SCL sheaths and one with inverse sheaths, each with sharply different presheath distributions. As we show for the first time in 1D-1V simulations, a SCL and inverse equilibrium are both possible in plasmas with the same upstream properties (e.g., same N and Te). However, maintaining a true SCL equilibrium requires no ionization or charge exchange collisions in the sheath, or else cold ion accumulation in the SCL's "dip" forces a transition to the inverse. This suggests that only a monotonic inverse type sheath potential should exist at any plasma-facing surface with strong emission, whether be a divertor plate, emissive probe, dust grain, Hall thruster channel wall, sunlit object in space, etc. Nevertheless, SCL sheaths might still be possible if the ions in the dip can escape. Our simulations demonstrate ways in which SCL and inverse regimes might be distinguished experimentally based on large-scale presheath effects, without having to probe inside the sheath.

Research and application of spectral inversion technique in frequency domain to improve resolution of converted PS-wave

NASA Astrophysics Data System (ADS)

Zhang, Hua; He, Zhen-Hua; Li, Ya-Lin; Li, Rui; He, Guamg-Ming; Li, Zhong

2017-06-01

Multi-wave exploration is an effective means for improving precision in the exploration and development of complex oil and gas reservoirs that are dense and have low permeability. However, converted wave data is characterized by a low signal-to-noise ratio and low resolution, because the conventional deconvolution technology is easily affected by the frequency range limits, and there is limited scope for improving its resolution. The spectral inversion techniques is used to identify λ/8 thin layers and its breakthrough regarding band range limits has greatly improved the seismic resolution. The difficulty associated with this technology is how to use the stable inversion algorithm to obtain a high-precision reflection coefficient, and then to use this reflection coefficient to reconstruct broadband data for processing. In this paper, we focus on how to improve the vertical resolution of the converted PS-wave for multi-wave data processing. Based on previous research, we propose a least squares inversion algorithm with a total variation constraint, in which we uses the total variance as a priori information to solve under-determined problems, thereby improving the accuracy and stability of the inversion. Here, we simulate the Gaussian fitting amplitude spectrum to obtain broadband wavelet data, which we then process to obtain a higher resolution converted wave. We successfully apply the proposed inversion technology in the processing of high-resolution data from the Penglai region to obtain higher resolution converted wave data, which we then verify in a theoretical test. Improving the resolution of converted PS-wave data will provide more accurate data for subsequent velocity inversion and the extraction of reservoir reflection information.

Wavelet extractor: A Bayesian well-tie and wavelet extraction program

NASA Astrophysics Data System (ADS)

Gunning, James; Glinsky, Michael E.

2006-06-01

We introduce a new open-source toolkit for the well-tie or wavelet extraction problem of estimating seismic wavelets from seismic data, time-to-depth information, and well-log suites. The wavelet extraction model is formulated as a Bayesian inverse problem, and the software will simultaneously estimate wavelet coefficients, other parameters associated with uncertainty in the time-to-depth mapping, positioning errors in the seismic imaging, and useful amplitude-variation-with-offset (AVO) related parameters in multi-stack extractions. It is capable of multi-well, multi-stack extractions, and uses continuous seismic data-cube interpolation to cope with the problem of arbitrary well paths. Velocity constraints in the form of checkshot data, interpreted markers, and sonic logs are integrated in a natural way. The Bayesian formulation allows computation of full posterior uncertainties of the model parameters, and the important problem of the uncertain wavelet span is addressed uses a multi-model posterior developed from Bayesian model selection theory. The wavelet extraction tool is distributed as part of the Delivery seismic inversion toolkit. A simple log and seismic viewing tool is included in the distribution. The code is written in Java, and thus platform independent, but the Seismic Unix (SU) data model makes the inversion particularly suited to Unix/Linux environments. It is a natural companion piece of software to Delivery, having the capacity to produce maximum likelihood wavelet and noise estimates, but will also be of significant utility to practitioners wanting to produce wavelet estimates for other inversion codes or purposes. The generation of full parameter uncertainties is a crucial function for workers wishing to investigate questions of wavelet stability before proceeding to more advanced inversion studies.

EEG-distributed inverse solutions for a spherical head model

NASA Astrophysics Data System (ADS)

Riera, J. J.; Fuentes, M. E.; Valdés, P. A.; Ohárriz, Y.

1998-08-01

The theoretical study of the minimum norm solution to the MEG inverse problem has been carried out in previous papers for the particular case of spherical symmetry. However, a similar study for the EEG is remarkably more difficult due to the very complicated nature of the expression relating the voltage differences on the scalp to the primary current density (PCD) even for this simple symmetry. This paper introduces the use of the electric lead field (ELF) on the dyadic formalism in the spherical coordinate system to overcome such a drawback using an expansion of the ELF in terms of longitudinal and orthogonal vector fields. This approach allows us to represent EEG Fourier coefficients on a 2-sphere in terms of a current multipole expansion. The choice of a suitable basis for the Hilbert space of the PCDs on the brain region allows the current multipole moments to be related by spatial transfer functions to the PCD spectral coefficients. Properties of the most used distributed inverse solutions are explored on the basis of these results. Also, a part of the ELF null space is completely characterized and those spherical components of the PCD which are possible silent candidates are discussed.

Towards quantifying uncertainty in Greenland's contribution to 21st century sea-level rise

NASA Astrophysics Data System (ADS)

Perego, M.; Tezaur, I.; Price, S. F.; Jakeman, J.; Eldred, M.; Salinger, A.; Hoffman, M. J.

2015-12-01

We present recent work towards developing a methodology for quantifying uncertainty in Greenland's 21st century contribution to sea-level rise. While we focus on uncertainties associated with the optimization and calibration of the basal sliding parameter field, the methodology is largely generic and could be applied to other (or multiple) sets of uncertain model parameter fields. The first step in the workflow is the solution of a large-scale, deterministic inverse problem, which minimizes the mismatch between observed and computed surface velocities by optimizing the two-dimensional coefficient field in a linear-friction sliding law. We then expand the deviation in this coefficient field from its estimated "mean" state using a reduced basis of Karhunen-Loeve Expansion (KLE) vectors. A Bayesian calibration is used to determine the optimal coefficient values for this expansion. The prior for the Bayesian calibration can be computed using the Hessian of the deterministic inversion or using an exponential covariance kernel. The posterior distribution is then obtained using Markov Chain Monte Carlo run on an emulator of the forward model. Finally, the uncertainty in the modeled sea-level rise is obtained by performing an ensemble of forward propagation runs. We present and discuss preliminary results obtained using a moderate-resolution model of the Greenland Ice sheet. As demonstrated in previous work, the primary difficulty in applying the complete workflow to realistic, high-resolution problems is that the effective dimension of the parameter space is very large.

Ground-Based Microwave Radiometric Remote Sensing of the Tropical Atmosphere

NASA Astrophysics Data System (ADS)

Han, Yong

A partially developed 9-channel ground-based microwave radiometer for the Department of Meteorology at Penn State was completed and tested. Complementary units were added, corrections to both hardware and software were made, and system software was corrected and upgraded. Measurements from this radiometer were used to infer tropospheric temperature, water vapor and cloud liquid water. The various weighting functions at each of the 9 channels were calculated and analyzed to estimate the sensitivities of the brightness temperatures to the desired atmospheric variables. The mathematical inversion problem, in a linear form, was viewed in terms of the theory of linear algebra. Several methods for solving the inversion problem were reviewed. Radiometric observations were conducted during the 1990 Tropical Cyclone Motion Experiment. The radiometer was installed on the island of Saipan in a tropical region. During this experiment, the radiometer was calibrated by using tipping curve and radiosonde data as well as measurements of the radiation from a blackbody absorber. A linear statistical method was first applied for the data inversion. The inversion coefficients in the equation were obtained using a large number of radiosonde profiles from Guam and a radiative transfer model. Retrievals were compared with those from local, Saipan, radiosonde measurements. Water vapor profiles, integrated water vapor, and integrated liquid water were retrieved successfully. For temperature profile retrievals, however, it was shown that the radiometric measurements with experimental noises added no more profile information to the inversion than that which was available from a climatological mean. Although successful retrievals of the geopotential heights were made, it was shown that they were determined mainly by the surface pressure measurements. The reasons why the radiometer did not contribute to the retrievals of temperature profiles and geopotential heights were discussed. A method was developed to derive the integrated water vapor and liquid water from combined radiometer and ceilometer measurements. Under certain assumptions, the cloud absorption coefficients and mean radiating temperature, used in the physical or statistical inversion equation, were determined from the measurements. It was shown that significant improvement on radiometric measurements of the integrated liquid water can be gained with this method.

Adaptive Filtering in the Wavelet Transform Domain Via Genetic Algorithms

DTIC Science & Technology

2004-08-01

inverse transform process. 2. BACKGROUND The image processing research conducted at the AFRL/IFTA Reconfigurable Computing Laboratory has been...coefficients from the wavelet domain back into the original signal domain. In other words, the inverse transform produces the original signal x(t) from the...coefficients for an inverse wavelet transform, such that the MSE of images reconstructed by this inverse transform is significantly less than the mean squared

Joint time/frequency-domain inversion of reflection data for seabed geoacoustic profiles and uncertainties.

PubMed

Dettmer, Jan; Dosso, Stan E; Holland, Charles W

2008-03-01

This paper develops a joint time/frequency-domain inversion for high-resolution single-bounce reflection data, with the potential to resolve fine-scale profiles of sediment velocity, density, and attenuation over small seafloor footprints (approximately 100 m). The approach utilizes sequential Bayesian inversion of time- and frequency-domain reflection data, employing ray-tracing inversion for reflection travel times and a layer-packet stripping method for spherical-wave reflection-coefficient inversion. Posterior credibility intervals from the travel-time inversion are passed on as prior information to the reflection-coefficient inversion. Within the reflection-coefficient inversion, parameter information is passed from one layer packet inversion to the next in terms of marginal probability distributions rotated into principal components, providing an efficient approach to (partially) account for multi-dimensional parameter correlations with one-dimensional, numerical distributions. Quantitative geoacoustic parameter uncertainties are provided by a nonlinear Gibbs sampling approach employing full data error covariance estimation (including nonstationary effects) and accounting for possible biases in travel-time picks. Posterior examination of data residuals shows the importance of including data covariance estimates in the inversion. The joint inversion is applied to data collected on the Malta Plateau during the SCARAB98 experiment.

Aerodynamic coefficients in generalized unsteady thin airfoil theory

NASA Technical Reports Server (NTRS)

Williams, M. H.

1980-01-01

Two cases are considered: (1) rigid body motion of an airfoil-flap combination consisting of vertical translation of given amplitude, rotation of given amplitude about a specified axis, and rotation of given amplitude of the control surface alone about its hinge; the upwash for this problem is defined mathematically; and (2) sinusoidal gust of given amplitude and wave number, for which the upwash is defined mathematically. Simple universal formulas are presented for the most important aerodynamic coefficients in unsteady thin airfoil theory. The lift and moment induced by a generalized gust are evaluated explicitly in terms of the gust wavelength. Similarly, in the control surface problem, the lift, moment, and hinge moments are given as explicit algebraic functions of hinge location. These results can be used together with any of the standard numerical inversion routines for the elementary loads (pitch and heave).

Are two plasma equilibrium states possible when the emission coefficient exceeds unity?

DOE PAGES

Campanell, Michael D.; Umansky, M. V.

2017-02-28

Two floating sheath solutions with strong electron emission in planar geometry have been proposed, a “space-charge limited” (SCL) sheath and an “inverse” sheath. SCL and inverse models contain different assumptions about conditions outside the sheath (e.g., the velocity of ions entering the sheath). So it is not yet clear whether both sheaths are possible in practice, or only one. Here we treat the global presheath-sheath problem for a plasma produced volumetrically between two planar walls. We show that all equilibrium requirements (a) floating condition, (b) plasma shielding, and (c) presheath force balance, can indeed be satisfied in two different waysmore » when the emission coefficient γ > 1. There is one solution with SCL sheaths and one with inverse sheaths, each with sharply different presheath distributions. As we show for the first time in 1D-1V simulations, a SCL and inverse equilibrium are both possible in plasmas with the same upstream properties (e.g., same N and Te). However, maintaining a true SCL equilibrium requires no ionization or charge exchange collisions in the sheath, or else cold ion accumulation in the SCL's “dip” forces a transition to the inverse. This suggests that only a monotonic inverse type sheath potential should exist at any plasma-facing surface with strong emission, whether be a divertor plate, emissive probe, dust grain, Hall thruster channel wall, sunlit object in space, etc. Nevertheless, SCL sheaths might still be possible if the ions in the dip can escape. Finally, our simulations demonstrate ways in which SCL and inverse regimes might be distinguished experimentally based on large-scale presheath effects, without having to probe inside the sheath.« less

Identification of diffusive transport properties of poly(vinyl alcohol) hydrogels from reservoir test.

PubMed

Kazimierska-Drobny, Katarzyna; Kaczmarek, Mariusz

2013-12-01

In this paper the identification of diffusion coefficient, retardation factor and surface distribution coefficient for selected salts in poly(vinyl alcohol) hydrogels is performed. The identification of the transport parameters is based on the previously developed inverse problem technique using experimental data from the reservoir test and the solution of the diffusive transport equation with linear equilibrium sorption. The estimated values of diffusion coefficient are: for physiological fluid (6.30±0.10)×10(-10) m(2)/s, for 1 M NaCl (6.42±0.39)×10(-10) m(2)/s, and for 1 M KCl (7.94±0.38)×10(-10) m(2)/s. The retardation factor for all tested materials and salts is equal or close to one. The average value of the effective surface distribution coefficient is equal to 0.5. © 2013 Elsevier B.V. All rights reserved.

Multiscale image contrast amplification (MUSICA)

NASA Astrophysics Data System (ADS)

Vuylsteke, Pieter; Schoeters, Emile P.

1994-05-01

This article presents a novel approach to the problem of detail contrast enhancement, based on multiresolution representation of the original image. The image is decomposed into a weighted sum of smooth, localized, 2D basis functions at multiple scales. Each transform coefficient represents the amount of local detail at some specific scale and at a specific position in the image. Detail contrast is enhanced by non-linear amplification of the transform coefficients. An inverse transform is then applied to the modified coefficients. This yields a uniformly contrast- enhanced image without artefacts. The MUSICA-algorithm is being applied routinely to computed radiography images of chest, skull, spine, shoulder, pelvis, extremities, and abdomen examinations, with excellent acceptance. It is useful for a wide range of applications in the medical, graphical, and industrial area.

Inversion of residual stress profiles from ultrasonic Rayleigh wave dispersion data

NASA Astrophysics Data System (ADS)

Mora, P.; Spies, M.

2018-05-01

We investigate theoretically and with synthetic data the performance of several inversion methods to infer a residual stress state from ultrasonic surface wave dispersion data. We show that this particular problem may reveal in relevant materials undesired behaviors for some methods that could be reliably applied to infer other properties. We focus on two methods, one based on a Taylor-expansion, and another one based on a piecewise linear expansion regularized by a singular value decomposition. We explain the instabilities of the Taylor-based method by highlighting singularities in the series of coefficients. At the same time, we show that the other method can successfully provide performances which only weakly depend on the material.

Partial-fraction expansion and inverse Laplace transform of a rational function with real coefficients

NASA Technical Reports Server (NTRS)

Chang, F.-C.; Mott, H.

1974-01-01

This paper presents a technique for the partial-fraction expansion of functions which are ratios of polynomials with real coefficients. The expansion coefficients are determined by writing the polynomials as Taylor's series and obtaining the Laurent series expansion of the function. The general formula for the inverse Laplace transform is also derived.

Landslide caracteristics determination using bayesian inversion and seismic recording

NASA Astrophysics Data System (ADS)

Mangeney, A.; Moretti, L.; Capdeville, Y.; Stutzmann, E.; Bodin, T.; Bouchut, F.

2014-12-01

Gravitational instabilities, such as landslides, avalanches, or debris flows, play a key role in erosional processes and represent one of the major natural hazards in mountainous, coastal, and volcanic regions. Despite the great amount of field, experimental and numerical work devoted to this problem, the understanding of the physical processes at work in gravitational flows is still an open issue, in particular due to the lack of observations relevant to their dynamics. In this context, the seismic signal generated by gravitational flows is a unique opportunity to obtain information on their dynamics and characteristics. Here we present the study of the 1997 Boxing Day landslide that occurred in Montserrat. We accessed the force applied by the landslide to the ground surface responsible of the seismic waves by inverting the seismic waveform recorded (force-time function). This force was then used as a constraint in a bayesian inversion problem where the forward problem is the force-time function calculation obtained by simulating the landslide with the SHALTOP model (mangeney et al., 2007). With this method, we are able to give an estimate of the rheology (friction coefficient) and the initial shape of the collapsing mass. The volume retrieved is very similar to that obtained by field observations. The friction coefficient determined is also similar to that constrained by former studies or to that predicted by empirical laws (Lucas et al., 2014). Furthermore the method permits to give an estimate of the error made on these parameters.

Joule-Thomson inversion curves and related coefficients for several simple fluids

NASA Technical Reports Server (NTRS)

Hendricks, R. C.; Peller, I. C.; Baron, A. K.

1972-01-01

The equations of state (PVT relations) for methane, oxygen, argon, carbon dioxide, carbon monoxide, neon, hydrogen, and helium were used to establish Joule-Thomson inversion curves for each fluid. The principle of corresponding states was applied to the inversion curves, and a generalized inversion curve for fluids with small acentric factors was developed. The quantum fluids (neon, hydrogen, and helium) were excluded from the generalization, but available data for the fluids xenon and krypton were included. The critical isenthalpic Joule-Thomson coefficient mu sub c was determined; and a simplified approximation mu sub c approximates T sub c divided by 6P sub c was found adequate, where T sub c and P sub c are the temperature and pressure at the thermodynamic critical point. The maximum inversion temperatures were obtained from the second virial coefficient (maximum (B/T)).

Site Distribution and Aliasing Effects in the Inversion for Load Coefficients and Geocenter Motion from GPS Data

NASA Technical Reports Server (NTRS)

Wu, Xiaoping; Argus, Donald F.; Heflin, Michael B.; Ivins, Erik R.; Webb, Frank H.

2002-01-01

Precise GPS measurements of elastic relative site displacements due to surface mass loading offer important constraints on global surface mass transport. We investigate effects of site distribution and aliasing by higher-degree (n greater than or equal 2) loading terms on inversion of GPS data for n = 1 load coefficients and geocenter motion. Covariance and simulation analyses are conducted to assess the sensitivity of the inversion to aliasing and mismodeling errors and possible uncertainties in the n = 1 load coefficient determination. We found that the use of center-of-figure approximation in the inverse formulation could cause 10- 15% errors in the inverted load coefficients. n = 1 load estimates may be contaminated significantly by unknown higher-degree terms, depending on the load scenario and the GPS site distribution. The uncertainty in n = 1 zonal load estimate is at the level of 80 - 95% for two load scenarios.

A numerical analysis for non-linear radiation in MHD flow around a cylindrical surface with chemically reactive species

NASA Astrophysics Data System (ADS)

Khan, Junaid Ahmad; Mustafa, M.

2018-03-01

Boundary layer flow around a stretchable rough cylinder is modeled by taking into account boundary slip and transverse magnetic field effects. The main concern is to resolve heat/mass transfer problem considering non-linear radiative heat transfer and temperature/concentration jump aspects. Using conventional similarity approach, the equations of motion and heat transfer are converted into a boundary value problem whose solution is computed by shooting method for broad range of slip coefficients. The proposed numerical scheme appears to improve as the strengths of magnetic field and slip coefficients are enhanced. Axial velocity and temperature are considerably influenced by a parameter M which is inversely proportional to the radius of cylinder. A significant change in temperature profile is depicted for growing wall to ambient temperature ratio. Relevant physical quantities such as wall shear stress, local Nusselt number and local Sherwood number are elucidated in detail.

New solitary wave and multiple soliton solutions for fifth order nonlinear evolution equation with time variable coefficients

NASA Astrophysics Data System (ADS)

Jaradat, H. M.; Syam, Muhammed; Jaradat, M. M. M.; Mustafa, Zead; Moman, S.

2018-03-01

In this paper, we investigate the multiple soliton solutions and multiple singular soliton solutions of a class of the fifth order nonlinear evolution equation with variable coefficients of t using the simplified bilinear method based on a transformation method combined with the Hirota's bilinear sense. In addition, we present analysis for some parameters such as the soliton amplitude and the characteristic line. Several equation in the literature are special cases of the class which we discuss such as Caudrey-Dodd-Gibbon equation and Sawada-Kotera. Comparison with several methods in the literature, such as Helmholtz solution of the inverse variational problem, rational exponential function method, tanh method, homotopy perturbation method, exp-function method, and coth method, are made. From these comparisons, we conclude that the proposed method is efficient and our solutions are correct. It is worth mention that the proposed solution can solve many physical problems.

Adaptive Filtering in the Wavelet Transform Domain via Genetic Algorithms

DTIC Science & Technology

2004-08-06

wavelet transforms. Whereas the term “evolved” pertains only to the altered wavelet coefficients used during the inverse transform process. 2...words, the inverse transform produces the original signal x(t) from the wavelet and scaling coefficients. )()( ,, tdtx nk n nk k ψ...reconstruct the original signal as accurately as possible. The inverse transform reconstructs an approximation of the original signal (Burrus

3D Hydraulic tomography from joint inversion of the hydraulic heads and self-potential data. (Invited)

NASA Astrophysics Data System (ADS)

Jardani, A.; Soueid Ahmed, A.; Revil, A.; Dupont, J.

2013-12-01

Pumping tests are usually employed to predict the hydraulic conductivity filed from the inversion of the head measurements. Nevertheless, the inverse problem is strongly underdetermined and a reliable imaging requires a considerable number of wells. We propose to add more information to the inversion of the heads by adding (non-intrusive) streaming potentials (SP) data. The SP corresponds to perturbations in the local electrical field caused directly by the fow of the ground water. These SP are obtained with a set of the non-polarising electrodes installed at the ground surface. We developed a geostatistical method for the estimation of the hydraulic conductivity field from measurements of hydraulic heads and SP during pumping and injection experiments. We use the adjoint state method and a recent petrophysical formulation of the streaming potential problem in which the streaming coupling coefficient is derived from the hydraulic conductivity allowed reducing of the unknown parameters. The geostatistical inverse framework is applied to three synthetic case studies with different number of the wells and electrodes used to measure the hydraulic heads and the streaming potentials. To evaluate the benefits of the incorporating of the streaming potential to the hydraulic data, we compared the cases in which the data are coupled or not to map the hydraulic conductivity. The results of the inversion revealed that a dense distribution of electrodes can be used to infer the heterogeneities in the hydraulic conductivity field. Incorporating the streaming potential information to the hydraulic head data improves the estimate of hydraulic conductivity field especially when the number of piezometers is limited.

Sparseness- and continuity-constrained seismic imaging

NASA Astrophysics Data System (ADS)

Herrmann, Felix J.

2005-04-01

Non-linear solution strategies to the least-squares seismic inverse-scattering problem with sparseness and continuity constraints are proposed. Our approach is designed to (i) deal with substantial amounts of additive noise (SNR < 0 dB); (ii) use the sparseness and locality (both in position and angle) of directional basis functions (such as curvelets and contourlets) on the model: the reflectivity; and (iii) exploit the near invariance of these basis functions under the normal operator, i.e., the scattering-followed-by-imaging operator. Signal-to-noise ratio and the continuity along the imaged reflectors are significantly enhanced by formulating the solution of the seismic inverse problem in terms of an optimization problem. During the optimization, sparseness on the basis and continuity along the reflectors are imposed by jointly minimizing the l1- and anisotropic diffusion/total-variation norms on the coefficients and reflectivity, respectively. [Joint work with Peyman P. Moghaddam was carried out as part of the SINBAD project, with financial support secured through ITF (the Industry Technology Facilitator) from the following organizations: BG Group, BP, ExxonMobil, and SHELL. Additional funding came from the NSERC Discovery Grants 22R81254.

Theoretical stability in coefficient inverse problems for general hyperbolic equations with numerical reconstruction

NASA Astrophysics Data System (ADS)

Yu, Jie; Liu, Yikan; Yamamoto, Masahiro

2018-04-01

In this article, we investigate the determination of the spatial component in the time-dependent second order coefficient of a hyperbolic equation from both theoretical and numerical aspects. By the Carleman estimates for general hyperbolic operators and an auxiliary Carleman estimate, we establish local Hölder stability with either partial boundary or interior measurements under certain geometrical conditions. For numerical reconstruction, we minimize a Tikhonov functional which penalizes the gradient of the unknown function. Based on the resulting variational equation, we design an iteration method which is updated by solving a Poisson equation at each step. One-dimensional prototype examples illustrate the numerical performance of the proposed iteration.

Estimation of splitting functions from Earth's normal mode spectra using the neighbourhood algorithm

NASA Astrophysics Data System (ADS)

Pachhai, Surya; Tkalčić, Hrvoje; Masters, Guy

2016-01-01

The inverse problem for Earth structure from normal mode data is strongly non-linear and can be inherently non-unique. Traditionally, the inversion is linearized by taking partial derivatives of the complex spectra with respect to the model parameters (i.e. structure coefficients), and solved in an iterative fashion. This method requires that the earthquake source model is known. However, the release of energy in large earthquakes used for the analysis of Earth's normal modes is not simple. A point source approximation is often inadequate, and a more complete account of energy release at the source is required. In addition, many earthquakes are required for the solution to be insensitive to the initial constraints and regularization. In contrast to an iterative approach, the autoregressive linear inversion technique conveniently avoids the need for earthquake source parameters, but it also requires a number of events to achieve full convergence when a single event does not excite all singlets well. To build on previous improvements, we develop a technique to estimate structure coefficients (and consequently, the splitting functions) using a derivative-free parameter search, known as neighbourhood algorithm (NA). We implement an efficient forward method derived using the autoregresssion of receiver strips, and this allows us to search over a multiplicity of structure coefficients in a relatively short time. After demonstrating feasibility of the use of NA in synthetic cases, we apply it to observations of the inner core sensitive mode 13S2. The splitting function of this mode is dominated by spherical harmonic degree 2 axisymmetric structure and is consistent with the results obtained from the autoregressive linear inversion. The sensitivity analysis of multiple events confirms the importance of the Bolivia, 1994 earthquake. When this event is used in the analysis, as little as two events are sufficient to constrain the splitting functions of 13S2 mode. Apart from not requiring the knowledge of earthquake source, the newly developed technique provides an approximate uncertainty measure of the structure coefficients and allows us to control the type of structure solved for, for example to establish if elastic structure is sufficient.

Multimodal, high-dimensional, model-based, Bayesian inverse problems with applications in biomechanics

NASA Astrophysics Data System (ADS)

Franck, I. M.; Koutsourelakis, P. S.

2017-01-01

This paper is concerned with the numerical solution of model-based, Bayesian inverse problems. We are particularly interested in cases where the cost of each likelihood evaluation (forward-model call) is expensive and the number of unknown (latent) variables is high. This is the setting in many problems in computational physics where forward models with nonlinear PDEs are used and the parameters to be calibrated involve spatio-temporarily varying coefficients, which upon discretization give rise to a high-dimensional vector of unknowns. One of the consequences of the well-documented ill-posedness of inverse problems is the possibility of multiple solutions. While such information is contained in the posterior density in Bayesian formulations, the discovery of a single mode, let alone multiple, poses a formidable computational task. The goal of the present paper is two-fold. On one hand, we propose approximate, adaptive inference strategies using mixture densities to capture multi-modal posteriors. On the other, we extend our work in [1] with regard to effective dimensionality reduction techniques that reveal low-dimensional subspaces where the posterior variance is mostly concentrated. We validate the proposed model by employing Importance Sampling which confirms that the bias introduced is small and can be efficiently corrected if the analyst wishes to do so. We demonstrate the performance of the proposed strategy in nonlinear elastography where the identification of the mechanical properties of biological materials can inform non-invasive, medical diagnosis. The discovery of multiple modes (solutions) in such problems is critical in achieving the diagnostic objectives.

Joint Model and Parameter Dimension Reduction for Bayesian Inversion Applied to an Ice Sheet Flow Problem

NASA Astrophysics Data System (ADS)

Ghattas, O.; Petra, N.; Cui, T.; Marzouk, Y.; Benjamin, P.; Willcox, K.

2016-12-01

Model-based projections of the dynamics of the polar ice sheets play a central role in anticipating future sea level rise. However, a number of mathematical and computational challenges place significant barriers on improving predictability of these models. One such challenge is caused by the unknown model parameters (e.g., in the basal boundary conditions) that must be inferred from heterogeneous observational data, leading to an ill-posed inverse problem and the need to quantify uncertainties in its solution. In this talk we discuss the problem of estimating the uncertainty in the solution of (large-scale) ice sheet inverse problems within the framework of Bayesian inference. Computing the general solution of the inverse problem--i.e., the posterior probability density--is intractable with current methods on today's computers, due to the expense of solving the forward model (3D full Stokes flow with nonlinear rheology) and the high dimensionality of the uncertain parameters (which are discretizations of the basal sliding coefficient field). To overcome these twin computational challenges, it is essential to exploit problem structure (e.g., sensitivity of the data to parameters, the smoothing property of the forward model, and correlations in the prior). To this end, we present a data-informed approach that identifies low-dimensional structure in both parameter space and the forward model state space. This approach exploits the fact that the observations inform only a low-dimensional parameter space and allows us to construct a parameter-reduced posterior. Sampling this parameter-reduced posterior still requires multiple evaluations of the forward problem, therefore we also aim to identify a low dimensional state space to reduce the computational cost. To this end, we apply a proper orthogonal decomposition (POD) approach to approximate the state using a low-dimensional manifold constructed using ``snapshots'' from the parameter reduced posterior, and the discrete empirical interpolation method (DEIM) to approximate the nonlinearity in the forward problem. We show that using only a limited number of forward solves, the resulting subspaces lead to an efficient method to explore the high-dimensional posterior.

Controlled wavelet domain sparsity for x-ray tomography

NASA Astrophysics Data System (ADS)

Purisha, Zenith; Rimpeläinen, Juho; Bubba, Tatiana; Siltanen, Samuli

2018-01-01

Tomographic reconstruction is an ill-posed inverse problem that calls for regularization. One possibility is to require sparsity of the unknown in an orthonormal wavelet basis. This, in turn, can be achieved by variational regularization, where the penalty term is the sum of the absolute values of the wavelet coefficients. The primal-dual fixed point algorithm showed that the minimizer of the variational regularization functional can be computed iteratively using a soft-thresholding operation. Choosing the soft-thresholding parameter \

Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations

NASA Astrophysics Data System (ADS)

Zhi, Longxiao; Gu, Hanming

2018-03-01

The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor series expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain the P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion doesn't need certain assumptions and can estimate more parameters simultaneously. It has a better applicability. Meanwhile, by using the generalized linear method, the inversion is easily implemented and its calculation cost is small. We use the theoretical model to generate synthetic seismic records to test and analyze the influence of random noise. The results can prove the availability and anti-noise-interference ability of our method. We also apply the inversion to actual field data and prove the feasibility of our method in actual situation.

An Inverse Interpolation Method Utilizing In-Flight Strain Measurements for Determining Loads and Structural Response of Aerospace Vehicles

NASA Technical Reports Server (NTRS)

Shkarayev, S.; Krashantisa, R.; Tessler, A.

2004-01-01

An important and challenging technology aimed at the next generation of aerospace vehicles is that of structural health monitoring. The key problem is to determine accurately, reliably, and in real time the applied loads, stresses, and displacements experienced in flight, with such data establishing an information database for structural health monitoring. The present effort is aimed at developing a finite element-based methodology involving an inverse formulation that employs measured surface strains to recover the applied loads, stresses, and displacements in an aerospace vehicle in real time. The computational procedure uses a standard finite element model (i.e., "direct analysis") of a given airframe, with the subsequent application of the inverse interpolation approach. The inverse interpolation formulation is based on a parametric approximation of the loading and is further constructed through a least-squares minimization of calculated and measured strains. This procedure results in the governing system of linear algebraic equations, providing the unknown coefficients that accurately define the load approximation. Numerical simulations are carried out for problems involving various levels of structural approximation. These include plate-loading examples and an aircraft wing box. Accuracy and computational efficiency of the proposed method are discussed in detail. The experimental validation of the methodology by way of structural testing of an aircraft wing is also discussed.

Three Least-Squares Minimization Approaches to Interpret Gravity Data Due to Dipping Faults

NASA Astrophysics Data System (ADS)

Abdelrahman, E. M.; Essa, K. S.

2015-02-01

We have developed three different least-squares minimization approaches to determine, successively, the depth, dip angle, and amplitude coefficient related to the thickness and density contrast of a buried dipping fault from first moving average residual gravity anomalies. By defining the zero-anomaly distance and the anomaly value at the origin of the moving average residual profile, the problem of depth determination is transformed into a constrained nonlinear gravity inversion. After estimating the depth of the fault, the dip angle is estimated by solving a nonlinear inverse problem. Finally, after estimating the depth and dip angle, the amplitude coefficient is determined using a linear equation. This method can be applied to residuals as well as to measured gravity data because it uses the moving average residual gravity anomalies to estimate the model parameters of the faulted structure. The proposed method was tested on noise-corrupted synthetic and real gravity data. In the case of the synthetic data, good results are obtained when errors are given in the zero-anomaly distance and the anomaly value at the origin, and even when the origin is determined approximately. In the case of practical data (Bouguer anomaly over Gazal fault, south Aswan, Egypt), the fault parameters obtained are in good agreement with the actual ones and with those given in the published literature.

Method for Calculating the Optical Diffuse Reflection Coefficient for the Ocular Fundus

NASA Astrophysics Data System (ADS)

Lisenko, S. A.; Kugeiko, M. M.

2016-07-01

We have developed a method for calculating the optical diffuse reflection coefficient for the ocular fundus, taking into account multiple scattering of light in its layers (retina, epithelium, choroid) and multiple refl ection of light between layers. The method is based on the formulas for optical "combination" of the layers of the medium, in which the optical parameters of the layers (absorption and scattering coefficients) are replaced by some effective values, different for cases of directional and diffuse illumination of the layer. Coefficients relating the effective optical parameters of the layers and the actual values were established based on the results of a Monte Carlo numerical simulation of radiation transport in the medium. We estimate the uncertainties in retrieval of the structural and morphological parameters for the fundus from its diffuse reflectance spectrum using our method. We show that the simulated spectra correspond to the experimental data and that the estimates of the fundus parameters obtained as a result of solving the inverse problem are reasonable.

The effects of atmospheric processes on tehran smog forming.

PubMed

Mohammadi, H; Cohen, D; Babazadeh, M; Rokni, L

2012-01-01

Air pollution is one of the most important problems in urban areas that always threaten citizen's health. Photochemical smog is one of the main factors of air pollution in large cities like Tehran. Usually smog is not only a part of nature, but is being analyzed as an independent matter, which highly affects on the nature. It has been used as relationship between atmospheric elements such as temperature, pressure, relative humidity, wind speed with inversion in the time of smog forming and weather map in 500 Hpa level during 9 years descriptive static by using correlation coefficient in this analyze. Results show that there is a meaningful correlation between atmospheric elements and smog forming. This relation is seen between monthly average of these elements and monthly average of smog forming. However, when temperature decreases, corresponding pressure will increase and result of this will be smog forming. Usually smog increases in cold months of year due to enter cold high pressure air masses in Iran during December and January that is simultaneous with decreasing temperature and air pressure increases and inversion height distance decreases from the earth surface which cause to integrate air pollution under its surface, will cause to form smog in Tehran. It shows a meaningful and strong relation, based on resultant relations by correlation coefficient from inversion height and smog forming, so that obtained figure is more than 60% .

Effective scattering coefficient of the cerebral spinal fluid in adult head models for diffuse optical imaging

NASA Astrophysics Data System (ADS)

Custo, Anna; Wells, William M., III; Barnett, Alex H.; Hillman, Elizabeth M. C.; Boas, David A.

2006-07-01

An efficient computation of the time-dependent forward solution for photon transport in a head model is a key capability for performing accurate inversion for functional diffuse optical imaging of the brain. The diffusion approximation to photon transport is much faster to simulate than the physically correct radiative transport equation (RTE); however, it is commonly assumed that scattering lengths must be much smaller than all system dimensions and all absorption lengths for the approximation to be accurate. Neither of these conditions is satisfied in the cerebrospinal fluid (CSF). Since line-of-sight distances in the CSF are small, of the order of a few millimeters, we explore the idea that the CSF scattering coefficient may be modeled by any value from zero up to the order of the typical inverse line-of-sight distance, or approximately 0.3 mm-1, without significantly altering the calculated detector signals or the partial path lengths relevant for functional measurements. We demonstrate this in detail by using a Monte Carlo simulation of the RTE in a three-dimensional head model based on clinical magnetic resonance imaging data, with realistic optode geometries. Our findings lead us to expect that the diffusion approximation will be valid even in the presence of the CSF, with consequences for faster solution of the inverse problem.

Undetermined Coefficient Problems for Quasi-Linear Parabolic Equations

DTIC Science & Technology

1989-12-18

a student of John Burns, spent 3 years at Brown working with Tom Banks. His speciality is in control theory, in particular for viscoelastic...diffusion equation, SIAM J. Appld Maih, 39, (2), (1980), 272-289. [ 3 ] J. R. Cannon and H. M. Yin, A uniqueness theorem for a class of parabolic inverse...2.6) where H is a C’ function. This equation is of second kind Volterra type and can be u!uiquely solved for the function 0. Thus k = A

A numerical procedure for solving the inverse scattering problem for stratified dielectric media

NASA Astrophysics Data System (ADS)

Vogelzang, E.; Yevick, D.; Ferwerda, H. A.

1983-05-01

In this paper the refractive index profile of a dielectric stratified medium, terminated by a perfect conductor, is calculated from the complex reflection coefficient for monochromatic plane waves, incident from different directions. The advantage of this approach is that the dispersion of the refractive index does not enter the calculations. The calculation is based on the Marchenko and Gelfand-Levitan equations taking into account the bound modes of the layer. Some illustrative numerical examples are presented.

Mathematical Modeling of Ultraporous Nonmetallic Reticulated Materials

NASA Astrophysics Data System (ADS)

Alifanov, O. M.; Cherepanov, V. V.; Morzhukhina, A. V.

2015-01-01

We have developed an imitation statistical mathematical model reflecting the structure and the thermal, electrophysical, and optical properties of nonmetallic ultraporous reticulated materials. This model, in combination with a nonstationary thermal experiment and methods of the theory of inverse heat transfer problems, permits determining the little-studied characteristics of the above materials such as the radiative and conductive heat conductivities, the spectral scattering and absorption coefficients, the scattering indicatrix, and the dielectric constants, which are of great practical interest but are difficult to investigate.

An Algorithm for the Vertical Structure of Aerosol Extinction in the Lowest Kilometer of the Atmosphere: Rev. 1

DTIC Science & Technology

2017-11-01

inversion layer, or the well-mixed boundary layer. In such cases a low cloud ceiling is not present. In all instances the atmospheric extinction profiles...height, radiation fog depth, or the inversion layer height. The visibility regions and several representative vertical profiles of extinction are...the coefficient B can be found by B = ln(D/A) . (2) The coefficient B is sometimes a function of the cloud ceiling height, the inversion layer height

Multilevel Sequential Monte Carlo Samplers for Normalizing Constants

DOE PAGES

Moral, Pierre Del; Jasra, Ajay; Law, Kody J. H.; ...

2017-08-24

This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the discrete approximation error must be balanced. A multilevel strategy is utilized to substantially reduce the cost to obtain a given error level in the approximation as compared to standard estimators. Two estimators are considered and relative variance bounds are given. The theoretical results are numerically illustrated for two Bayesian inverse problems arising from elliptic partial differential equations (PDEs). The examples involve the inversion of observations of themore » solution of (i) a 1-dimensional Poisson equation to infer the diffusion coefficient, and (ii) a 2-dimensional Poisson equation to infer the external forcing.« less

Neural network approach for the calculation of potential coefficients in quantum mechanics

NASA Astrophysics Data System (ADS)

Ossandón, Sebastián; Reyes, Camilo; Cumsille, Patricio; Reyes, Carlos M.

2017-05-01

A numerical method based on artificial neural networks is used to solve the inverse Schrödinger equation for a multi-parameter class of potentials. First, the finite element method was used to solve repeatedly the direct problem for different parametrizations of the chosen potential function. Then, using the attainable eigenvalues as a training set of the direct radial basis neural network a map of new eigenvalues was obtained. This relationship was later inverted and refined by training an inverse radial basis neural network, allowing the calculation of the unknown parameters and therefore estimating the potential function. Three numerical examples are presented in order to prove the effectiveness of the method. The results show that the method proposed has the advantage to use less computational resources without a significant accuracy loss.

Technical Note: Atmospheric CO2 inversions on the mesoscale using data-driven prior uncertainties: methodology and system evaluation

NASA Astrophysics Data System (ADS)

Kountouris, Panagiotis; Gerbig, Christoph; Rödenbeck, Christian; Karstens, Ute; Koch, Thomas Frank; Heimann, Martin

2018-03-01

Atmospheric inversions are widely used in the optimization of surface carbon fluxes on a regional scale using information from atmospheric CO2 dry mole fractions. In many studies the prior flux uncertainty applied to the inversion schemes does not directly reflect the true flux uncertainties but is used to regularize the inverse problem. Here, we aim to implement an inversion scheme using the Jena inversion system and applying a prior flux error structure derived from a model-data residual analysis using high spatial and temporal resolution over a full year period in the European domain. We analyzed the performance of the inversion system with a synthetic experiment, in which the flux constraint is derived following the same residual analysis but applied to the model-model mismatch. The synthetic study showed a quite good agreement between posterior and true fluxes on European, country, annual and monthly scales. Posterior monthly and country-aggregated fluxes improved their correlation coefficient with the known truth by 7 % compared to the prior estimates when compared to the reference, with a mean correlation of 0.92. The ratio of the SD between the posterior and reference and between the prior and reference was also reduced by 33 % with a mean value of 1.15. We identified temporal and spatial scales on which the inversion system maximizes the derived information; monthly temporal scales at around 200 km spatial resolution seem to maximize the information gain.

The solar occultation technique for remote sensing of particulates in the earth's atmosphere. I - The inversion of horizon radiances from space

NASA Technical Reports Server (NTRS)

Schuerman, D. W.; Giovane, F.; Greenberg, J. M.

1976-01-01

The aerosol scattering coefficient as a function of height can be recovered from a direct inversion of the single-scattering horizon radiance provided the sun is above the horizon and an independent measurement of extinction as a function of height is made. Aerosol detection is effected by means of spacecraft measurements of the horizon radiance made during periods of spacecraft twilight. A solar occultation technique which allows the twilight measurements to be made when the sun is still above the horizon greatly reduces the complexity of the inversion problem. The second part of the paper reports on the use of a coronograph aboard Skylab to photograph the horizon just before spacecraft twilight in order to monitor the aerosol component above the tropopause. The coronograph picture, centered on 26.5 degrees E longitude and 63.0 degrees S latitude, shows that the aerosol layer peaks at a height of 48 plus or minus 1 km.

Estimation of interfacial heat transfer coefficient in inverse heat conduction problems based on artificial fish swarm algorithm

NASA Astrophysics Data System (ADS)

Wang, Xiaowei; Li, Huiping; Li, Zhichao

2018-04-01

The interfacial heat transfer coefficient (IHTC) is one of the most important thermal physical parameters which have significant effects on the calculation accuracy of physical fields in the numerical simulation. In this study, the artificial fish swarm algorithm (AFSA) was used to evaluate the IHTC between the heated sample and the quenchant in a one-dimensional heat conduction problem. AFSA is a global optimization method. In order to speed up the convergence speed, a hybrid method which is the combination of AFSA and normal distribution method (ZAFSA) was presented. The IHTC evaluated by ZAFSA were compared with those attained by AFSA and the advanced-retreat method and golden section method. The results show that the reasonable IHTC is obtained by using ZAFSA, the convergence of hybrid method is well. The algorithm based on ZAFSA can not only accelerate the convergence speed, but also reduce the numerical oscillation in the evaluation of IHTC.

Dimension-independent likelihood-informed MCMC

DOE PAGES

Cui, Tiangang; Law, Kody J. H.; Marzouk, Youssef M.

2015-10-08

Many Bayesian inference problems require exploring the posterior distribution of highdimensional parameters that represent the discretization of an underlying function. Our work introduces a family of Markov chain Monte Carlo (MCMC) samplers that can adapt to the particular structure of a posterior distribution over functions. There are two distinct lines of research that intersect in the methods we develop here. First, we introduce a general class of operator-weighted proposal distributions that are well defined on function space, such that the performance of the resulting MCMC samplers is independent of the discretization of the function. Second, by exploiting local Hessian informationmore » and any associated lowdimensional structure in the change from prior to posterior distributions, we develop an inhomogeneous discretization scheme for the Langevin stochastic differential equation that yields operator-weighted proposals adapted to the non-Gaussian structure of the posterior. The resulting dimension-independent and likelihood-informed (DILI) MCMC samplers may be useful for a large class of high-dimensional problems where the target probability measure has a density with respect to a Gaussian reference measure. Finally, we use two nonlinear inverse problems in order to demonstrate the efficiency of these DILI samplers: an elliptic PDE coefficient inverse problem and path reconstruction in a conditioned diffusion.« less

The inverse problem of refraction travel times, part II: Quantifying refraction nonuniqueness using a three-layer model

USGS Publications Warehouse

Ivanov, J.; Miller, R.D.; Xia, J.; Steeples, D.

2005-01-01

This paper is the second of a set of two papers in which we study the inverse refraction problem. The first paper, "Types of Geophysical Nonuniqueness through Minimization," studies and classifies the types of nonuniqueness that exist when solving inverse problems depending on the participation of a priori information required to obtain reliable solutions of inverse geophysical problems. In view of the classification developed, in this paper we study the type of nonuniqueness associated with the inverse refraction problem. An approach for obtaining a realistic solution to the inverse refraction problem is offered in a third paper that is in preparation. The nonuniqueness of the inverse refraction problem is examined by using a simple three-layer model. Like many other inverse geophysical problems, the inverse refraction problem does not have a unique solution. Conventionally, nonuniqueness is considered to be a result of insufficient data and/or error in the data, for any fixed number of model parameters. This study illustrates that even for overdetermined and error free data, nonlinear inverse refraction problems exhibit exact-data nonuniqueness, which further complicates the problem of nonuniqueness. By evaluating the nonuniqueness of the inverse refraction problem, this paper targets the improvement of refraction inversion algorithms, and as a result, the achievement of more realistic solutions. The nonuniqueness of the inverse refraction problem is examined initially by using a simple three-layer model. The observations and conclusions of the three-layer model nonuniqueness study are used to evaluate the nonuniqueness of more complicated n-layer models and multi-parameter cell models such as in refraction tomography. For any fixed number of model parameters, the inverse refraction problem exhibits continuous ranges of exact-data nonuniqueness. Such an unfavorable type of nonuniqueness can be uniquely solved only by providing abundant a priori information. Insufficient a priori information during the inversion is the reason why refraction methods often may not produce desired results or even fail. This work also demonstrates that the application of the smoothing constraints, typical when solving ill-posed inverse problems, has a dual and contradictory role when applied to the ill-posed inverse problem of refraction travel times. This observation indicates that smoothing constraints may play such a two-fold role when applied to other inverse problems. Other factors that contribute to inverse-refraction-problem nonuniqueness are also considered, including indeterminacy, statistical data-error distribution, numerical error and instability, finite data, and model parameters. ?? Birkha??user Verlag, Basel, 2005.

Application of kernel method in fluorescence molecular tomography

NASA Astrophysics Data System (ADS)

Zhao, Yue; Baikejiang, Reheman; Li, Changqing

2017-02-01

Reconstruction of fluorescence molecular tomography (FMT) is an ill-posed inverse problem. Anatomical guidance in the FMT reconstruction can improve FMT reconstruction efficiently. We have developed a kernel method to introduce the anatomical guidance into FMT robustly and easily. The kernel method is from machine learning for pattern analysis and is an efficient way to represent anatomical features. For the finite element method based FMT reconstruction, we calculate a kernel function for each finite element node from an anatomical image, such as a micro-CT image. Then the fluorophore concentration at each node is represented by a kernel coefficient vector and the corresponding kernel function. In the FMT forward model, we have a new system matrix by multiplying the sensitivity matrix with the kernel matrix. Thus, the kernel coefficient vector is the unknown to be reconstructed following a standard iterative reconstruction process. We convert the FMT reconstruction problem into the kernel coefficient reconstruction problem. The desired fluorophore concentration at each node can be calculated accordingly. Numerical simulation studies have demonstrated that the proposed kernel-based algorithm can improve the spatial resolution of the reconstructed FMT images. In the proposed kernel method, the anatomical guidance can be obtained directly from the anatomical image and is included in the forward modeling. One of the advantages is that we do not need to segment the anatomical image for the targets and background.

Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations

NASA Astrophysics Data System (ADS)

Zhi, L.; Gu, H.

2017-12-01

The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion has a better applicability. It doesn't need some assumptions and can estimate more parameters simultaneously. Meanwhile, by using the generalized linear method, the inversion is easily realized and its calculation amount is small. We use the Marmousi model to generate synthetic seismic records to test and analyze the influence of random noise. Without noise, all estimation results are relatively accurate. With the increase of noise, P-wave velocity change and oil saturation change are stable and less affected by noise. S-wave velocity change is most affected by noise. Finally we use the actual field data of time-lapse seismic prospecting to process and the results can prove the availability and feasibility of our method in actual situation.

Zernike expansion of derivatives and Laplacians of the Zernike circle polynomials.

PubMed

Janssen, A J E M

2014-07-01

The partial derivatives and Laplacians of the Zernike circle polynomials occur in various places in the literature on computational optics. In a number of cases, the expansion of these derivatives and Laplacians in the circle polynomials are required. For the first-order partial derivatives, analytic results are scattered in the literature. Results start as early as 1942 in Nijboer's thesis and continue until present day, with some emphasis on recursive computation schemes. A brief historic account of these results is given in the present paper. By choosing the unnormalized version of the circle polynomials, with exponential rather than trigonometric azimuthal dependence, and by a proper combination of the two partial derivatives, a concise form of the expressions emerges. This form is appropriate for the formulation and solution of a model wavefront sensing problem of reconstructing a wavefront on the level of its expansion coefficients from (measurements of the expansion coefficients of) the partial derivatives. It turns out that the least-squares estimation problem arising here decouples per azimuthal order m, and per m the generalized inverse solution assumes a concise analytic form so that singular value decompositions are avoided. The preferred version of the circle polynomials, with proper combination of the partial derivatives, also leads to a concise analytic result for the Zernike expansion of the Laplacian of the circle polynomials. From these expansions, the properties of the Laplacian as a mapping from the space of circle polynomials of maximal degree N, as required in the study of the Neumann problem associated with the transport-of-intensity equation, can be read off within a single glance. Furthermore, the inverse of the Laplacian on this space is shown to have a concise analytic form.

Improved Modeling and Prediction of Surface Wave Amplitudes

DTIC Science & Technology

2017-05-31

structures and derived attenuation coefficients from the Eurasian Q inversion study. 15. SUBJECT TERMS nuclear explosion monitoring, surface waves, membrane...24 4.6 Inversion of Eurasian Attenuation Data for Q Structure ........................................ 31 4.6.1 Data used in the Q Inversion ...33 4.6.2 Q Inversion Results

A TV-constrained decomposition method for spectral CT

NASA Astrophysics Data System (ADS)

Guo, Xiaoyue; Zhang, Li; Xing, Yuxiang

2017-03-01

Spectral CT is attracting more and more attention in medicine, industrial nondestructive testing and security inspection field. Material decomposition is an important issue to a spectral CT to discriminate materials. Because of the spectrum overlap of energy channels, as well as the correlation of basis functions, it is well acknowledged that decomposition step in spectral CT imaging causes noise amplification and artifacts in component coefficient images. In this work, we propose materials decomposition via an optimization method to improve the quality of decomposed coefficient images. On the basis of general optimization problem, total variance minimization is constrained on coefficient images in our overall objective function with adjustable weights. We solve this constrained optimization problem under the framework of ADMM. Validation on both a numerical dental phantom in simulation and a real phantom of pig leg on a practical CT system using dual-energy imaging is executed. Both numerical and physical experiments give visually obvious better reconstructions than a general direct inverse method. SNR and SSIM are adopted to quantitatively evaluate the image quality of decomposed component coefficients. All results demonstrate that the TV-constrained decomposition method performs well in reducing noise without losing spatial resolution so that improving the image quality. The method can be easily incorporated into different types of spectral imaging modalities, as well as for cases with energy channels more than two.

A theory of the inverse magnetoelectric effect in layered magnetostrictive-piezoelectric structures

NASA Astrophysics Data System (ADS)

Filippov, D. A.; Radchenko, G. S.; Firsova, T. O.; Galkina, T. A.

2017-05-01

A theory of the inverse magnetoelectric effect in layered structures has been presented. The theory is based on solving the equations of elastodynamics and electrostatics separately for the magnetostrictive and piezoelectric phases, taking into account the conditions at the interface between the phases. Expressions for the coefficient of inverse magnetoelectric conversion through the parameters characterizing the magnetostrictive and piezoelectric phases have been obtained. Theoretical dependences of the inverse magnetoelectric conversion coefficient on the frequency of the alternating-current electric field for the three-layer PZT-Ni-PZT structure and the two-layer terfenol- D-PZT structure have been calculated. The results of the calculations are in good agreement with the experimental data.

Blocky inversion of multichannel elastic impedance for elastic parameters

NASA Astrophysics Data System (ADS)

Mozayan, Davoud Karami; Gholami, Ali; Siahkoohi, Hamid Reza

2018-04-01

Petrophysical description of reservoirs requires proper knowledge of elastic parameters like P- and S-wave velocities (Vp and Vs) and density (ρ), which can be retrieved from pre-stack seismic data using the concept of elastic impedance (EI). We propose an inversion algorithm which recovers elastic parameters from pre-stack seismic data in two sequential steps. In the first step, using the multichannel blind seismic inversion method (exploited recently for recovering acoustic impedance from post-stack seismic data), high-resolution blocky EI models are obtained directly from partial angle-stacks. Using an efficient total-variation (TV) regularization, each angle-stack is inverted independently in a multichannel form without prior knowledge of the corresponding wavelet. The second step involves inversion of the resulting EI models for elastic parameters. Mathematically, under some assumptions, the EI's are linearly described by the elastic parameters in the logarithm domain. Thus a linear weighted least squares inversion is employed to perform this step. Accuracy of the concept of elastic impedance in predicting reflection coefficients at low and high angles of incidence is compared with that of exact Zoeppritz elastic impedance and the role of low frequency content in the problem is discussed. The performance of the proposed inversion method is tested using synthetic 2D data sets obtained from the Marmousi model and also 2D field data sets. The results confirm the efficiency and accuracy of the proposed method for inversion of pre-stack seismic data.

Magnetic Resonance Elastography: Measurement of Hepatic Stiffness Using Different Direct Inverse Problem Reconstruction Methods in Healthy Volunteers and Patients with Liver Disease.

PubMed

Saito, Shigeyoshi; Tanaka, Keiko; Hashido, Takashi

2016-02-01

The purpose of this study was to compare the mean hepatic stiffness values obtained by the application of two different direct inverse problem reconstruction methods to magnetic resonance elastography (MRE). Thirteen healthy men (23.2±2.1 years) and 16 patients with liver diseases (78.9±4.3 years; 12 men and 4 women) were examined for this study using a 3.0 T-MRI. The healthy volunteers underwent three consecutive scans, two 70-Hz waveform and a 50-Hz waveform scans. On the other hand, the patients with liver disease underwent scanning using the 70-Hz waveform only. The MRE data for each subject was processed twice for calculation of the mean hepatic stiffness (Pa), once using the multiscale direct inversion (MSDI) and once using the multimodel direct inversion (MMDI). There were no significant differences in the mean stiffness values among the scans obtained with two 70-Hz and different waveforms. However, the mean stiffness values obtained with the MSDI technique (with mask: 2895.3±255.8 Pa, without mask: 2940.6±265.4 Pa) were larger than those obtained with the MMDI technique (with mask: 2614.0±242.1 Pa, without mask: 2699.2±273.5 Pa). The reproducibility of measurements obtained using the two techniques was high for both the healthy volunteers [intraclass correlation coefficients (ICCs): 0.840-0.953] and the patients (ICC: 0.830-0.995). These results suggest that knowledge of the characteristics of different direct inversion algorithms is important for longitudinal liver stiffness assessments such as the comparison of different scanners and evaluation of the response to fibrosis therapy.

Ground-based microwave radiometric remote sensing of the tropical atmosphere

DOE Office of Scientific and Technical Information (OSTI.GOV)

Han, Yong.

1992-01-01

A partially developed 9-channel ground-based microwave radiometer for the Department of Meteorology at Penn State was completed and tested. Complementary units were added, corrections to both hardware and software were made, and system software was corrected and upgraded. Measurements from this radiometer were used to infer tropospheric temperature, water vapor and cloud liquid water. The various weighting functions at each of the 9 channels were calculated and analyzed to estimate the sensitivities of the brightness temperature to the desired atmospheric variables. The mathematical inversion problem, in a linear form, was viewed in terms of the theory of linear algebra. Severalmore » methods for solving the inversion problem were reviewed. Radiometric observations were conducted during the 1990 Tropical Cyclone Motion Experiment. The radiometer was installed on the island of Saipan in a tropical region. The radiometer was calibrated using tipping curve and radiosonde data as well as measurements of the radiation from a blackbody absorber. A linear statistical method was applied for the data inversion. The inversion coefficients in the equation were obtained using a large number of radiosonde profiles from Guam and a radiative transfer model. Retrievals were compared with those from local, Saipan, radiosonde measurements. Water vapor profiles, integrated water vapor, and integrated liquid water were retrieved successfully. For temperature profile retrievals, however, the radiometric measurements with experimental noises added no more profile information to the inversion than that they were determined mainly by the surface pressure measurements. A method was developed to derive the integrated water vapor and liquid water from combined radiometer and ceilometer measurements. Significant improvement on radiometric measurements of the integrated liquid water can be gained with this method.« less

A New Model of Jupiter's Magnetic Field From Juno's First Nine Orbits

NASA Astrophysics Data System (ADS)

Connerney, J. E. P.; Kotsiaros, S.; Oliversen, R. J.; Espley, J. R.; Joergensen, J. L.; Joergensen, P. S.; Merayo, J. M. G.; Herceg, M.; Bloxham, J.; Moore, K. M.; Bolton, S. J.; Levin, S. M.

2018-03-01

A spherical harmonic model of the magnetic field of Jupiter is obtained from vector magnetic field observations acquired by the Juno spacecraft during its first nine polar orbits about the planet. Observations acquired during eight of these orbits provide the first truly global coverage of Jupiter's magnetic field with a coarse longitudinal separation of 45° between perijoves. The magnetic field is represented with a degree 20 spherical harmonic model for the planetary ("internal") field, combined with a simple model of the magnetodisc for the field ("external") due to distributed magnetospheric currents. Partial solution of the underdetermined inverse problem using generalized inverse techniques yields a model ("Juno Reference Model through Perijove 9") of the planetary magnetic field with spherical harmonic coefficients well determined through degree and order 10, providing the first detailed view of a planetary dynamo beyond Earth.

The general linear inverse problem - Implication of surface waves and free oscillations for earth structure.

NASA Technical Reports Server (NTRS)

Wiggins, R. A.

1972-01-01

The discrete general linear inverse problem reduces to a set of m equations in n unknowns. There is generally no unique solution, but we can find k linear combinations of parameters for which restraints are determined. The parameter combinations are given by the eigenvectors of the coefficient matrix. The number k is determined by the ratio of the standard deviations of the observations to the allowable standard deviations in the resulting solution. Various linear combinations of the eigenvectors can be used to determine parameter resolution and information distribution among the observations. Thus we can determine where information comes from among the observations and exactly how it constraints the set of possible models. The application of such analyses to surface-wave and free-oscillation observations indicates that (1) phase, group, and amplitude observations for any particular mode provide basically the same type of information about the model; (2) observations of overtones can enhance the resolution considerably; and (3) the degree of resolution has generally been overestimated for many model determinations made from surface waves.

Inversion of very large matrices encountered in large scale problems of photogrammetry and photographic astrometry

NASA Technical Reports Server (NTRS)

Brown, D. C.

1971-01-01

The simultaneous adjustment of very large nets of overlapping plates covering the celestial sphere becomes computationally feasible by virtue of a twofold process that generates a system of normal equations having a bordered-banded coefficient matrix, and solves such a system in a highly efficient manner. Numerical results suggest that when a well constructed spherical net is subjected to a rigorous, simultaneous adjustment, the exercise of independently established control points is neither required for determinancy nor for production of accurate results.

Applications of Bayesian spectrum representation in acoustics

NASA Astrophysics Data System (ADS)

Botts, Jonathan M.

This dissertation utilizes a Bayesian inference framework to enhance the solution of inverse problems where the forward model maps to acoustic spectra. A Bayesian solution to filter design inverts a acoustic spectra to pole-zero locations of a discrete-time filter model. Spatial sound field analysis with a spherical microphone array is a data analysis problem that requires inversion of spatio-temporal spectra to directions of arrival. As with many inverse problems, a probabilistic analysis results in richer solutions than can be achieved with ad-hoc methods. In the filter design problem, the Bayesian inversion results in globally optimal coefficient estimates as well as an estimate the most concise filter capable of representing the given spectrum, within a single framework. This approach is demonstrated on synthetic spectra, head-related transfer function spectra, and measured acoustic reflection spectra. The Bayesian model-based analysis of spatial room impulse responses is presented as an analogous problem with equally rich solution. The model selection mechanism provides an estimate of the number of arrivals, which is necessary to properly infer the directions of simultaneous arrivals. Although, spectrum inversion problems are fairly ubiquitous, the scope of this dissertation has been limited to these two and derivative problems. The Bayesian approach to filter design is demonstrated on an artificial spectrum to illustrate the model comparison mechanism and then on measured head-related transfer functions to show the potential range of application. Coupled with sampling methods, the Bayesian approach is shown to outperform least-squares filter design methods commonly used in commercial software, confirming the need for a global search of the parameter space. The resulting designs are shown to be comparable to those that result from global optimization methods, but the Bayesian approach has the added advantage of a filter length estimate within the same unified framework. The application to reflection data is useful for representing frequency-dependent impedance boundaries in finite difference acoustic simulations. Furthermore, since the filter transfer function is a parametric model, it can be modified to incorporate arbitrary frequency weighting and account for the band-limited nature of measured reflection spectra. Finally, the model is modified to compensate for dispersive error in the finite difference simulation, from the filter design process. Stemming from the filter boundary problem, the implementation of pressure sources in finite difference simulation is addressed in order to assure that schemes properly converge. A class of parameterized source functions is proposed and shown to offer straightforward control of residual error in the simulation. Guided by the notion that the solution to be approximated affects the approximation error, sources are designed which reduce residual dispersive error to the size of round-off errors. The early part of a room impulse response can be characterized by a series of isolated plane waves. Measured with an array of microphones, plane waves map to a directional response of the array or spatial intensity map. Probabilistic inversion of this response results in estimates of the number and directions of image source arrivals. The model-based inversion is shown to avoid ambiguities associated with peak-finding or inspection of the spatial intensity map. For this problem, determining the number of arrivals in a given frame is critical for properly inferring the state of the sound field. This analysis is effectively compression of the spatial room response, which is useful for analysis or encoding of the spatial sound field. Parametric, model-based formulations of these problems enhance the solution in all cases, and a Bayesian interpretation provides a principled approach to model comparison and parameter estimation. v

Calculation method for steady-state pollutant concentration in mixing zones considering variable lateral diffusion coefficient.

PubMed

Wu, Wen; Wu, Zhouhu; Song, Zhiwen

2017-07-01

Prediction of the pollutant mixing zone (PMZ) near the discharge outfall in Huangshaxi shows large error when using the methods based on the constant lateral diffusion assumption. The discrepancy is due to the lack of consideration of the diffusion coefficient variation. The variable lateral diffusion coefficient is proposed to be a function of the longitudinal distance from the outfall. Analytical solution of the two-dimensional advection-diffusion equation of a pollutant is derived and discussed. Formulas to characterize the geometry of the PMZ are derived based on this solution, and a standard curve describing the boundary of the PMZ is obtained by proper choices of the normalization scales. The change of PMZ topology due to the variable diffusion coefficient is then discussed using these formulas. The criterion of assuming the lateral diffusion coefficient to be constant without large error in PMZ geometry is found. It is also demonstrated how to use these analytical formulas in the inverse problems including estimating the lateral diffusion coefficient in rivers by convenient measurements, and determining the maximum allowable discharge load based on the limitations of the geometrical scales of the PMZ. Finally, applications of the obtained formulas to onsite PMZ measurements in Huangshaxi present excellent agreement.

Design of Robust Adaptive Unbalance Response Controllers for Rotors with Magnetic Bearings

NASA Technical Reports Server (NTRS)

Knospe, Carl R.; Tamer, Samir M.; Fedigan, Stephen J.

1996-01-01

Experimental results have recently demonstrated that an adaptive open loop control strategy can be highly effective in the suppression of unbalance induced vibration on rotors supported in active magnetic bearings. This algorithm, however, relies upon a predetermined gain matrix. Typically, this matrix is determined by an optimal control formulation resulting in the choice of the pseudo-inverse of the nominal influence coefficient matrix as the gain matrix. This solution may result in problems with stability and performance robustness since the estimated influence coefficient matrix is not equal to the actual influence coefficient matrix. Recently, analysis tools have been developed to examine the robustness of this control algorithm with respect to structured uncertainty. Herein, these tools are extended to produce a design procedure for determining the adaptive law's gain matrix. The resulting control algorithm has a guaranteed convergence rate and steady state performance in spite of the uncertainty in the rotor system. Several examples are presented which demonstrate the effectiveness of this approach and its advantages over the standard optimal control formulation.

2D deblending using the multi-scale shaping scheme

NASA Astrophysics Data System (ADS)

Li, Qun; Ban, Xingan; Gong, Renbin; Li, Jinnuo; Ge, Qiang; Zu, Shaohuan

2018-01-01

Deblending can be posed as an inversion problem, which is ill-posed and requires constraint to obtain unique and stable solution. In blended record, signal is coherent, whereas interference is incoherent in some domains (e.g., common receiver domain and common offset domain). Due to the different sparsity, coefficients of signal and interference locate in different curvelet scale domains and have different amplitudes. Take into account the two differences, we propose a 2D multi-scale shaping scheme to constrain the sparsity to separate the blended record. In the domain where signal concentrates, the multi-scale scheme passes all the coefficients representing signal, while, in the domain where interference focuses, the multi-scale scheme suppresses the coefficients representing interference. Because the interference is suppressed evidently at each iteration, the constraint of multi-scale shaping operator in all scale domains are weak to guarantee the convergence of algorithm. We evaluate the performance of the multi-scale shaping scheme and the traditional global shaping scheme by using two synthetic and one field data examples.

Numerical methods for the inverse problem of density functional theory

DOE PAGES

Jensen, Daniel S.; Wasserman, Adam

2017-07-17

Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one-dimensional finite and periodic modelmore » systems.« less

Numerical methods for the inverse problem of density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jensen, Daniel S.; Wasserman, Adam

Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one-dimensional finite and periodic modelmore » systems.« less

Using the sensors of shaft position for simulation of misalignments of shafting supports of turbounits

NASA Astrophysics Data System (ADS)

Kumenko, A. I.; Kostyukov, V. N.; Kuz'minykh, N. Yu.; Timin, A. V.; Boichenko, S. N.

2017-09-01

Examples of using the method developed for the earlier proposed concept of the monitoring system of the technical condition of a turbounit are presented. The solution methods of the inverse problem—the calculation of misalignments of supports based on the measurement results of positions of rotor pins in the borings of bearings during the operation of a turbounit—are demonstrated. The results of determination of static responses of supports at operation misalignments are presented. The examples of simulation and calculation of misalignments of supports are made for the three-bearing "high-pressure rotor-middle-pressure rotor" (HPR-MPR) system of a turbounit with 250 MW capacity and for 14-supporting shafting of a turbounit with 1000 MW capacity. The calculation results of coefficients of the stiffness matrix of shaftings and testing of methods for solving the inverse problem by modeling are presented. The high accuracy of the solution of the inverse problem at the inversion of the stiffness matrix of shafting used for determining the correcting centerings of rotors of multisupporting shafting is revealed. The stiffness matrix can be recommended to analyze the influence of displacements of one or several supports on changing the support responses of shafting of the turbounit during adjustment after assembling or repair. It is proposed to use the considered methods of evaluation of misalignments in the monitoring systems of changing the mutual position of supports and centerings of rotors by half-couplings of turbounits, especially for seismically dangerous regions and regions with increased sagging of foundations due to watering of soils.

Computational methods for the identification of spatially varying stiffness and damping in beams

NASA Technical Reports Server (NTRS)

Banks, H. T.; Rosen, I. G.

1986-01-01

A numerical approximation scheme for the estimation of functional parameters in Euler-Bernoulli models for the transverse vibration of flexible beams with tip bodies is developed. The method permits the identification of spatially varying flexural stiffness and Voigt-Kelvin viscoelastic damping coefficients which appear in the hybrid system of ordinary and partial differential equations and boundary conditions describing the dynamics of such structures. An inverse problem is formulated as a least squares fit to data subject to constraints in the form of a vector system of abstract first order evolution equations. Spline-based finite element approximations are used to finite dimensionalize the problem. Theoretical convergence results are given and numerical studies carried out on both conventional (serial) and vector computers are discussed.

Self-Inversion of the Image of a Small-Scale Opaque Object in the Process of Focusing of the Illuminating Beam in an Absorbing Medium

NASA Astrophysics Data System (ADS)

Bubis, E. L.; Lozhrkarev, V. V.; Stepanov, A. N.; Smirnov, A. I.; Martynov, V. O.; Mal'shakova, O. A.; Silin, D. E.; Gusev, S. A.

2017-03-01

We describe the process of adaptive self-inversion of an image (nonlinear switching) of smallscale opaque object, when the amplitude-modulated laser beam, which illuminates it, is focused in a weakly absorbing medium. It is shown that, despite the nonlocal character of the process, which is due to thermal nonlinearity, the brightness-inverse image is characterized by acceptable quality and a high conversion coefficient. It is shown that the coefficient of conversion of the original image to the inverse one depends on the ratio of the object dimensions and the size of the illuminating beam, and decreases sharply for relatively large objects. The obtained experimental data agree with the numerical calculations. Inversion of the images of several model objects and microdefects in a nonlinear KDP crystal is demonstrated.

A spherical harmonic approach for the determination of HCP texture from ultrasound: A solution to the inverse problem

NASA Astrophysics Data System (ADS)

Lan, Bo; Lowe, Michael J. S.; Dunne, Fionn P. E.

2015-10-01

A new spherical convolution approach has been presented which couples HCP single crystal wave speed (the kernel function) with polycrystal c-axis pole distribution function to give the resultant polycrystal wave speed response. The three functions have been expressed as spherical harmonic expansions thus enabling application of the de-convolution technique to enable any one of the three to be determined from knowledge of the other two. Hence, the forward problem of determination of polycrystal wave speed from knowledge of single crystal wave speed response and the polycrystal pole distribution has been solved for a broad range of experimentally representative HCP polycrystal textures. The technique provides near-perfect representation of the sensitivity of wave speed to polycrystal texture as well as quantitative prediction of polycrystal wave speed. More importantly, a solution to the inverse problem is presented in which texture, as a c-axis distribution function, is determined from knowledge of the kernel function and the polycrystal wave speed response. It has also been explained why it has been widely reported in the literature that only texture coefficients up to 4th degree may be obtained from ultrasonic measurements. Finally, the de-convolution approach presented provides the potential for the measurement of polycrystal texture from ultrasonic wave speed measurements.

Optimization-Based Approach for Joint X-Ray Fluorescence and Transmission Tomographic Inversion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Di, Zichao; Leyffer, Sven; Wild, Stefan M.

2016-01-01

Fluorescence tomographic reconstruction, based on the detection of photons coming from fluorescent emission, can be used for revealing the internal elemental composition of a sample. On the other hand, conventional X-ray transmission tomography can be used for reconstructing the spatial distribution of the absorption coefficient inside a sample. In this work, we integrate both X-ray fluorescence and X-ray transmission data modalities and formulate a nonlinear optimization-based approach for reconstruction of the elemental composition of a given object. This model provides a simultaneous reconstruction of both the quantitative spatial distribution of all elements and the absorption effect in the sample. Mathematicallymore » speaking, we show that compared with the single-modality inversion (i.e., the X-ray transmission or fluorescence alone), the joint inversion provides a better-posed problem, which implies a better recovery. Therefore, the challenges in X-ray fluorescence tomography arising mainly from the effects of self-absorption in the sample are partially mitigated. The use of this technique is demonstrated on the reconstruction of several synthetic samples.« less

Waveform Tomography of Two-Dimensional Three-Component Seismic Data for HTI Anisotropic Media

NASA Astrophysics Data System (ADS)

Gao, Fengxia; Wang, Yanghua; Wang, Yun

2018-06-01

Reservoirs with vertically aligned fractures can be represented equivalently by horizontal transverse isotropy (HTI) media. But inverting for the anisotropic parameters of HTI media is a challenging inverse problem, because of difficulties inherent in a multiple parameter inversion. In this paper, when we invert for the anisotropic parameters, we consider for the first time the azimuthal rotation of a two-dimensional seismic survey line from the symmetry of HTI. The established wave equations for the HTI media with azimuthal rotation consist of nine elastic coefficients, expressed in terms of five modified Thomsen parameters. The latter are parallel to the Thomsen parameters for describing velocity characteristics of weak vertical transverse isotropy media. We analyze the sensitivity differences of the five modified Thomsen parameters from their radiation patterns, and attempt to balance the magnitude and sensitivity differences between the parameters through normalization and tuning factors which help to update the model parameters properly. We demonstrate an effective inversion strategy by inverting velocity parameters in the first stage and updates the five modified Thomsen parameters simultaneously in the second stage, for generating reliably reconstructed models.

Recovery of the parameters of cancellous bone by inversion of effective velocities, and transmission and reflection coefficients

NASA Astrophysics Data System (ADS)

Buchanan, James L.; Gilbert, Robert P.; Ou, Miao-jung Y.

2011-12-01

Estimating the parameters of an elastic or poroelastic medium from reflected or transmitted acoustic data is an important but difficult problem. Use of the Nelder-Mead simplex method to minimize an objective function measuring the discrepancy between some observable and its value calculated from a model for a trial set of parameters has been tried by several authors. In this paper, the difficulty with this direct approach, which is the existence of numerous local minima of the objective function, is documented for the in vitro experiment in which a specimen in a water tank is subject to an ultrasonic pulse. An indirect approach, based on the numerical solution of the equations for a set of ‘effective’ velocities and transmission coefficients, is then observed empirically to ameliorate the difficulties posed by the direct approach.

Variational methods for direct/inverse problems of atmospheric dynamics and chemistry

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Penenko, Alexey; Tsvetova, Elena

2013-04-01

We present a variational approach for solving direct and inverse problems of atmospheric hydrodynamics and chemistry. It is important that the accurate matching of numerical schemes has to be provided in the chain of objects: direct/adjoint problems - sensitivity relations - inverse problems, including assimilation of all available measurement data. To solve the problems we have developed a new enhanced set of cost-effective algorithms. The matched description of the multi-scale processes is provided by a specific choice of the variational principle functionals for the whole set of integrated models. Then all functionals of variational principle are approximated in space and time by splitting and decomposition methods. Such approach allows us to separately consider, for example, the space-time problems of atmospheric chemistry in the frames of decomposition schemes for the integral identity sum analogs of the variational principle at each time step and in each of 3D finite-volumes. To enhance the realization efficiency, the set of chemical reactions is divided on the subsets related to the operators of production and destruction. Then the idea of the Euler's integrating factors is applied in the frames of the local adjoint problem technique [1]-[3]. The analytical solutions of such adjoint problems play the role of integrating factors for differential equations describing atmospheric chemistry. With their help, the system of differential equations is transformed to the equivalent system of integral equations. As a result we avoid the construction and inversion of preconditioning operators containing the Jacobi matrixes which arise in traditional implicit schemes for ODE solution. This is the main advantage of our schemes. At the same time step but on the different stages of the "global" splitting scheme, the system of atmospheric dynamic equations is solved. For convection - diffusion equations for all state functions in the integrated models we have developed the monotone and stable discrete-analytical numerical schemes [1]-[3] conserving the positivity of the chemical substance concentrations and possessing the properties of energy and mass balance that are postulated in the general variational principle for integrated models. All algorithms for solution of transport, diffusion and transformation problems are direct (without iterations). The work is partially supported by the Programs No 4 of Presidium RAS and No 3 of Mathematical Department of RAS, by RFBR project 11-01-00187 and Integrating projects of SD RAS No 8 and 35. Our studies are in the line with the goals of COST Action ES1004. References Penenko V., Tsvetova E. Discrete-analytical methods for the implementation of variational principles in environmental applications// Journal of computational and applied mathematics, 2009, v. 226, 319-330. Penenko A.V. Discrete-analytic schemes for solving an inverse coefficient heat conduction problem in a layered medium with gradient methods// Numerical Analysis and Applications, 2012, V. 5, pp 326-341. V. Penenko, E. Tsvetova. Variational methods for constructing the monotone approximations for atmospheric chemistry models //Numerical Analysis and Applications, 2013 (in press).

Genetic Algorithms Evolve Optimized Transforms for Signal Processing Applications

DTIC Science & Technology

2005-04-01

coefficient sets describing inverse transforms and matched forward/ inverse transform pairs that consistently outperform wavelets for image compression and reconstruction applications under conditions subject to quantization error.

Nozzle cooling of hot surfaces with various orientations

NASA Astrophysics Data System (ADS)

Ondrouskova, Jana; Luks, Tomas; Horsky, Jaroslav

2012-04-01

The aim of this research is an investigation of hot surface orientation influence on heat transfer during cooling by a nozzle. Two types of nozzles were used for the experiments (air-mist nozzle and hydraulic nozzle). A test plate was cooled in three positions - top, side and bottom position. The aim was to simulate a cooling situation in the secondary zone of a continuous casting machine. Temperature was measured in seven locations under the cooled surface by thermocouples. These data were used for an inverse heat conduction problem and then boundary conditions were computed. These boundary conditions are represented by surface temperature, heat transfer coefficient and heat flux. Results from an inverse calculation were compared in each position of thermocouples separately. The total cooling intensity was specified for all configurations of nozzles and test plate orientation. Results are summarised in a graphical and numerical format.

Final Technical Report for "Applied Mathematics Research: Simulation Based Optimization and Application to Electromagnetic Inverse Problems"

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haber, Eldad

2014-03-17

The focus of research was: Developing adaptive mesh for the solution of Maxwell's equations; Developing a parallel framework for time dependent inverse Maxwell's equations; Developing multilevel methods for optimization problems with inequality constraints; A new inversion code for inverse Maxwell's equations in the 0th frequency (DC resistivity); A new inversion code for inverse Maxwell's equations in low frequency regime. Although the research concentrated on electromagnetic forward and in- verse problems the results of the research was applied to the problem of image registration.

Easy way to determine quantitative spatial resolution distribution for a general inverse problem

NASA Astrophysics Data System (ADS)

An, M.; Feng, M.

2013-12-01

The spatial resolution computation of a solution was nontrivial and more difficult than solving an inverse problem. Most geophysical studies, except for tomographic studies, almost uniformly neglect the calculation of a practical spatial resolution. In seismic tomography studies, a qualitative resolution length can be indicatively given via visual inspection of the restoration of a synthetic structure (e.g., checkerboard tests). An effective strategy for obtaining quantitative resolution length is to calculate Backus-Gilbert resolution kernels (also referred to as a resolution matrix) by matrix operation. However, not all resolution matrices can provide resolution length information, and the computation of resolution matrix is often a difficult problem for very large inverse problems. A new class of resolution matrices, called the statistical resolution matrices (An, 2012, GJI), can be directly determined via a simple one-parameter nonlinear inversion performed based on limited pairs of random synthetic models and their inverse solutions. The total procedure were restricted to forward/inversion processes used in the real inverse problem and were independent of the degree of inverse skill used in the solution inversion. Spatial resolution lengths can be directly given during the inversion. Tests on 1D/2D/3D model inversion demonstrated that this simple method can be at least valid for a general linear inverse problem.

On the inverse Magnus effect for flow past a rotating cylinder

NASA Astrophysics Data System (ADS)

John, Benzi; Gu, Xiao-Jun; Barber, Robert W.; Emerson, David R.

2016-11-01

Flow past a rotating cylinder has been investigated using the direct simulation Monte Carlo method. The study focuses on the occurrence of the inverse Magnus effect under subsonic flow conditions. In particular, the variations in the coefficients of lift and drag have been investigated as a function of the Knudsen and Reynolds numbers. Additionally, a temperature sensitivity study has been carried out to assess the influence of the wall temperature on the computed aerodynamic coefficients. It has been found that both the Reynolds number and the cylinder wall temperature significantly affect the drag as well as the onset of lift inversion in the transition flow regime.

Fast, Nonlinear, Fully Probabilistic Inversion of Large Geophysical Problems

NASA Astrophysics Data System (ADS)

Curtis, A.; Shahraeeni, M.; Trampert, J.; Meier, U.; Cho, G.

2010-12-01

Almost all Geophysical inverse problems are in reality nonlinear. Fully nonlinear inversion including non-approximated physics, and solving for probability distribution functions (pdf’s) that describe the solution uncertainty, generally requires sampling-based Monte-Carlo style methods that are computationally intractable in most large problems. In order to solve such problems, physical relationships are usually linearized leading to efficiently-solved, (possibly iterated) linear inverse problems. However, it is well known that linearization can lead to erroneous solutions, and in particular to overly optimistic uncertainty estimates. What is needed across many Geophysical disciplines is a method to invert large inverse problems (or potentially tens of thousands of small inverse problems) fully probabilistically and without linearization. This talk shows how very large nonlinear inverse problems can be solved fully probabilistically and incorporating any available prior information using mixture density networks (driven by neural network banks), provided the problem can be decomposed into many small inverse problems. In this talk I will explain the methodology, compare multi-dimensional pdf inversion results to full Monte Carlo solutions, and illustrate the method with two applications: first, inverting surface wave group and phase velocities for a fully-probabilistic global tomography model of the Earth’s crust and mantle, and second inverting industrial 3D seismic data for petrophysical properties throughout and around a subsurface hydrocarbon reservoir. The latter problem is typically decomposed into 104 to 105 individual inverse problems, each solved fully probabilistically and without linearization. The results in both cases are sufficiently close to the Monte Carlo solution to exhibit realistic uncertainty, multimodality and bias. This provides far greater confidence in the results, and in decisions made on their basis.

Joint inversion of NMR and SIP data to estimate pore size distribution of geomaterials

NASA Astrophysics Data System (ADS)

Niu, Qifei; Zhang, Chi

2018-03-01

There are growing interests in using geophysical tools to characterize the microstructure of geomaterials because of the non-invasive nature and the applicability in field. In these applications, multiple types of geophysical data sets are usually processed separately, which may be inadequate to constrain the key feature of target variables. Therefore, simultaneous processing of multiple data sets could potentially improve the resolution. In this study, we propose a method to estimate pore size distribution by joint inversion of nuclear magnetic resonance (NMR) T2 relaxation and spectral induced polarization (SIP) spectra. The petrophysical relation between NMR T2 relaxation time and SIP relaxation time is incorporated in a nonlinear least squares problem formulation, which is solved using Gauss-Newton method. The joint inversion scheme is applied to a synthetic sample and a Berea sandstone sample. The jointly estimated pore size distributions are very close to the true model and results from other experimental method. Even when the knowledge of the petrophysical models of the sample is incomplete, the joint inversion can still capture the main features of the pore size distribution of the samples, including the general shape and relative peak positions of the distribution curves. It is also found from the numerical example that the surface relaxivity of the sample could be extracted with the joint inversion of NMR and SIP data if the diffusion coefficient of the ions in the electrical double layer is known. Comparing to individual inversions, the joint inversion could improve the resolution of the estimated pore size distribution because of the addition of extra data sets. The proposed approach might constitute a first step towards a comprehensive joint inversion that can extract the full pore geometry information of a geomaterial from NMR and SIP data.

Adults' understanding of inversion concepts: how does performance on addition and subtraction inversion problems compare to performance on multiplication and division inversion problems?

PubMed

Robinson, Katherine M; Ninowski, Jerilyn E

2003-12-01

Problems of the form a + b - b have been used to assess conceptual understanding of the relationship between addition and subtraction. No study has investigated the same relationship between multiplication and division on problems of the form d x e / e. In both types of inversion problems, no calculation is required if the inverse relationship between the operations is understood. Adult participants solved addition/subtraction and multiplication/division inversion (e.g., 9 x 22 / 22) and standard (e.g., 2 + 27 - 28) problems. Participants started to use the inversion strategy earlier and more frequently on addition/subtraction problems. Participants took longer to solve both types of multiplication/division problems. Overall, conceptual understanding of the relationship between multiplication and division was not as strong as that between addition and subtraction. One explanation for this difference in performance is that the operation of division is more weakly represented and understood than the other operations and that this weakness affects performance on problems of the form d x e / e.

Decomposing Large Inverse Problems with an Augmented Lagrangian Approach: Application to Joint Inversion of Body-Wave Travel Times and Surface-Wave Dispersion Measurements

NASA Astrophysics Data System (ADS)

Reiter, D. T.; Rodi, W. L.

2015-12-01

Constructing 3D Earth models through the joint inversion of large geophysical data sets presents numerous theoretical and practical challenges, especially when diverse types of data and model parameters are involved. Among the challenges are the computational complexity associated with large data and model vectors and the need to unify differing model parameterizations, forward modeling methods and regularization schemes within a common inversion framework. The challenges can be addressed in part by decomposing the inverse problem into smaller, simpler inverse problems that can be solved separately, providing one knows how to merge the separate inversion results into an optimal solution of the full problem. We have formulated an approach to the decomposition of large inverse problems based on the augmented Lagrangian technique from optimization theory. As commonly done, we define a solution to the full inverse problem as the Earth model minimizing an objective function motivated, for example, by a Bayesian inference formulation. Our decomposition approach recasts the minimization problem equivalently as the minimization of component objective functions, corresponding to specified data subsets, subject to the constraints that the minimizing models be equal. A standard optimization algorithm solves the resulting constrained minimization problems by alternating between the separate solution of the component problems and the updating of Lagrange multipliers that serve to steer the individual solution models toward a common model solving the full problem. We are applying our inversion method to the reconstruction of the·crust and upper-mantle seismic velocity structure across Eurasia.· Data for the inversion comprise a large set of P and S body-wave travel times·and fundamental and first-higher mode Rayleigh-wave group velocities.

Integration of experimental and computational methods for identifying geometric, thermal and diffusive properties of biomaterials

NASA Astrophysics Data System (ADS)

Weres, Jerzy; Kujawa, Sebastian; Olek, Wiesław; Czajkowski, Łukasz

2016-04-01

Knowledge of physical properties of biomaterials is important in understanding and designing agri-food and wood processing industries. In the study presented in this paper computational methods were developed and combined with experiments to enhance identification of agri-food and forest product properties, and to predict heat and water transport in such products. They were based on the finite element model of heat and water transport and supplemented with experimental data. Algorithms were proposed for image processing, geometry meshing, and inverse/direct finite element modelling. The resulting software system was composed of integrated subsystems for 3D geometry data acquisition and mesh generation, for 3D geometry modelling and visualization, and for inverse/direct problem computations for the heat and water transport processes. Auxiliary packages were developed to assess performance, accuracy and unification of data access. The software was validated by identifying selected properties and using the estimated values to predict the examined processes, and then comparing predictions to experimental data. The geometry, thermal conductivity, specific heat, coefficient of water diffusion, equilibrium water content and convective heat and water transfer coefficients in the boundary layer were analysed. The estimated values, used as an input for simulation of the examined processes, enabled reduction in the uncertainty associated with predictions.

Fully probabilistic seismic source inversion - Part 2: Modelling errors and station covariances

NASA Astrophysics Data System (ADS)

Stähler, Simon C.; Sigloch, Karin

2016-11-01

Seismic source inversion, a central task in seismology, is concerned with the estimation of earthquake source parameters and their uncertainties. Estimating uncertainties is particularly challenging because source inversion is a non-linear problem. In a companion paper, Stähler and Sigloch (2014) developed a method of fully Bayesian inference for source parameters, based on measurements of waveform cross-correlation between broadband, teleseismic body-wave observations and their modelled counterparts. This approach yields not only depth and moment tensor estimates but also source time functions. A prerequisite for Bayesian inference is the proper characterisation of the noise afflicting the measurements, a problem we address here. We show that, for realistic broadband body-wave seismograms, the systematic error due to an incomplete physical model affects waveform misfits more strongly than random, ambient background noise. In this situation, the waveform cross-correlation coefficient CC, or rather its decorrelation D = 1 - CC, performs more robustly as a misfit criterion than ℓp norms, more commonly used as sample-by-sample measures of misfit based on distances between individual time samples. From a set of over 900 user-supervised, deterministic earthquake source solutions treated as a quality-controlled reference, we derive the noise distribution on signal decorrelation D = 1 - CC of the broadband seismogram fits between observed and modelled waveforms. The noise on D is found to approximately follow a log-normal distribution, a fortunate fact that readily accommodates the formulation of an empirical likelihood function for D for our multivariate problem. The first and second moments of this multivariate distribution are shown to depend mostly on the signal-to-noise ratio (SNR) of the CC measurements and on the back-azimuthal distances of seismic stations. By identifying and quantifying this likelihood function, we make D and thus waveform cross-correlation measurements usable for fully probabilistic sampling strategies, in source inversion and related applications such as seismic tomography.

Parallelized Three-Dimensional Resistivity Inversion Using Finite Elements And Adjoint State Methods

NASA Astrophysics Data System (ADS)

Schaa, Ralf; Gross, Lutz; Du Plessis, Jaco

2015-04-01

The resistivity method is one of the oldest geophysical exploration methods, which employs one pair of electrodes to inject current into the ground and one or more pairs of electrodes to measure the electrical potential difference. The potential difference is a non-linear function of the subsurface resistivity distribution described by an elliptic partial differential equation (PDE) of the Poisson type. Inversion of measured potentials solves for the subsurface resistivity represented by PDE coefficients. With increasing advances in multichannel resistivity acquisition systems (systems with more than 60 channels and full waveform recording are now emerging), inversion software require efficient storage and solver algorithms. We developed the finite element solver Escript, which provides a user-friendly programming environment in Python to solve large-scale PDE-based problems (see https://launchpad.net/escript-finley). Using finite elements, highly irregular shaped geology and topography can readily be taken into account. For the 3D resistivity problem, we have implemented the secondary potential approach, where the PDE is decomposed into a primary potential caused by the source current and the secondary potential caused by changes in subsurface resistivity. The primary potential is calculated analytically, and the boundary value problem for the secondary potential is solved using nodal finite elements. This approach removes the singularity caused by the source currents and provides more accurate 3D resistivity models. To solve the inversion problem we apply a 'first optimize then discretize' approach using the quasi-Newton scheme in form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method (see Gross & Kemp 2013). The evaluation of the cost function requires the solution of the secondary potential PDE for each source current and the solution of the corresponding adjoint-state PDE for the cost function gradients with respect to the subsurface resistivity. The Hessian of the regularization term is used as preconditioner which requires an additional PDE solution in each iteration step. As it turns out, the relevant PDEs are naturally formulated in the finite element framework. Using the domain decomposition method provided in Escript, the inversion scheme has been parallelized for distributed memory computers with multi-core shared memory nodes. We show numerical examples from simple layered models to complex 3D models and compare with the results from other methods. The inversion scheme is furthermore tested on a field data example to characterise localised freshwater discharge in a coastal environment.. References: L. Gross and C. Kemp (2013) Large Scale Joint Inversion of Geophysical Data using the Finite Element Method in escript. ASEG Extended Abstracts 2013, http://dx.doi.org/10.1071/ASEG2013ab306

Spectrophotometric Method for Differentiation of Human Skin Melanoma. I. Optical Diffuse Reflection Coefficient

NASA Astrophysics Data System (ADS)

Petruk, V. G.; Ivanov, A. P.; Kvaternyuk, S. M.; Barun, V. V.

2016-03-01

We have designed an experimental setup, based on two integrating spheres, that lets us measure the optical diffuse reflectance spectra (diffuse reflection coefficient vs. wavelength) of human skin quickly under clinical conditions in vivo. For the wavelength interval 520-1100 nm, we give the values of the diffuse reflection coefficient for healthy tissue, skin with a benign nevus, and skin with a malignant melanoma for a large group of test subjects. We experimentally established a number of wavelengths in the red-near IR region of the spectrum which can be used for early differential diagnosis of nevi and melanoma in patient cancer screening. According to the Kramer-Welch test, the probability of the diffuse reflection coefficient for skin with melanoma and a nevus having different distributions is >0.94, and at many wavelengths it is >0.999. By solving the inverse problem, we estimated the changes in a number of structural and biophysical parameters of the tissue on going from healthy skin to nevus and melanoma. The results obtained can provide a basis for developing a clinical approach to identifying the risk of malignant transformation of the skin before surgery and histological analysis of the tissue.

SU-E-J-161: Inverse Problems for Optical Parameters in Laser Induced Thermal Therapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fahrenholtz, SJ; Stafford, RJ; Fuentes, DT

Purpose: Magnetic resonance-guided laser-induced thermal therapy (MRgLITT) is investigated as a neurosurgical intervention for oncological applications throughout the body by active post market studies. Real-time MR temperature imaging is used to monitor ablative thermal delivery in the clinic. Additionally, brain MRgLITT could improve through effective planning for laser fiber's placement. Mathematical bioheat models have been extensively investigated but require reliable patient specific physical parameter data, e.g. optical parameters. This abstract applies an inverse problem algorithm to characterize optical parameter data obtained from previous MRgLITT interventions. Methods: The implemented inverse problem has three primary components: a parameter-space search algorithm, a physicsmore » model, and training data. First, the parameter-space search algorithm uses a gradient-based quasi-Newton method to optimize the effective optical attenuation coefficient, μ-eff. A parameter reduction reduces the amount of optical parameter-space the algorithm must search. Second, the physics model is a simplified bioheat model for homogeneous tissue where closed-form Green's functions represent the exact solution. Third, the training data was temperature imaging data from 23 MRgLITT oncological brain ablations (980 nm wavelength) from seven different patients. Results: To three significant figures, the descriptive statistics for μ-eff were 1470 m{sup −1} mean, 1360 m{sup −1} median, 369 m{sup −1} standard deviation, 933 m{sup −1} minimum and 2260 m{sup −1} maximum. The standard deviation normalized by the mean was 25.0%. The inverse problem took <30 minutes to optimize all 23 datasets. Conclusion: As expected, the inferred average is biased by underlying physics model. However, the standard deviation normalized by the mean is smaller than literature values and indicates an increased precision in the characterization of the optical parameters needed to plan MRgLITT procedures. This investigation demonstrates the potential for the optimization and validation of more sophisticated bioheat models that incorporate the uncertainty of the data into the predictions, e.g. stochastic finite element methods.« less

Children's Understanding of the Arithmetic Concepts of Inversion and Associativity

ERIC Educational Resources Information Center

Robinson, Katherine M.; Ninowski, Jerilyn E.; Gray, Melissa L.

2006-01-01

Previous studies have shown that even preschoolers can solve inversion problems of the form a + b - b by using the knowledge that addition and subtraction are inverse operations. In this study, a new type of inversion problem of the form d x e [divided by] e was also examined. Grade 6 and 8 students solved inversion problems of both types as well…

A Geophysical Inversion Model Enhancement Technique Based on the Blind Deconvolution

NASA Astrophysics Data System (ADS)

Zuo, B.; Hu, X.; Li, H.

2011-12-01

A model-enhancement technique is proposed to enhance the geophysical inversion model edges and details without introducing any additional information. Firstly, the theoretic correctness of the proposed geophysical inversion model-enhancement technique is discussed. An inversion MRM (model resolution matrix) convolution approximating PSF (Point Spread Function) method is designed to demonstrate the correctness of the deconvolution model enhancement method. Then, a total-variation regularization blind deconvolution geophysical inversion model-enhancement algorithm is proposed. In previous research, Oldenburg et al. demonstrate the connection between the PSF and the geophysical inverse solution. Alumbaugh et al. propose that more information could be provided by the PSF if we return to the idea of it behaving as an averaging or low pass filter. We consider the PSF as a low pass filter to enhance the inversion model basis on the theory of the PSF convolution approximation. Both the 1D linear and the 2D magnetotelluric inversion examples are used to analyze the validity of the theory and the algorithm. To prove the proposed PSF convolution approximation theory, the 1D linear inversion problem is considered. It shows the ratio of convolution approximation error is only 0.15%. The 2D synthetic model enhancement experiment is presented. After the deconvolution enhancement, the edges of the conductive prism and the resistive host become sharper, and the enhancement result is closer to the actual model than the original inversion model according the numerical statistic analysis. Moreover, the artifacts in the inversion model are suppressed. The overall precision of model increases 75%. All of the experiments show that the structure details and the numerical precision of inversion model are significantly improved, especially in the anomalous region. The correlation coefficient between the enhanced inversion model and the actual model are shown in Fig. 1. The figure illustrates that more information and details structure of the actual model are enhanced through the proposed enhancement algorithm. Using the proposed enhancement method can help us gain a clearer insight into the results of the inversions and help make better informed decisions.

Analysis of 3D poroelastodynamics using BEM based on modified time-step scheme

NASA Astrophysics Data System (ADS)

Igumnov, L. A.; Petrov, A. N.; Vorobtsov, I. V.

2017-10-01

The development of 3d boundary elements modeling of dynamic partially saturated poroelastic media using a stepping scheme is presented in this paper. Boundary Element Method (BEM) in Laplace domain and the time-stepping scheme for numerical inversion of the Laplace transform are used to solve the boundary value problem. The modified stepping scheme with a varied integration step for quadrature coefficients calculation using the symmetry of the integrand function and integral formulas of Strongly Oscillating Functions was applied. The problem with force acting on a poroelastic prismatic console end was solved using the developed method. A comparison of the results obtained by the traditional stepping scheme with the solutions obtained by this modified scheme shows that the computational efficiency is better with usage of combined formulas.

Estimation of Dynamic Friction Process of the Akatani Landslide Based on the Waveform Inversion and Numerical Simulation

NASA Astrophysics Data System (ADS)

Yamada, M.; Mangeney, A.; Moretti, L.; Matsushi, Y.

2014-12-01

Understanding physical parameters, such as frictional coefficients, velocity change, and dynamic history, is important issue for assessing and managing the risks posed by deep-seated catastrophic landslides. Previously, landslide motion has been inferred qualitatively from topographic changes caused by the event, and occasionally from eyewitness reports. However, these conventional approaches are unable to evaluate source processes and dynamic parameters. In this study, we use broadband seismic recordings to trace the dynamic process of the deep-seated Akatani landslide that occurred on the Kii Peninsula, Japan, which is one of the best recorded large slope failures. Based on the previous results of waveform inversions and precise topographic surveys done before and after the event, we applied numerical simulations using the SHALTOP numerical model (Mangeney et al., 2007). This model describes homogeneous continuous granular flows on a 3D topography based on a depth averaged thin layer approximation. We assume a Coulomb's friction law with a constant friction coefficient, i. e. the friction is independent of the sliding velocity. We varied the friction coefficients in the simulation so that the resulting force acting on the surface agrees with the single force estimated from the seismic waveform inversion. Figure shows the force history of the east-west components after the band-pass filtering between 10-100 seconds. The force history of the simulation with frictional coefficient 0.27 (thin red line) the best agrees with the result of seismic waveform inversion (thick gray line). Although the amplitude is slightly different, phases are coherent for the main three pulses. This is an evidence that the point-source approximation works reasonably well for this particular event. The friction coefficient during the sliding was estimated to be 0.38 based on the seismic waveform inversion performed by the previous study and on the sliding block model (Yamada et al., 2013), whereas the frictional coefficient estimated from the numerical simulation was about 0.27. This discrepancy may be due to the digital elevation model, to the other forces such as pressure gradients and centrifugal acceleration included in the model. However, quantitative interpretation of this difference requires further investigation.

Inverse problem of flame surface properties of wood using a repulsive particle swarm optimization algorithm

NASA Astrophysics Data System (ADS)

Yoon, Kyung-Beom; Park, Won-Hee

2015-04-01

The convective heat transfer coefficient and surface emissivity before and after flame occurrence on a wood specimen surface and the flame heat flux were estimated using the repulsive particle swarm optimization algorithm and cone heater test results. The cone heater specified in the ISO 5660 standards was used, and six cone heater heat fluxes were tested. Preservative-treated Douglas fir 21 mm in thickness was used as the wood specimen in the tests. This study confirmed that the surface temperature of the specimen, which was calculated using the convective heat transfer coefficient, surface emissivity and flame heat flux on the wood specimen by a repulsive particle swarm optimization algorithm, was consistent with the measured temperature. Considering the measurement errors in the surface temperature of the specimen, the applicability of the optimization method considered in this study was evaluated.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Sun Ung, E-mail: sunung@umich.edu; Monroe, Charles W., E-mail: cwmonroe@umich.edu

The inverse problem of parameterizing intermolecular potentials given macroscopic transport and thermodynamic data is addressed. Procedures are developed to create arbitrary-precision algorithms for transport collision integrals, using the Lennard-Jones (12–6) potential as an example. Interpolation formulas are produced that compute these collision integrals to four-digit accuracy over the reduced-temperature range 0.3≤T{sup ⁎}≤400, allowing very fast computation. Lennard-Jones parameters for neon, argon, and krypton are determined by simultaneously fitting the observed temperature dependences of their viscosities and second virial coefficients—one of the first times that a thermodynamic and a dynamic property have been used simultaneously for Lennard-Jones parameterization. In addition tomore » matching viscosities and second virial coefficients within the bounds of experimental error, the determined Lennard-Jones parameters are also found to predict the thermal conductivity and self-diffusion coefficient accurately, supporting the value of the Lennard-Jones (12–6) potential for noble-gas transport-property correlation.« less

Experimental determination of the viscous flow permeability of porous materials by measuring reflected low frequency acoustic waves

NASA Astrophysics Data System (ADS)

Berbiche, A.; Sadouki, M.; Fellah, Z. E. A.; Ogam, E.; Fellah, M.; Mitri, F. G.; Depollier, C.

2016-01-01

An acoustic reflectivity method is proposed for measuring the permeability or flow resistivity of air-saturated porous materials. In this method, a simplified expression of the reflection coefficient is derived in the Darcy's regime (low frequency range), which does not depend on frequency and porosity. Numerical simulations show that the reflection coefficient of a porous material can be approximated by its simplified expression obtained from its Taylor development to the first order. This approximation is good especially for resistive materials (of low permeability) and for the lower frequencies. The permeability is reconstructed by solving the inverse problem using waves reflected by plastic foam samples, at different frequency bandwidths in the Darcy regime. The proposed method has the advantage of being simple compared to the conventional methods that use experimental reflected data, and is complementary to the transmissivity method, which is more adapted to low resistive materials (high permeability).

Multivariate space - time analysis of PRE-STORM precipitation

NASA Technical Reports Server (NTRS)

Polyak, Ilya; North, Gerald R.; Valdes, Juan B.

1994-01-01

This paper presents the methodologies and results of the multivariate modeling and two-dimensional spectral and correlation analysis of PRE-STORM rainfall gauge data. Estimated parameters of the models for the specific spatial averages clearly indicate the eastward and southeastward wave propagation of rainfall fluctuations. A relationship between the coefficients of the diffusion equation and the parameters of the stochastic model of rainfall fluctuations is derived that leads directly to the exclusive use of rainfall data to estimate advection speed (about 12 m/s) as well as other coefficients of the diffusion equation of the corresponding fields. The statistical methodology developed here can be used for confirmation of physical models by comparison of the corresponding second-moment statistics of the observed and simulated data, for generating multiple samples of any size, for solving the inverse problem of the hydrodynamic equations, and for application in some other areas of meteorological and climatological data analysis and modeling.

Inverse obstacle problem for the scalar Helmholtz equation

NASA Astrophysics Data System (ADS)

Crosta, Giovanni F.

1994-07-01

The method presented is aimed at identifying the shape of an axially symmetric, sound soft acoustic scatterer from knowledge of the incident plane wave and of the scattering amplitude. The method relies on the approximate back propagation (ABP) of the estimated far field coefficients to the obstacle boundary and iteratively minimizes a boundary defect, without the addition of any penalty term. The ABP operator owes its structure to the properties of complete families of linearly independent solutions of Helmholtz equation. If the obstacle is known, as it happens in simulations, the theory also provides some independent means of predicting the performance of the ABP method. The ABP algorithm and the related computer code are outlined. Several reconstruction examples are considered, where noise is added to the estimated far field coefficients and other errors are deliberately introduced in the data. Many numerical and graphical results are provided.

Confidence set inference with a prior quadratic bound

NASA Technical Reports Server (NTRS)

Backus, George E.

1988-01-01

In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z = (z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y(0)=(y sub 1(0),...,y sub D(0)) knowledge of the statistical distribution of the random errors in y(0). The data space Y containing y(0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x (e.g., energy or dissipation rate), Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. CSI is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface. Neither the heat flow nor the energy bound is strong enough to permit estimation of B(r) at single points on the CMB, but the heat flow bound permits estimation of uniform averages of B(r) over discs on the CMB, and both bounds permit weighted disc-averages with continous weighting kernels. Both bounds also permit estimation of low-degree Gauss coefficients at the CMB. The heat flow bound resolves them up to degree 8 if the crustal field at satellite altitudes must be treated as a systematic error, but can resolve to degree 11 under the most favorable statistical treatment of the crust. These two limits produce circles of confusion on the CMB with diameters of 25 deg and 19 deg respectively.

Comparative evolution of the inverse problems (Introduction to an interdisciplinary study of the inverse problems)

NASA Technical Reports Server (NTRS)

Sabatier, P. C.

1972-01-01

The progressive realization of the consequences of nonuniqueness imply an evolution of both the methods and the centers of interest in inverse problems. This evolution is schematically described together with the various mathematical methods used. A comparative description is given of inverse methods in scientific research, with examples taken from mathematics, quantum and classical physics, seismology, transport theory, radiative transfer, electromagnetic scattering, electrocardiology, etc. It is hoped that this paper will pave the way for an interdisciplinary study of inverse problems.

Microwave photonic filters with negative coefficients based on phase inversion in an electro-optic modulator.

PubMed

Capmany, José; Pastor, Daniel; Martinez, Alfonso; Ortega, Beatriz; Sales, Salvador

2003-08-15

We report on a novel technical approach to the implementation of photonic rf filters that is based on the pi phase inversion that a rf modulating signal suffers in an electro-optic Mach-Zehnder modulator, which depends on whether the positive or the negative linear slope of the signal's modulation transfer function is employed. Experimental evidence is provided of the implementation of filters with negative coefficients that shows excellent agreement with results predicted by the theory.

Electron transport in electrically biased inverse parabolic double-barrier structure

NASA Astrophysics Data System (ADS)

M, Bati; S, Sakiroglu; I, Sokmen

2016-05-01

A theoretical study of resonant tunneling is carried out for an inverse parabolic double-barrier structure subjected to an external electric field. Tunneling transmission coefficient and density of states are analyzed by using the non-equilibrium Green’s function approach based on the finite difference method. It is found that the resonant peak of the transmission coefficient, being unity for a symmetrical case, reduces under the applied electric field and depends strongly on the variation of the structure parameters.

Using sparse regularization for multi-resolution tomography of the ionosphere

NASA Astrophysics Data System (ADS)

Panicciari, T.; Smith, N. D.; Mitchell, C. N.; Da Dalt, F.; Spencer, P. S. J.

2015-10-01

Computerized ionospheric tomography (CIT) is a technique that allows reconstructing the state of the ionosphere in terms of electron content from a set of slant total electron content (STEC) measurements. It is usually denoted as an inverse problem. In this experiment, the measurements are considered coming from the phase of the GPS signal and, therefore, affected by bias. For this reason the STEC cannot be considered in absolute terms but rather in relative terms. Measurements are collected from receivers not evenly distributed in space and together with limitations such as angle and density of the observations, they are the cause of instability in the operation of inversion. Furthermore, the ionosphere is a dynamic medium whose processes are continuously changing in time and space. This can affect CIT by limiting the accuracy in resolving structures and the processes that describe the ionosphere. Some inversion techniques are based on ℓ2 minimization algorithms (i.e. Tikhonov regularization) and a standard approach is implemented here using spherical harmonics as a reference to compare the new method. A new approach is proposed for CIT that aims to permit sparsity in the reconstruction coefficients by using wavelet basis functions. It is based on the ℓ1 minimization technique and wavelet basis functions due to their properties of compact representation. The ℓ1 minimization is selected because it can optimize the result with an uneven distribution of observations by exploiting the localization property of wavelets. Also illustrated is how the inter-frequency biases on the STEC are calibrated within the operation of inversion, and this is used as a way for evaluating the accuracy of the method. The technique is demonstrated using a simulation, showing the advantage of ℓ1 minimization to estimate the coefficients over the ℓ2 minimization. This is in particular true for an uneven observation geometry and especially for multi-resolution CIT.

Dynamic data integration and stochastic inversion of a confined aquifer

NASA Astrophysics Data System (ADS)

Wang, D.; Zhang, Y.; Irsa, J.; Huang, H.; Wang, L.

2013-12-01

Much work has been done in developing and applying inverse methods to aquifer modeling. The scope of this paper is to investigate the applicability of a new direct method for large inversion problems and to incorporate uncertainty measures in the inversion outcomes (Wang et al., 2013). The problem considered is a two-dimensional inverse model (50×50 grid) of steady-state flow for a heterogeneous ground truth model (500×500 grid) with two hydrofacies. From the ground truth model, decreasing number of wells (12, 6, 3) were sampled for facies types, based on which experimental indicator histograms and directional variograms were computed. These parameters and models were used by Sequential Indicator Simulation to generate 100 realizations of hydrofacies patterns in a 100×100 (geostatistical) grid, which were conditioned to the facies measurements at wells. These realizations were smoothed with Simulated Annealing, coarsened to the 50×50 inverse grid, before they were conditioned with the direct method to the dynamic data, i.e., observed heads and groundwater fluxes at the same sampled wells. A set of realizations of estimated hydraulic conductivities (Ks), flow fields, and boundary conditions were created, which centered on the 'true' solutions from solving the ground truth model. Both hydrofacies conductivities were computed with an estimation accuracy of ×10% (12 wells), ×20% (6 wells), ×35% (3 wells) of the true values. For boundary condition estimation, the accuracy was within × 15% (12 wells), 30% (6 wells), and 50% (3 wells) of the true values. The inversion system of equations was solved with LSQR (Paige et al, 1982), for which coordinate transform and matrix scaling preprocessor were used to improve the condition number (CN) of the coefficient matrix. However, when the inverse grid was refined to 100×100, Gaussian Noise Perturbation was used to limit the growth of the CN before the matrix solve. To scale the inverse problem up (i.e., without smoothing and coarsening and therefore reducing the associated estimation uncertainty), a parallel LSQR solver was written and verified. For the 50×50 grid, the parallel solver sped up the serial solution time by 14X using 4 CPUs (research on parallel performance and scaling is ongoing). A sensitivity analysis was conducted to examine the relation between the observed data and the inversion outcomes, where measurement errors of increasing magnitudes (i.e., ×1, 2, 5, 10% of the total head variation and up to ×2% of the total flux variation) were imposed on the observed data. Inversion results were stable but the accuracy of Ks and boundary estimation degraded with increasing errors, as expected. In particular, quality of the observed heads is critical to hydraulic head recovery, while quality of the observed fluxes plays a dominant role in K estimation. References: Wang, D., Y. Zhang, J. Irsa, H. Huang, and L. Wang (2013), Data integration and stochastic inversion of a confined aquifer with high performance computing, Advances in Water Resources, in preparation. Paige, C. C., and M. A. Saunders (1982), LSQR: an algorithm for sparse linear equations and sparse least squares, ACM Transactions on Mathematical Software, 8(1), 43-71.

BOOK REVIEW: Inverse Problems. Activities for Undergraduates

NASA Astrophysics Data System (ADS)

Yamamoto, Masahiro

2003-06-01

This book is a valuable introduction to inverse problems. In particular, from the educational point of view, the author addresses the questions of what constitutes an inverse problem and how and why we should study them. Such an approach has been eagerly awaited for a long time. Professor Groetsch, of the University of Cincinnati, is a world-renowned specialist in inverse problems, in particular the theory of regularization. Moreover, he has made a remarkable contribution to educational activities in the field of inverse problems, which was the subject of his previous book (Groetsch C W 1993 Inverse Problems in the Mathematical Sciences (Braunschweig: Vieweg)). For this reason, he is one of the most qualified to write an introductory book on inverse problems. Without question, inverse problems are important, necessary and appear in various aspects. So it is crucial to introduce students to exercises in inverse problems. However, there are not many introductory books which are directly accessible by students in the first two undergraduate years. As a consequence, students often encounter diverse concrete inverse problems before becoming aware of their general principles. The main purpose of this book is to present activities to allow first-year undergraduates to learn inverse theory. To my knowledge, this book is a rare attempt to do this and, in my opinion, a great success. The author emphasizes that it is very important to teach inverse theory in the early years. He writes; `If students consider only the direct problem, they are not looking at the problem from all sides .... The habit of always looking at problems from the direct point of view is intellectually limiting ...' (page 21). The book is very carefully organized so that teachers will be able to use it as a textbook. After an introduction in chapter 1, sucessive chapters deal with inverse problems in precalculus, calculus, differential equations and linear algebra. In order to let one gain some insight into the nature of inverse problems and the appropriate mode of thought, chapter 1 offers historical vignettes, most of which have played an essential role in the development of natural science. These vignettes cover the first successful application of `non-destructive testing' by Archimedes (page 4) via Newton's laws of motion up to literary tomography, and readers will be able to enjoy a wide overview of inverse problems. Therefore, as the author asks, the reader should not skip this chapter. This may not be hard to do, since the headings of the sections are quite intriguing (`Archimedes' Bath', `Another World', `Got the Time?', `Head Games', etc). The author embarks on the technical approach to inverse problems in chapter 2. He has elegantly designed each section with a guide specifying course level, objective, mathematical and scientifical background and appropriate technology (e.g. types of calculators required). The guides are designed such that teachers may be able to construct effective and attractive courses by themselves. The book is not intended to offer one rigidly determined course, but should be used flexibly and independently according to the situation. Moreover, every section closes with activities which can be chosen according to the students' interests and levels of ability. Some of these exercises do not have ready solutions, but require long-term study, so readers are not required to solve all of them. After chapter 5, which contains discrete inverse problems such as the algebraic reconstruction technique and the Backus - Gilbert method, there are answers and commentaries to the activities. Finally, scripts in MATLAB are attached, although they can also be downloaded from the author's web page (http://math.uc.edu/~groetsch/). This book is aimed at students but it will be very valuable to researchers wishing to retain a wide overview of inverse problems in the midst of busy research activities. A Japanese version was published in 2002.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Starchenko, S. V., E-mail: sstarchenko@mail.ru

The optimum (to my mind) scaling of the combined thermal and compositional convection in a rapidly rotating plane layer is proposed.This scaling follows from self-consistent estimates of typical physical quantities. Similarity coefficients are introduced for the ratio convection dissipation/convection generation (s) and the ratio thermal convection/compositional convection (r). The third new and most important coefficient δ is the ratio of the characteristic size normal to the axis of rotation to the layer thickness. The faster the rotation, the lower δ. In the case of the liquid Earth core, δ ~ 10{sup –3} substitutes for the generally accepted Ekman number (Emore » ~ 10{sup –15}) and s ~ 10{sup –6} substitutes for the inverse Rayleigh number 1/Ra ~ 10{sup –30}. It is found that, at turbulent transport coefficients, number s and the Prandtl number are on the order of unity for any objects and δ is independent of transport coefficients. As a result of expansion in powers of δ, an initially 3D system of six variables is simplified to an almost 2D system of four variables without δ. The problem of convection excitation in the main volume is algebraically solved and this problem for critical values is analytically solved. Dispersion relations and general expressions for critical wavenumbers, numbers s (which determine Rayleigh numbers), other critical parameters, and asymptotic solutions are derived. Numerical estimates are made for the liquid cores in the planets that resemble the Earth. Further possible applications of the results obtained are proposed for the interior of planets, moons, their oceans, stars, and experimental objects.« less

Implanting Strong Spin-Orbit Coupling at Magnetoelectric Interfaces

DTIC Science & Technology

2017-12-19

one is polar. Because the broken inversion symmetry in the polar structure is driven by a combination of the Sr-Ca cation mismatch and the octahedral...ME coefficient without breaking the inversion symmetry manifest a large boost of the ME effect with strong spin-orbit coupling. Results on the polar... inversion center. These peaks are absent in the nonpolar structure and appear here due to the A-site ordering and the resulting inversion symmetry

Probabilistic numerical methods for PDE-constrained Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Cockayne, Jon; Oates, Chris; Sullivan, Tim; Girolami, Mark

2017-06-01

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem. In particular, this drives statistical inferences to be more conservative in the presence of significant solver error. Theoretical results are presented describing rates of convergence for the posteriors in both the forward and inverse problems. This method is tested on a challenging inverse problem with a nonlinear forward model.

An inverse problem strategy based on forward model evaluations: Gradient-based optimization without adjoint solves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aguilo Valentin, Miguel Alejandro

2016-07-01

This study presents a new nonlinear programming formulation for the solution of inverse problems. First, a general inverse problem formulation based on the compliance error functional is presented. The proposed error functional enables the computation of the Lagrange multipliers, and thus the first order derivative information, at the expense of just one model evaluation. Therefore, the calculation of the Lagrange multipliers does not require the solution of the computationally intensive adjoint problem. This leads to significant speedups for large-scale, gradient-based inverse problems.

Physics-based Inverse Problem to Deduce Marine Atmospheric Boundary Layer Parameters

DTIC Science & Technology

2017-03-07

please find the Final Technical Report with SF 298 for Dr. Erin E. Hackett’s ONR grant entitled Physics-based Inverse Problem to Deduce Marine...From- To) 07/03/2017 Final Technica l Dec 2012- Dec 2016 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Physics-based Inverse Problem to Deduce Marine...SUPPLEMENTARY NOTES 14. ABSTRACT This report describes research results related to the development and implementation of an inverse problem approach for

Aerosol characteristics inversion based on the improved lidar ratio profile with the ground-based rotational Raman-Mie lidar

NASA Astrophysics Data System (ADS)

Ji, Hongzhu; Zhang, Yinchao; Chen, Siying; Chen, He; Guo, Pan

2018-06-01

An iterative method, based on a derived inverse relationship between atmospheric backscatter coefficient and aerosol lidar ratio, is proposed to invert the lidar ratio profile and aerosol extinction coefficient. The feasibility of this method is investigated theoretically and experimentally. Simulation results show the inversion accuracy of aerosol optical properties for iterative method can be improved in the near-surface aerosol layer and the optical thick layer. Experimentally, as a result of the reduced insufficiency error and incoherence error, the aerosol optical properties with higher accuracy can be obtained in the near-surface region and the region of numerical derivative distortion. In addition, the particle component can be distinguished roughly based on this improved lidar ratio profile.

Improved identification of the solution space of aerosol microphysical properties derived from the inversion of profiles of lidar optical data, part 1: theory.

PubMed

Kolgotin, Alexei; Müller, Detlef; Chemyakin, Eduard; Romanov, Anton

2016-12-01

Multiwavelength Raman/high spectral resolution lidars that measure backscatter coefficients at 355, 532, and 1064 nm and extinction coefficients at 355 and 532 nm can be used for the retrieval of particle microphysical parameters, such as effective and mean radius, number, surface-area and volume concentrations, and complex refractive index, from inversion algorithms. In this study, we carry out a correlation analysis in order to investigate the degree of dependence that may exist between the optical data taken with lidar and the underlying microphysical parameters. We also investigate if the correlation properties identified in our study can be used as a priori or a posteriori constraints for our inversion scheme so that the inversion results can be improved. We made the simplifying assumption of error-free optical data in order to find out what correlations exist in the best case situation. Clearly, for practical applications, erroneous data need to be considered too. On the basis of simulations with synthetic optical data, we find the following results, which hold true for arbitrary particle size distributions, i.e., regardless of the modality or the shape of the size distribution function: surface-area concentrations and extinction coefficients are linearly correlated with a correlation coefficient above 0.99. We also find a correlation coefficient above 0.99 for the extinction coefficient versus (1) the ratio of the volume concentration to effective radius and (2) the product of the number concentration times the sum of the squares of the mean radius and standard deviation of the investigated particle size distributions. Besides that, we find that for particles of any mode fraction of the particle size distribution, the complex refractive index is uniquely defined by extinction- and backscatter-related Ångström exponents, lidar ratios at two wavelengths, and an effective radius.

A novel inverse numerical modeling method for the estimation of water and salt mass transfer coefficients during ultrasonic assisted-osmotic dehydration of cucumber cubes.

PubMed

Kiani, Hosein; Karimi, Farzaneh; Labbafi, Mohsen; Fathi, Morteza

2018-06-01

The objective of this paper was to study the moisture and salt diffusivity during ultrasonic assisted-osmotic dehydration of cucumbers. Experimental measurements of moisture and salt concentration versus time were carried out and an inverse numerical method was performed by coupling a CFD package (OpenFOAM) with a parameter estimation software (DAKOTA) to determine mass transfer coefficients. A good agreement between experimental and numerical results was observed. Mass transfer coefficients were from 3.5 × 10 -9 to 7 × 10 -9  m/s for water and from 4.8 × 10 -9  m/s to 7.4 × 10 -9  m/s for salt at different conditions (diffusion coefficients of around 3.5 × 10 -12 -11.5 × 10 -12  m 2 /s for water and 5 × 10 -12  m/s-12 × 10 -12  m 2 /s for salt). Ultrasound irradiation could increase the mass transfer coefficient. The values obtained by this method were closer to the actual data. The inverse simulation method can be an accurate technique to study the mass transfer phenomena during food processing. Copyright © 2018 Elsevier B.V. All rights reserved.

The Baker-Akhiezer Function and Factorization of the Chebotarev-Khrapkov Matrix

NASA Astrophysics Data System (ADS)

Antipov, Yuri A.

2014-10-01

A new technique is proposed for the solution of the Riemann-Hilbert problem with the Chebotarev-Khrapkov matrix coefficient {G(t) = α1(t)I + α2(t)Q(t)} , {α1(t), α2(t) in H(L)} , I = diag{1, 1}, Q(t) is a {2×2} zero-trace polynomial matrix. This problem has numerous applications in elasticity and diffraction theory. The main feature of the method is the removal of essential singularities of the solution to the associated homogeneous scalar Riemann-Hilbert problem on the hyperelliptic surface of an algebraic function by means of the Baker-Akhiezer function. The consequent application of this function for the derivation of the general solution to the vector Riemann-Hilbert problem requires the finding of the {ρ} zeros of the Baker-Akhiezer function ({ρ} is the genus of the surface). These zeros are recovered through the solution to the associated Jacobi problem of inversion of abelian integrals or, equivalently, the determination of the zeros of the associated degree-{ρ} polynomial and solution of a certain linear algebraic system of {ρ} equations.

Mixed finite-difference scheme for free vibration analysis of noncircular cylinders

NASA Technical Reports Server (NTRS)

Noor, A. K.; Stephens, W. B.

1973-01-01

A mixed finite-difference scheme is presented for the free-vibration analysis of simply supported closed noncircular cylindrical shells. The problem is formulated in terms of eight first-order differential equations in the circumferential coordinate which possess a symmetric coefficient matrix and are free of the derivatives of the elastic and geometric characteristics of the shell. In the finite-difference discretization, two interlacing grids are used for the different fundamental unknowns in such a way as to avoid averaging in the difference-quotient expressions used for the first derivative. The resulting finite-difference equations are symmetric. The inverse-power method is used for obtaining the eigenvalues and eigenvectors.

Globally Convergent Methods for Solving Coefficient Inverse Problems for Time Dependent Maxwell Equations

DTIC Science & Technology

2014-08-19

geode (heterogeneous): Rock two spherical layers and air inside 13 Blind A piece of rock Rock 14 Blind A plastic bottle filled with coffee grounds... Coffee grounds 15 Blind A ceramic mug Ceramic 16 Blind A cylinder and a block at 3 cm separation Metal/Metal 17 Blind An aluminum can and a block Metal...2.5 cm 1.0 1.52 1.31 (outer) (two layers) 1.25 (inner) 1.28 (average) 13 Rock 2.0 cm 2.3 cm 1.0 1.34 1.34 14 Coffee grounds 2.0 cm 2.5 cm 1.0 1.46

A comparison of lidar inversion methods for cirrus applications

NASA Technical Reports Server (NTRS)

Elouragini, Salem; Flamant, Pierre H.

1992-01-01

Several methods for inverting the lidar equation are suggested as means to derive the cirrus optical properties (beta backscatter, alpha extinction coefficients, and delta optical depth) at one wavelength. The lidar equation can be inverted in a linear or logarithmic form; either solution assumes a linear relationship: beta = kappa(alpha), where kappa is the lidar ratio. A number of problems prevent us from calculating alpha (or beta) with a good accuracy. Some of these are as follows: (1) the multiple scattering effect (most authors neglect it); (2) an absolute calibration of the lidar system (difficult and sometimes not possible); (3) lack of accuracy on the lidar ratio k (taken as constant, but in fact it varies with range and cloud species); and (4) the determination of boundary condition for logarithmic solution which depends on signal to noise ration (SNR) at cloud top. An inversion in a linear form needs an absolute calibration of the system. In practice one uses molecular backscattering below the cloud to calibrate the system. This method is not permanent because the lower atmosphere turbidity is variable. For a logarithmic solution, a reference extinction coefficient (alpha(sub f)) at cloud top is required. Several methods to determine alpha(sub f) were suggested. We tested these methods at low SNR. This led us to propose two new methods referenced as S1 and S2.

A Forward Glimpse into Inverse Problems through a Geology Example

ERIC Educational Resources Information Center

Winkel, Brian J.

2012-01-01

This paper describes a forward approach to an inverse problem related to detecting the nature of geological substrata which makes use of optimization techniques in a multivariable calculus setting. The true nature of the related inverse problem is highlighted. (Contains 2 figures.)

Laser radiation in active amplifying media treated as a transport problem - Transfer equation derived and exactly solved

NASA Astrophysics Data System (ADS)

Gupta, S. R. D.; Gupta, Santanu D.

1991-10-01

The flow of laser radiation in a plane-parallel cylindrical slab of active amplifying medium with axial symmetry is treated as a problem in radiative transfer. The appropriate one-dimensional transfer equation describing the transfer of laser radiation has been derived by an appeal to Einstein's A, B coefficients (describing the processes of stimulated line absorption, spontaneous line emission, and stimulated line emission sustained by population inversion in the medium) and considering the 'rate equations' to completely establish the rational of the transfer equation obtained. The equation is then exactly solved and the angular distribution of the emergent laser beam intensity is obtained; its numerically computed values are given in tables and plotted in graphs showing the nature of peaks of the emerging laser beam intensity about the axis of the laser cylinder.

Hydrologic Process Parameterization of Electrical Resistivity Imaging of Solute Plumes Using POD McMC

NASA Astrophysics Data System (ADS)

Awatey, M. T.; Irving, J.; Oware, E. K.

2016-12-01

Markov chain Monte Carlo (McMC) inversion frameworks are becoming increasingly popular in geophysics due to their ability to recover multiple equally plausible geologic features that honor the limited noisy measurements. Standard McMC methods, however, become computationally intractable with increasing dimensionality of the problem, for example, when working with spatially distributed geophysical parameter fields. We present a McMC approach based on a sparse proper orthogonal decomposition (POD) model parameterization that implicitly incorporates the physics of the underlying process. First, we generate training images (TIs) via Monte Carlo simulations of the target process constrained to a conceptual model. We then apply POD to construct basis vectors from the TIs. A small number of basis vectors can represent most of the variability in the TIs, leading to dimensionality reduction. A projection of the starting model into the reduced basis space generates the starting POD coefficients. At each iteration, only coefficients within a specified sampling window are resimulated assuming a Gaussian prior. The sampling window grows at a specified rate as the number of iteration progresses starting from the coefficients corresponding to the highest ranked basis to those of the least informative basis. We found this gradual increment in the sampling window to be more stable compared to resampling all the coefficients right from the first iteration. We demonstrate the performance of the algorithm with both synthetic and lab-scale electrical resistivity imaging of saline tracer experiments, employing the same set of basis vectors for all inversions. We consider two scenarios of unimodal and bimodal plumes. The unimodal plume is consistent with the hypothesis underlying the generation of the TIs whereas bimodality in plume morphology was not theorized. We show that uncertainty quantification using McMC can proceed in the reduced dimensionality space while accounting for the physics of the underlying process.

Experimental determination of surface heat transfer coefficient in a dry ice-ethanol cooling bath using a numerical approach.

PubMed

Santos, M V; Sansinena, M; Zaritzky, N; Chirife, J

BACKGROUND: Dry ice-ethanol bath (-78 degree C) have been widely used in low temperature biological research to attain rapid cooling of samples below freezing temperature. The prediction of cooling rates of biological samples immersed in dry ice-ethanol bath is of practical interest in cryopreservation. The cooling rate can be obtained using mathematical models representing the heat conduction equation in transient state. Additionally, at the solid cryogenic-fluid interface, the knowledge of the surface heat transfer coefficient (h) is necessary for the convective boundary condition in order to correctly establish the mathematical problem. The study was to apply numerical modeling to obtain the surface heat transfer coefficient of a dry ice-ethanol bath. A numerical finite element solution of heat conduction equation was used to obtain surface heat transfer coefficients from measured temperatures at the center of polytetrafluoroethylene and polymethylmetacrylate cylinders immersed in a dry ice-ethanol cooling bath. The numerical model considered the temperature dependence of thermophysical properties of plastic materials used. A negative linear relationship is observed between cylinder diameter and heat transfer coefficient in the liquid bath, the calculated h values were 308, 135 and 62.5 W/(m 2 K) for PMMA 1.3, PTFE 2.59 and 3.14 cm in diameter, respectively. The calculated heat transfer coefficients were consistent among several replicates; h in dry ice-ethanol showed an inverse relationship with cylinder diameter.

Small-scale Scheimpflug lidar for aerosol extinction coefficient and vertical atmospheric transmittance detection.

PubMed

Sun, Guodong; Qin, Laian; Hou, Zaihong; Jing, Xu; He, Feng; Tan, Fengfu; Zhang, Silong

2018-03-19

In this paper, a new prototypical Scheimpflug lidar capable of detecting the aerosol extinction coefficient and vertical atmospheric transmittance at 1 km above the ground is described. The lidar system operates at 532 nm and can be used to detect aerosol extinction coefficients throughout an entire day. Then, the vertical atmospheric transmittance can be determined from the extinction coefficients with the equation of numerical integration in this area. CCD flat fielding of the image data is used to mitigate the effects of pixel sensitivity variation. An efficient method of two-dimensional wavelet transform according to a local threshold value has been proposed to reduce the Gaussian white noise in the lidar signal. Furthermore, a new iteration method of backscattering ratio based on genetic algorithm is presented to calculate the aerosol extinction coefficient and vertical atmospheric transmittance. Some simulations are performed to reduce the different levels of noise in the simulated signal in order to test the precision of the de-noising method and inversion algorithm. The simulation result shows that the root-mean-square errors of extinction coefficients are all less than 0.02 km -1 , and that the relative errors of the atmospheric transmittance between the model and inversion data are below 0.56% for all cases. The feasibility of the instrument and the inversion algorithm have also been verified by an optical experiment. The average relative errors of aerosol extinction coefficients between the Scheimpflug lidar and the conventional backscattering elastic lidar are 3.54% and 2.79% in the full overlap heights of two time points, respectively. This work opens up new possibilities of using a small-scale Scheimpflug lidar system for the remote sensing of atmospheric aerosols.

LAI inversion from optical reflectance using a neural network trained with a multiple scattering model

NASA Technical Reports Server (NTRS)

Smith, James A.

1992-01-01

The inversion of the leaf area index (LAI) canopy parameter from optical spectral reflectance measurements is obtained using a backpropagation artificial neural network trained using input-output pairs generated by a multiple scattering reflectance model. The problem of LAI estimation over sparse canopies (LAI < 1.0) with varying soil reflectance backgrounds is particularly difficult. Standard multiple regression methods applied to canopies within a single homogeneous soil type yield good results but perform unacceptably when applied across soil boundaries, resulting in absolute percentage errors of >1000 percent for low LAI. Minimization methods applied to merit functions constructed from differences between measured reflectances and predicted reflectances using multiple-scattering models are unacceptably sensitive to a good initial guess for the desired parameter. In contrast, the neural network reported generally yields absolute percentage errors of <30 percent when weighting coefficients trained on one soil type were applied to predicted canopy reflectance at a different soil background.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Di, Zichao; Leyffer, Sven; Wild, Stefan M.

Fluorescence tomographic reconstruction, based on the detection of photons coming from fluorescent emission, can be used for revealing the internal elemental composition of a sample. On the other hand, conventional X-ray transmission tomography can be used for reconstructing the spatial distribution of the absorption coefficient inside a sample. In this work, we integrate both X-ray fluorescence and X-ray transmission data modalities and formulate a nonlinear optimization-based approach for reconstruction of the elemental composition of a given object. This model provides a simultaneous reconstruction of both the quantitative spatial distribution of all elements and the absorption effect in the sample. Mathematicallymore » speaking, we show that compared with the single-modality inversion (i.e., the X-ray transmission or fluorescence alone), the joint inversion provides a better-posed problem, which implies a better recovery. Therefore, the challenges in X-ray fluorescence tomography arising mainly from the effects of self-absorption in the sample are partially mitigated. The use of this technique is demonstrated on the reconstruction of several synthetic samples.« less

Cybernetic group method of data handling (GMDH) statistical learning for hyperspectral remote sensing inverse problems in coastal ocean optics

NASA Astrophysics Data System (ADS)

Filippi, Anthony Matthew

For complex systems, sufficient a priori knowledge is often lacking about the mathematical or empirical relationship between cause and effect or between inputs and outputs of a given system. Automated machine learning may offer a useful solution in such cases. Coastal marine optical environments represent such a case, as the optical remote sensing inverse problem remains largely unsolved. A self-organizing, cybernetic mathematical modeling approach known as the group method of data handling (GMDH), a type of statistical learning network (SLN), was used to generate explicit spectral inversion models for optically shallow coastal waters. Optically shallow water light fields represent a particularly difficult challenge in oceanographic remote sensing. Several algorithm-input data treatment combinations were utilized in multiple experiments to automatically generate inverse solutions for various inherent optical property (IOP), bottom optical property (BOP), constituent concentration, and bottom depth estimations. The objective was to identify the optimal remote-sensing reflectance Rrs(lambda) inversion algorithm. The GMDH also has the potential of inductive discovery of physical hydro-optical laws. Simulated data were used to develop generalized, quasi-universal relationships. The Hydrolight numerical forward model, based on radiative transfer theory, was used to compute simulated above-water remote-sensing reflectance Rrs(lambda) psuedodata, matching the spectral channels and resolution of the experimental Naval Research Laboratory Ocean PHILLS (Portable Hyperspectral Imager for Low-Light Spectroscopy) sensor. The input-output pairs were for GMDH and artificial neural network (ANN) model development, the latter of which was used as a baseline, or control, algorithm. Both types of models were applied to in situ and aircraft data. Also, in situ spectroradiometer-derived Rrs(lambda) were used as input to an optimization-based inversion procedure. Target variables included bottom depth z b, chlorophyll a concentration [chl- a], spectral bottom irradiance reflectance Rb(lambda), and spectral total absorption a(lambda) and spectral total backscattering bb(lambda) coefficients. When applying the cybernetic and neural models to in situ HyperTSRB-derived Rrs, the difference in the means of the absolute error of the inversion estimates for zb was significant (alpha = 0.05). GMDH yielded significantly better zb than the ANN. The ANN model posted a mean absolute error (MAE) of 0.62214 m, compared with 0.55161 m for GMDH.

Bayesian approach to inverse statistical mechanics.

PubMed

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

Bayesian approach to inverse statistical mechanics

NASA Astrophysics Data System (ADS)

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

Hydraulic Conductivity Estimation using Bayesian Model Averaging and Generalized Parameterization

NASA Astrophysics Data System (ADS)

Tsai, F. T.; Li, X.

2006-12-01

Non-uniqueness in parameterization scheme is an inherent problem in groundwater inverse modeling due to limited data. To cope with the non-uniqueness problem of parameterization, we introduce a Bayesian Model Averaging (BMA) method to integrate a set of selected parameterization methods. The estimation uncertainty in BMA includes the uncertainty in individual parameterization methods as the within-parameterization variance and the uncertainty from using different parameterization methods as the between-parameterization variance. Moreover, the generalized parameterization (GP) method is considered in the geostatistical framework in this study. The GP method aims at increasing the flexibility of parameterization through the combination of a zonation structure and an interpolation method. The use of BMP with GP avoids over-confidence in a single parameterization method. A normalized least-squares estimation (NLSE) is adopted to calculate the posterior probability for each GP. We employee the adjoint state method for the sensitivity analysis on the weighting coefficients in the GP method. The adjoint state method is also applied to the NLSE problem. The proposed methodology is implemented to the Alamitos Barrier Project (ABP) in California, where the spatially distributed hydraulic conductivity is estimated. The optimal weighting coefficients embedded in GP are identified through the maximum likelihood estimation (MLE) where the misfits between the observed and calculated groundwater heads are minimized. The conditional mean and conditional variance of the estimated hydraulic conductivity distribution using BMA are obtained to assess the estimation uncertainty.

Fault Tolerant Signal Processing Using Finite Fields and Error-Correcting Codes.

DTIC Science & Technology

1983-06-01

Decimation in Frequency Form, Fast Inverse Transform F-18 F-4 Part of Decimation in Time Form, Fast Inverse Transform F-21 I . LIST OF TABLES fable Title Page...F-2 Intermediate Variables In A Fast Inverse Transform F-14 Accession For NTIS GRA&il DTIC TAB E Unannounced El ** Dist ribut ion/ ____ AvailabilitY...component polynomials may be transformed to an equiva- lent series of multiplications of the related transform ’.. coefficients. The inverse transform of

Inverse Modelling Problems in Linear Algebra Undergraduate Courses

ERIC Educational Resources Information Center

Martinez-Luaces, Victor E.

2013-01-01

This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

An inverse problem in thermal imaging

NASA Technical Reports Server (NTRS)

Bryan, Kurt; Caudill, Lester F., Jr.

1994-01-01

This paper examines uniqueness and stability results for an inverse problem in thermal imaging. The goal is to identify an unknown boundary of an object by applying a heat flux and measuring the induced temperature on the boundary of the sample. The problem is studied both in the case in which one has data at every point on the boundary of the region and the case in which only finitely many measurements are available. An inversion procedure is developed and used to study the stability of the inverse problem for various experimental configurations.

Inverse problems in quantum chemistry

NASA Astrophysics Data System (ADS)

Karwowski, Jacek

Inverse problems constitute a branch of applied mathematics with well-developed methodology and formalism. A broad family of tasks met in theoretical physics, in civil and mechanical engineering, as well as in various branches of medical and biological sciences has been formulated as specific implementations of the general theory of inverse problems. In this article, it is pointed out that a number of approaches met in quantum chemistry can (and should) be classified as inverse problems. Consequently, the methodology used in these approaches may be enriched by applying ideas and theorems developed within the general field of inverse problems. Several examples, including the RKR method for the construction of potential energy curves, determining parameter values in semiempirical methods, and finding external potentials for which the pertinent Schrödinger equation is exactly solvable, are discussed in detail.

Application of a stochastic inverse to the geophysical inverse problem

NASA Technical Reports Server (NTRS)

Jordan, T. H.; Minster, J. B.

1972-01-01

The inverse problem for gross earth data can be reduced to an undertermined linear system of integral equations of the first kind. A theory is discussed for computing particular solutions to this linear system based on the stochastic inverse theory presented by Franklin. The stochastic inverse is derived and related to the generalized inverse of Penrose and Moore. A Backus-Gilbert type tradeoff curve is constructed for the problem of estimating the solution to the linear system in the presence of noise. It is shown that the stochastic inverse represents an optimal point on this tradeoff curve. A useful form of the solution autocorrelation operator as a member of a one-parameter family of smoothing operators is derived.

Analysis of space telescope data collection system

NASA Technical Reports Server (NTRS)

Ingels, F. M.; Schoggen, W. O.

1982-01-01

An analysis of the expected performance for the Multiple Access (MA) system is provided. The analysis covers the expected bit error rate performance, the effects of synchronization loss, the problem of self-interference, and the problem of phase ambiguity. The problem of false acceptance of a command word due to data inversion is discussed. A mathematical determination of the probability of accepting an erroneous command word due to a data inversion is presented. The problem is examined for three cases: (1) a data inversion only, (2) a data inversion and a random error within the same command word, and a block (up to 256 48-bit words) containing both a data inversion and a random error.

PREFACE: The Second International Conference on Inverse Problems: Recent Theoretical Developments and Numerical Approaches

NASA Astrophysics Data System (ADS)

Cheng, Jin; Hon, Yiu-Chung; Seo, Jin Keun; Yamamoto, Masahiro

2005-01-01

The Second International Conference on Inverse Problems: Recent Theoretical Developments and Numerical Approaches was held at Fudan University, Shanghai from 16-21 June 2004. The first conference in this series was held at the City University of Hong Kong in January 2002 and it was agreed to hold the conference once every two years in a Pan-Pacific Asian country. The next conference is scheduled to be held at Hokkaido University, Sapporo, Japan in July 2006. The purpose of this series of biennial conferences is to establish and develop constant international collaboration, especially among the Pan-Pacific Asian countries. In recent decades, interest in inverse problems has been flourishing all over the globe because of both the theoretical interest and practical requirements. In particular, in Asian countries, one is witnessing remarkable new trends of research in inverse problems as well as the participation of many young talents. Considering these trends, the second conference was organized with the chairperson Professor Li Tat-tsien (Fudan University), in order to provide forums for developing research cooperation and to promote activities in the field of inverse problems. Because solutions to inverse problems are needed in various applied fields, we entertained a total of 92 participants at the second conference and arranged various talks which ranged from mathematical analyses to solutions of concrete inverse problems in the real world. This volume contains 18 selected papers, all of which have undergone peer review. The 18 papers are classified as follows: Surveys: four papers give reviews of specific inverse problems. Theoretical aspects: six papers investigate the uniqueness, stability, and reconstruction schemes. Numerical methods: four papers devise new numerical methods and their applications to inverse problems. Solutions to applied inverse problems: four papers discuss concrete inverse problems such as scattering problems and inverse problems in atmospheric sciences and oceanography. Last but not least is our gratitude. As editors we would like to express our sincere thanks to all the plenary and invited speakers, the members of the International Scientific Committee and the Advisory Board for the success of the conference, which has given rise to this present volume of selected papers. We would also like to thank Mr Wang Yanbo, Miss Wan Xiqiong and the graduate students at Fudan University for their effective work to make this conference a success. The conference was financially supported by the NFS of China, the Mathematical Center of Ministry of Education of China, E-Institutes of Shanghai Municipal Education Commission (No E03004) and Fudan University, Grant 15340027 from the Japan Society for the Promotion of Science, and Grant 15654015 from the Ministry of Education, Cultures, Sports and Technology.

Riemann–Hilbert problem approach for two-dimensional flow inverse scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Agaltsov, A. D., E-mail: agalets@gmail.com; Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr; IEPT RAS, 117997 Moscow

2014-10-15

We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.

Efficient Implementations of the Quadrature-Free Discontinuous Galerkin Method

NASA Technical Reports Server (NTRS)

Lockard, David P.; Atkins, Harold L.

1999-01-01

The efficiency of the quadrature-free form of the dis- continuous Galerkin method in two dimensions, and briefly in three dimensions, is examined. Most of the work for constant-coefficient, linear problems involves the volume and edge integrations, and the transformation of information from the volume to the edges. These operations can be viewed as matrix-vector multiplications. Many of the matrices are sparse as a result of symmetry, and blocking and specialized multiplication routines are used to account for the sparsity. By optimizing these operations, a 35% reduction in total CPU time is achieved. For nonlinear problems, the calculation of the flux becomes dominant because of the cost associated with polynomial products and inversion. This component of the work can be reduced by up to 75% when the products are approximated by truncating terms. Because the cost is high for nonlinear problems on general elements, it is suggested that simplified physics and the most efficient element types be used over most of the domain.

Implementation of one and three dimensional models for heat transfer coeffcient identification over the plate cooled by the circular water jets

NASA Astrophysics Data System (ADS)

Malinowski, Zbigniew; Cebo-Rudnicka, Agnieszka; Hadała, Beata; Szajding, Artur; Telejko, Tadeusz

2017-10-01

A cooling rate affects the mechanical properties of steel which strongly depend on microstructure evolution processes. The heat transfer boundary condition for the numerical simulation of steel cooling by water jets can be determined from the local one dimensional or from the three dimensional inverse solutions in space and time. In the present study the inconel plate has been heated to about 900 °C and then cooled by six circular water jets. The plate temperature has been measured by 30 thermocouples. The heat transfer coefficient and the heat flux distributions at the plate surface have been determined in time and space. The one dimensional solutions have given a local error to the heat transfer coefficient of about 35%. The three dimensional inverse solution has allowed reducing the local error to about 20%. The uncertainty test has confirmed that a better approximation of the heat transfer coefficient distribution over the cooled surface can be obtained even for limited number of thermocouples. In such a case it was necessary to constrain the inverse solution with the interpolated temperature sensors.

40 CFR 51.301 - Definitions.

Code of Federal Regulations, 2011 CFR

2011-07-01

... impairment. A deciview is a haze index derived from calculated light extinction, such that uniform changes in... (for the purposes of calculating deciview, the atmospheric light extinction coefficient must be... light extinction coefficient, expressed in inverse megameters (Mm−1). Existing stationary facility means...

40 CFR 51.301 - Definitions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... impairment. A deciview is a haze index derived from calculated light extinction, such that uniform changes in... (for the purposes of calculating deciview, the atmospheric light extinction coefficient must be... light extinction coefficient, expressed in inverse megameters (Mm−1). Existing stationary facility means...

40 CFR 51.301 - Definitions.

Code of Federal Regulations, 2012 CFR

2012-07-01

... impairment. A deciview is a haze index derived from calculated light extinction, such that uniform changes in... (for the purposes of calculating deciview, the atmospheric light extinction coefficient must be... light extinction coefficient, expressed in inverse megameters (Mm−1). Existing stationary facility means...

40 CFR 51.301 - Definitions.

Code of Federal Regulations, 2013 CFR

2013-07-01

... impairment. A deciview is a haze index derived from calculated light extinction, such that uniform changes in... (for the purposes of calculating deciview, the atmospheric light extinction coefficient must be... light extinction coefficient, expressed in inverse megameters (Mm−1). Existing stationary facility means...

A systematic linear space approach to solving partially described inverse eigenvalue problems

NASA Astrophysics Data System (ADS)

Hu, Sau-Lon James; Li, Haujun

2008-06-01

Most applications of the inverse eigenvalue problem (IEP), which concerns the reconstruction of a matrix from prescribed spectral data, are associated with special classes of structured matrices. Solving the IEP requires one to satisfy both the spectral constraint and the structural constraint. If the spectral constraint consists of only one or few prescribed eigenpairs, this kind of inverse problem has been referred to as the partially described inverse eigenvalue problem (PDIEP). This paper develops an efficient, general and systematic approach to solve the PDIEP. Basically, the approach, applicable to various structured matrices, converts the PDIEP into an ordinary inverse problem that is formulated as a set of simultaneous linear equations. While solving simultaneous linear equations for model parameters, the singular value decomposition method is applied. Because of the conversion to an ordinary inverse problem, other constraints associated with the model parameters can be easily incorporated into the solution procedure. The detailed derivation and numerical examples to implement the newly developed approach to symmetric Toeplitz and quadratic pencil (including mass, damping and stiffness matrices of a linear dynamic system) PDIEPs are presented. Excellent numerical results for both kinds of problem are achieved under the situations that have either unique or infinitely many solutions.

Convergence of Chahine's nonlinear relaxation inversion method used for limb viewing remote sensing

NASA Technical Reports Server (NTRS)

Chu, W. P.

1985-01-01

The application of Chahine's (1970) inversion technique to remote sensing problems utilizing the limb viewing geometry is discussed. The problem considered here involves occultation-type measurements and limb radiance-type measurements from either spacecraft or balloon platforms. The kernel matrix of the inversion problem is either an upper or lower triangular matrix. It is demonstrated that the Chahine inversion technique always converges, provided the diagonal elements of the kernel matrix are nonzero.

Computational inverse methods of heat source in fatigue damage problems

NASA Astrophysics Data System (ADS)

Chen, Aizhou; Li, Yuan; Yan, Bo

2018-04-01

Fatigue dissipation energy is the research focus in field of fatigue damage at present. It is a new idea to solve the problem of calculating fatigue dissipation energy by introducing inverse method of heat source into parameter identification of fatigue dissipation energy model. This paper introduces the research advances on computational inverse method of heat source and regularization technique to solve inverse problem, as well as the existing heat source solution method in fatigue process, prospects inverse method of heat source applying in fatigue damage field, lays the foundation for further improving the effectiveness of fatigue dissipation energy rapid prediction.

FOREWORD: 5th International Workshop on New Computational Methods for Inverse Problems

NASA Astrophysics Data System (ADS)

Vourc'h, Eric; Rodet, Thomas

2015-11-01

This volume of Journal of Physics: Conference Series is dedicated to the scientific research presented during the 5th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2015 (http://complement.farman.ens-cachan.fr/NCMIP_2015.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 29, 2015. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011, and secondly at the initiative of Institut Farman, in May 2012, May 2013 and May 2014. The New Computational Methods for Inverse Problems (NCMIP) workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, Kernel methods, learning methods, convex optimization, free discontinuity problems, metamodels, proper orthogonal decomposition, reduced models for the inversion, non-linear inverse scattering, image reconstruction and restoration, and applications (bio-medical imaging, non-destructive evaluation...). NCMIP 2015 was a one-day workshop held in May 2015 which attracted around 70 attendees. Each of the submitted papers has been reviewed by two reviewers. There have been 15 accepted papers. In addition, three international speakers were invited to present a longer talk. The workshop was supported by Institut Farman (ENS Cachan, CNRS) and endorsed by the following French research networks: GDR ISIS, GDR MIA, GDR MOA and GDR Ondes. The program committee acknowledges the following research laboratories: CMLA, LMT, LURPA and SATIE.

New Additions to the Toolkit for Forward/Inverse Problems in Electrocardiography within the SCIRun Problem Solving Environment.

PubMed

Coll-Font, Jaume; Burton, Brett M; Tate, Jess D; Erem, Burak; Swenson, Darrel J; Wang, Dafang; Brooks, Dana H; van Dam, Peter; Macleod, Rob S

2014-09-01

Cardiac electrical imaging often requires the examination of different forward and inverse problem formulations based on mathematical and numerical approximations of the underlying source and the intervening volume conductor that can generate the associated voltages on the surface of the body. If the goal is to recover the source on the heart from body surface potentials, the solution strategy must include numerical techniques that can incorporate appropriate constraints and recover useful solutions, even though the problem is badly posed. Creating complete software solutions to such problems is a daunting undertaking. In order to make such tools more accessible to a broad array of researchers, the Center for Integrative Biomedical Computing (CIBC) has made an ECG forward/inverse toolkit available within the open source SCIRun system. Here we report on three new methods added to the inverse suite of the toolkit. These new algorithms, namely a Total Variation method, a non-decreasing TMP inverse and a spline-based inverse, consist of two inverse methods that take advantage of the temporal structure of the heart potentials and one that leverages the spatial characteristics of the transmembrane potentials. These three methods further expand the possibilities of researchers in cardiology to explore and compare solutions to their particular imaging problem.

Discrete Haar transform and protein structure.

PubMed

Morosetti, S

1997-12-01

The discrete Haar transform of the sequence of the backbone dihedral angles (phi and psi) was performed over a set of X-ray protein structures of high resolution from the Brookhaven Protein Data Bank. Afterwards, the new dihedral angles were calculated by the inverse transform, using a growing number of Haar functions, from the lower to the higher degree. New structures were obtained using these dihedral angles, with standard values for bond lengths and angles, and with omega = 0 degree. The reconstructed structures were compared with the experimental ones, and analyzed by visual inspection and statistical analysis. When half of the Haar coefficients were used, all the reconstructed structures were not yet collapsed to a tertiary folding, but they showed yet realized most of the secondary motifs. These results indicate a substantial separation of structural information in the space of Haar transform, with the secondary structural information mainly present in the Haar coefficients of lower degrees, and the tertiary one present in the higher degree coefficients. Because of this separation, the representation of the folded structures in the space of Haar transform seems a promising candidate to encompass the problem of premature convergence in genetic algorithms.

Children's Understanding of the Inverse Relation between Multiplication and Division

ERIC Educational Resources Information Center

Robinson, Katherine M.; Dube, Adam K.

2009-01-01

Children's understanding of the inversion concept in multiplication and division problems (i.e., that on problems of the form "d multiplied by e/e" no calculations are required) was investigated. Children in Grades 6, 7, and 8 completed an inversion problem-solving task, an assessment of procedures task, and a factual knowledge task of simple…

A Volunteer Computing Project for Solving Geoacoustic Inversion Problems

NASA Astrophysics Data System (ADS)

Zaikin, Oleg; Petrov, Pavel; Posypkin, Mikhail; Bulavintsev, Vadim; Kurochkin, Ilya

2017-12-01

A volunteer computing project aimed at solving computationally hard inverse problems in underwater acoustics is described. This project was used to study the possibilities of the sound speed profile reconstruction in a shallow-water waveguide using a dispersion-based geoacoustic inversion scheme. The computational capabilities provided by the project allowed us to investigate the accuracy of the inversion for different mesh sizes of the sound speed profile discretization grid. This problem suits well for volunteer computing because it can be easily decomposed into independent simpler subproblems.

Acoustic parameters inversion and sediment properties in the Yellow River reservoir

NASA Astrophysics Data System (ADS)

Li, Chang-Zheng; Yang, Yong; Wang, Rui; Yan, Xiao-Fei

2018-03-01

The physical properties of silt in river reservoirs are important to river dynamics. Unfortunately, traditional techniques yield insufficient data. Based on porous media acoustic theory, we invert the acoustic parameters for the top river-bottom sediments. An explicit form of the acoustic reflection coefficient at the water-sediment interface is derived based on Biot's theory. The choice of parameters in the Biot model is discussed and the relation between acoustic and geological parameters is studied, including that between the reflection coefficient and porosity and the attenuation coefficient and permeability. The attenuation coefficient of the sound wave in the sediments is obtained by analyzing the shift of the signal frequency. The acoustic reflection coefficient at the water-sediment interface is extracted from the sonar signal. Thus, an inversion method of the physical parameters of the riverbottom surface sediments is proposed. The results of an experiment at the Sanmenxia reservoir suggest that the estimated grain size is close to the actual data. This demonstrates the ability of the proposed method to determine the physical parameters of sediments and estimate the grain size.

Identifing Atmospheric Pollutant Sources Using Artificial Neural Networks

NASA Astrophysics Data System (ADS)

Paes, F. F.; Campos, H. F.; Luz, E. P.; Carvalho, A. R.

2008-05-01

The estimation of the area source pollutant strength is a relevant issue for atmospheric environment. This characterizes an inverse problem in the atmospheric pollution dispersion. In the inverse analysis, an area source domain is considered, where the strength of such area source term is assumed unknown. The inverse problem is solved by using a supervised artificial neural network: multi-layer perceptron. The conection weights of the neural network are computed from delta rule - learning process. The neural network inversion is compared with results from standard inverse analysis (regularized inverse solution). In the regularization method, the inverse problem is formulated as a non-linear optimization approach, whose the objective function is given by the square difference between the measured pollutant concentration and the mathematical models, associated with a regularization operator. In our numerical experiments, the forward problem is addressed by a source-receptor scheme, where a regressive Lagrangian model is applied to compute the transition matrix. The second order maximum entropy regularization is used, and the regularization parameter is calculated by the L-curve technique. The objective function is minimized employing a deterministic scheme (a quasi-Newton algorithm) [1] and a stochastic technique (PSO: particle swarm optimization) [2]. The inverse problem methodology is tested with synthetic observational data, from six measurement points in the physical domain. The best inverse solutions were obtained with neural networks. References: [1] D. R. Roberti, D. Anfossi, H. F. Campos Velho, G. A. Degrazia (2005): Estimating Emission Rate and Pollutant Source Location, Ciencia e Natura, p. 131-134. [2] E.F.P. da Luz, H.F. de Campos Velho, J.C. Becceneri, D.R. Roberti (2007): Estimating Atmospheric Area Source Strength Through Particle Swarm Optimization. Inverse Problems, Desing and Optimization Symposium IPDO-2007, April 16-18, Miami (FL), USA, vol 1, p. 354-359.

40 CFR 51.301 - Definitions.

Code of Federal Regulations, 2014 CFR

2014-07-01

... impairment. A deciview is a haze index derived from calculated light extinction, such that uniform changes in... (for the purposes of calculating deciview, the atmospheric light extinction coefficient must be... extinction coefficient, expressed in inverse megameters (Mm−1). Existing stationary facility means any of the...

Reducing errors in the GRACE gravity solutions using regularization

NASA Astrophysics Data System (ADS)

Save, Himanshu; Bettadpur, Srinivas; Tapley, Byron D.

2012-09-01

The nature of the gravity field inverse problem amplifies the noise in the GRACE data, which creeps into the mid and high degree and order harmonic coefficients of the Earth's monthly gravity fields provided by GRACE. Due to the use of imperfect background models and data noise, these errors are manifested as north-south striping in the monthly global maps of equivalent water heights. In order to reduce these errors, this study investigates the use of the L-curve method with Tikhonov regularization. L-curve is a popular aid for determining a suitable value of the regularization parameter when solving linear discrete ill-posed problems using Tikhonov regularization. However, the computational effort required to determine the L-curve is prohibitively high for a large-scale problem like GRACE. This study implements a parameter-choice method, using Lanczos bidiagonalization which is a computationally inexpensive approximation to L-curve. Lanczos bidiagonalization is implemented with orthogonal transformation in a parallel computing environment and projects a large estimation problem on a problem of the size of about 2 orders of magnitude smaller for computing the regularization parameter. Errors in the GRACE solution time series have certain characteristics that vary depending on the ground track coverage of the solutions. These errors increase with increasing degree and order. In addition, certain resonant and near-resonant harmonic coefficients have higher errors as compared with the other coefficients. Using the knowledge of these characteristics, this study designs a regularization matrix that provides a constraint on the geopotential coefficients as a function of its degree and order. This regularization matrix is then used to compute the appropriate regularization parameter for each monthly solution. A 7-year time-series of the candidate regularized solutions (Mar 2003-Feb 2010) show markedly reduced error stripes compared with the unconstrained GRACE release 4 solutions (RL04) from the Center for Space Research (CSR). Post-fit residual analysis shows that the regularized solutions fit the data to within the noise level of GRACE. A time series of filtered hydrological model is used to confirm that signal attenuation for basins in the Total Runoff Integrating Pathways (TRIP) database over 320 km radii is less than 1 cm equivalent water height RMS, which is within the noise level of GRACE.

Iterative method for in situ measurement of lens aberrations in lithographic tools using CTC-based quadratic aberration model.

PubMed

Liu, Shiyuan; Xu, Shuang; Wu, Xiaofei; Liu, Wei

2012-06-18

This paper proposes an iterative method for in situ lens aberration measurement in lithographic tools based on a quadratic aberration model (QAM) that is a natural extension of the linear model formed by taking into account interactions among individual Zernike coefficients. By introducing a generalized operator named cross triple correlation (CTC), the quadratic model can be calculated very quickly and accurately with the help of fast Fourier transform (FFT). The Zernike coefficients up to the 37th order or even higher are determined by solving an inverse problem through an iterative procedure from several through-focus aerial images of a specially designed mask pattern. The simulation work has validated the theoretical derivation and confirms that such a method is simple to implement and yields a superior quality of wavefront estimate, particularly for the case when the aberrations are relatively large. It is fully expected that this method will provide a useful practical means for the in-line monitoring of the imaging quality of lithographic tools.

Application of stochastic particle swarm optimization algorithm to determine the graded refractive index distribution in participating media

NASA Astrophysics Data System (ADS)

Wei, Lin-Yang; Qi, Hong; Ren, Ya-Tao; Ruan, Li-Ming

2016-11-01

Inverse estimation of the refractive index distribution in one-dimensional participating media with graded refractive index (GRI) is investigated. The forward radiative transfer problem is solved by the Chebyshev collocation spectral method. The stochastic particle swarm optimization (SPSO) algorithm is employed to retrieve three kinds of GRI distribution, i.e. the linear, sinusoidal and quadratic GRI distribution. The retrieval accuracy of GRI distribution with different wall emissivity, optical thickness, absorption coefficients and scattering coefficients are discussed thoroughly. To improve the retrieval accuracy of quadratic GRI distribution, a double-layer model is proposed to supply more measurement information. The influence of measurement errors upon the precision of estimated results is also investigated. Considering the GRI distribution is unknown beforehand in practice, a quadratic function is employed to retrieve the linear GRI by SPSO algorithm. All the results show that the SPSO algorithm is applicable to retrieve different GRI distributions in participating media accurately even with noisy data.

Computationally effective solution of the inverse problem in time-of-flight spectroscopy.

PubMed

Kamran, Faisal; Abildgaard, Otto H A; Subash, Arman A; Andersen, Peter E; Andersson-Engels, Stefan; Khoptyar, Dmitry

2015-03-09

Photon time-of-flight (PTOF) spectroscopy enables the estimation of absorption and reduced scattering coefficients of turbid media by measuring the propagation time of short light pulses through turbid medium. The present investigation provides a comparison of the assessed absorption and reduced scattering coefficients from PTOF measurements of intralipid 20% and India ink-based optical phantoms covering a wide range of optical properties relevant for biological tissues and dairy products. Three different models are used to obtain the optical properties by fitting to measured temporal profiles: the Liemert-Kienle model (LKM), the diffusion model (DM) and a white Monte-Carlo (WMC) simulation-based algorithm. For the infinite space geometry, a very good agreement is found between the LKM and WMC, while the results obtained by the DM differ, indicating that the LKM can provide accurate estimation of the optical parameters beyond the limits of the diffusion approximation in a computational effective and accurate manner. This result increases the potential range of applications for PTOF spectroscopy within industrial and biomedical applications.

Laser Radiation in Active Amplifying Media Treated as a Transport Problem - Transfer Equation Derived and Exactly Solved

NASA Astrophysics Data System (ADS)

Das Gupta, Santanu; Das Gupta, S. R.

1991-10-01

The flow of laser radiation in a plane-parallel cylindrical slab of active amplifying medium with axial symmetry is treated as a problem in radiative transfer. The appropriate one-dimensional transfer equation describing the transfer of laser radiation has been derived by an appeal to Einstein'sA, B coefficients (describing the processes of stimulated line absorption, spontaneous line emission, and stimulated line emission sustained by population inversion in the medium) and considering the ‘rate equations’ to completely establish the rational of the transfer equation obtained. The equation is then exactly solved and the angular distribution of the emergent laser beam intensity is obtained; its numerically computed values are given in tables and plotted in graphs showing the nature of peaks of the emerging laser beam intensity about the axis of the laser cylinder.

Photoacoustic optical properties at UV, VIS, and near IR wavelengths for laboratory generated and winter time ambient urban aerosols

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gyawali, Madhu S.; Arnott, W. Patrick; Zaveri, Rahul A.

2012-03-08

We present the laboratory and ambient photoacoustic (PA) measurement of aerosol light absorption coefficients at ultraviolet wavelength (i.e., 355 nm) and compare with measurements at 405, 532, 870, and 1047 nm. Simultaneous measurements of aerosol light scattering coefficients were achieved by the integrating reciprocal nephelometer within the PA's acoustic resonator. Absorption and scattering measurements were carried out for various laboratory generated aerosols, including salt, incense, and kerosene soot to evaluate the instrument calibration and gain insight on the spectral dependence of aerosol light absorption and scattering. Ambient measurements were obtained in Reno, Nevada, between 18 December 2009 and 18 Januarymore » 2010. The measurement period included days with and without strong ground level temperature inversions, corresponding to highly polluted (freshly emitted aerosols) and relatively clean (aged aerosols) conditions. Particulate matter (PM) concentrations were measured and analyzed with other tracers of traffic emissions. The temperature inversion episodes caused very high concentration of PM{sub 2.5} and PM{sub 10} (particulate matter with aerodynamic diameters less than 2.5 {mu}m and 10 {mu}m, respectively) and gaseous pollutants: carbon monoxide (CO), nitric oxide (NO), and nitrogen dioxide (NO{sub 2}). The diurnal change of absorption and scattering coefficients during the polluted (inversion) days increased approximately by a factor of two for all wavelengths compared to the clean days. The spectral variation in aerosol absorption coefficients indicated a significant amount of absorbing aerosol from traffic emissions and residential wood burning. The analysis of single scattering albedo (SSA), Angstrom exponent of absorption (AEA), and Angstrom exponent of scattering (AES) for clean and polluted days provides evidences that the aerosol aging and coating process is suppressed by strong temperature inversion under cloudy conditions. In general, measured UV absorption coefficients were found to be much larger for biomass burning aerosol than for typical ambient aerosols.« less

Photoacoustic Optical Properties at UV, VIS, and near IR Wavelengths for Laboratory Generated and Winter Time Ambient Urban Aerosols

NASA Technical Reports Server (NTRS)

Gyawali, M.; Arnott, W. P.; Zaveri, R. A.; Song, C.; Moosmuller, H.; Liu, L.; Mishchenko, M. I.; Chen, L.-W.A.; Green, M. C.; Watson, J. G.;

Detection of Natural Fractures from Observed Surface Seismic Data Based on a Linear-Slip Model

NASA Astrophysics Data System (ADS)

Chen, Huaizhen; Zhang, Guangzhi

2018-03-01

Natural fractures play an important role in migration of hydrocarbon fluids. Based on a rock physics effective model, the linear-slip model, which defines fracture parameters (fracture compliances) for quantitatively characterizing the effects of fractures on rock total compliance, we propose a method to detect natural fractures from observed seismic data via inversion for the fracture compliances. We first derive an approximate PP-wave reflection coefficient in terms of fracture compliances. Using the approximate reflection coefficient, we derive azimuthal elastic impedance as a function of fracture compliances. An inversion method to estimate fracture compliances from seismic data is presented based on a Bayesian framework and azimuthal elastic impedance, which is implemented in a two-step procedure: a least-squares inversion for azimuthal elastic impedance and an iterative inversion for fracture compliances. We apply the inversion method to synthetic and real data to verify its stability and reasonability. Synthetic tests confirm that the method can make a stable estimation of fracture compliances in the case of seismic data containing a moderate signal-to-noise ratio for Gaussian noise, and the test on real data reveals that reasonable fracture compliances are obtained using the proposed method.

Adjusting for Confounding in Early Postlaunch Settings: Going Beyond Logistic Regression Models.

PubMed

Schmidt, Amand F; Klungel, Olaf H; Groenwold, Rolf H H

2016-01-01

Postlaunch data on medical treatments can be analyzed to explore adverse events or relative effectiveness in real-life settings. These analyses are often complicated by the number of potential confounders and the possibility of model misspecification. We conducted a simulation study to compare the performance of logistic regression, propensity score, disease risk score, and stabilized inverse probability weighting methods to adjust for confounding. Model misspecification was induced in the independent derivation dataset. We evaluated performance using relative bias confidence interval coverage of the true effect, among other metrics. At low events per coefficient (1.0 and 0.5), the logistic regression estimates had a large relative bias (greater than -100%). Bias of the disease risk score estimates was at most 13.48% and 18.83%. For the propensity score model, this was 8.74% and >100%, respectively. At events per coefficient of 1.0 and 0.5, inverse probability weighting frequently failed or reduced to a crude regression, resulting in biases of -8.49% and 24.55%. Coverage of logistic regression estimates became less than the nominal level at events per coefficient ≤5. For the disease risk score, inverse probability weighting, and propensity score, coverage became less than nominal at events per coefficient ≤2.5, ≤1.0, and ≤1.0, respectively. Bias of misspecified disease risk score models was 16.55%. In settings with low events/exposed subjects per coefficient, disease risk score methods can be useful alternatives to logistic regression models, especially when propensity score models cannot be used. Despite better performance of disease risk score methods than logistic regression and propensity score models in small events per coefficient settings, bias, and coverage still deviated from nominal.

Transform Decoding of Reed-Solomon Codes. Volume I. Algorithm and Signal Processing Structure

DTIC Science & Technology

1982-11-01

systematic channel co.’e. 1. lake the inverse transform of the r- ceived se, - nee. 2. Isolate the error syndrome from the inverse transform and use... inverse transform is identic l with interpolation of the polynomial a(z) from its n values. In order to generate a Reed-Solomon (n,k) cooce, we let the set...in accordance with the transform of equation (4). If we were to apply the inverse transform of equa- tion (6) to the coefficient sequence of A(z), we

Implement Method for Automated Testing of Markov Chain Convergence into INVERSE for ORNL12-RS-108J: Advanced Multi-Dimensional Forward and Inverse Modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bledsoe, Keith C.

2015-04-01

The DiffeRential Evolution Adaptive Metropolis (DREAM) method is a powerful optimization/uncertainty quantification tool used to solve inverse transport problems in Los Alamos National Laboratory’s INVERSE code system. The DREAM method has been shown to be adept at accurate uncertainty quantification, but it can be very computationally demanding. Previously, the DREAM method in INVERSE performed a user-defined number of particle transport calculations. This placed a burden on the user to guess the number of calculations that would be required to accurately solve any given problem. This report discusses a new approach that has been implemented into INVERSE, the Gelman-Rubin convergence metric.more » This metric automatically detects when an appropriate number of transport calculations have been completed and the uncertainty in the inverse problem has been accurately calculated. In a test problem with a spherical geometry, this method was found to decrease the number of transport calculations (and thus time required) to solve a problem by an average of over 90%. In a cylindrical test geometry, a 75% decrease was obtained.« less

Lidar extinction measurement in the mid infrared

NASA Astrophysics Data System (ADS)

Mitev, Valentin; Babichenko, S.; Borelli, R.; Fiorani, L.; Grigorov, I.; Nuvoli, M.; Palucci, A.; Pistilli, M.; Puiu, Ad.; Rebane, Ott; Santoro, S.

2014-11-01

We present a lidar measurement of atmospheric extinction coefficient. The measurement is performed by inversion of the backscatter lidar signal at wavelengths 3'000nm and 3'500nm. The inversion of the backscatter lidar signal was performed with constant extinction-to-backscatter ration values of 104 and exponential factor 0.1.

Three-dimensional facial recognition using passive long-wavelength infrared polarimetric imaging.

PubMed

Yuffa, Alex J; Gurton, Kristan P; Videen, Gorden

2014-12-20

We use a polarimetric camera to record the Stokes parameters and the degree of linear polarization of long-wavelength infrared radiation emitted by human faces. These Stokes images are combined with Fresnel relations to extract the surface normal at each pixel. Integrating over these surface normals yields a three-dimensional facial image. One major difficulty of this technique is that the normal vectors determined from the polarizations are not unique. We overcome this problem by introducing an additional boundary condition on the subject. The major sources of error in producing inversions are noise in the images caused by scattering of the background signal and the ambiguity in determining the surface normals from the Fresnel coefficients.

Characterization for stability in planar conductivities

NASA Astrophysics Data System (ADS)

Faraco, Daniel; Prats, Martí

2018-05-01

We find a complete characterization for sets of uniformly strongly elliptic and isotropic conductivities with stable recovery in the L2 norm when the data of the Calderón Inverse Conductivity Problem is obtained in the boundary of a disk and the conductivities are constant in a neighborhood of its boundary. To obtain this result, we present minimal a priori assumptions which turn out to be sufficient for sets of conductivities to have stable recovery in a bounded and rough domain. The condition is presented in terms of the integral moduli of continuity of the coefficients involved and their ellipticity bound as conjectured by Alessandrini in his 2007 paper, giving explicit quantitative control for every pair of conductivities.

An entropy method for induced drag minimization

NASA Technical Reports Server (NTRS)

Greene, George C.

1989-01-01

A fundamentally new approach to the aircraft minimum induced drag problem is presented. The method, a 'viscous lifting line', is based on the minimum entropy production principle and does not require the planar wake assumption. An approximate, closed form solution is obtained for several wing configurations including a comparison of wing extension, winglets, and in-plane wing sweep, with and without a constraint on wing-root bending moment. Like the classical lifting-line theory, this theory predicts that induced drag is proportional to the square of the lift coefficient and inversely proportioinal to the wing aspect ratio. Unlike the classical theory, it predicts that induced drag is Reynolds number dependent and that the optimum spanwise circulation distribution is non-elliptic.

Inversion of Attributes and Full Waveforms of Ground Penetrating Radar Data Using PEST

NASA Astrophysics Data System (ADS)

Jazayeri, S.; Kruse, S.; Esmaeili, S.

2015-12-01

We seek to establish a method, based on freely available software, for inverting GPR signals for the underlying physical properties (electrical permittivity, magnetic permeability, target geometries). Such a procedure should be useful for classroom instruction and for analyzing surface GPR surveys over simple targets. We explore the applicability of the PEST parameter estimation software package for GPR inversion (www.pesthomepage.org). PEST is designed to invert data sets with large numbers of parameters, and offers a variety of inversion methods. Although primarily used in hydrogeology, the code has been applied to a wide variety of physical problems. The PEST code requires forward model input; the forward model of the GPR signal is done with the GPRMax package (www.gprmax.com). The problem of extracting the physical characteristics of a subsurface anomaly from the GPR data is highly nonlinear. For synthetic models of simple targets in homogeneous backgrounds, we find PEST's nonlinear Gauss-Marquardt-Levenberg algorithm is preferred. This method requires an initial model, for which the weighted differences between model-generated data and those of the "true" synthetic model (the objective function) are calculated. In order to do this, the Jacobian matrix and the derivatives of the observation data in respect to the model parameters are computed using a finite differences method. Next, the iterative process of building new models by updating the initial values starts in order to minimize the objective function. Another measure of the goodness of the final acceptable model is the correlation coefficient which is calculated based on the method of Cooley and Naff. An accepted final model satisfies both of these conditions. Models to date show that physical properties of simple isolated targets against homogeneous backgrounds can be obtained from multiple traces from common-offset surface surveys. Ongoing work examines the inversion capabilities with more complex target geometries and heterogeneous soils.

Inverse Scattering Problem For The Schrödinger Equation With An Additional Quadratic Potential On The Entire Axis

NASA Astrophysics Data System (ADS)

Guseinov, I. M.; Khanmamedov, A. Kh.; Mamedova, A. F.

2018-04-01

We consider the Schrödinger equation with an additional quadratic potential on the entire axis and use the transformation operator method to study the direct and inverse problems of the scattering theory. We obtain the main integral equations of the inverse problem and prove that the basic equations are uniquely solvable.

Assessing non-uniqueness: An algebraic approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vasco, Don W.

Geophysical inverse problems are endowed with a rich mathematical structure. When discretized, most differential and integral equations of interest are algebraic (polynomial) in form. Techniques from algebraic geometry and computational algebra provide a means to address questions of existence and uniqueness for both linear and non-linear inverse problem. In a sense, the methods extend ideas which have proven fruitful in treating linear inverse problems.

QR code-based non-linear image encryption using Shearlet transform and spiral phase transform

NASA Astrophysics Data System (ADS)

Kumar, Ravi; Bhaduri, Basanta; Hennelly, Bryan

2018-02-01

In this paper, we propose a new quick response (QR) code-based non-linear technique for image encryption using Shearlet transform (ST) and spiral phase transform. The input image is first converted into a QR code and then scrambled using the Arnold transform. The scrambled image is then decomposed into five coefficients using the ST and the first Shearlet coefficient, C1 is interchanged with a security key before performing the inverse ST. The output after inverse ST is then modulated with a random phase mask and further spiral phase transformed to get the final encrypted image. The first coefficient, C1 is used as a private key for decryption. The sensitivity of the security keys is analysed in terms of correlation coefficient and peak signal-to noise ratio. The robustness of the scheme is also checked against various attacks such as noise, occlusion and special attacks. Numerical simulation results are shown in support of the proposed technique and an optoelectronic set-up for encryption is also proposed.

Fading channel simulator

DOEpatents

Argo, Paul E.; Fitzgerald, T. Joseph

1993-01-01

Fading channel effects on a transmitted communication signal are simulated with both frequency and time variations using a channel scattering function to affect the transmitted signal. A conventional channel scattering function is converted to a series of channel realizations by multiplying the square root of the channel scattering function by a complex number of which the real and imaginary parts are each independent variables. The two-dimensional inverse-FFT of this complex-valued channel realization yields a matrix of channel coefficients that provide a complete frequency-time description of the channel. The transmitted radio signal is segmented to provide a series of transmitted signal and each segment is subject to FFT to generate a series of signal coefficient matrices. The channel coefficient matrices and signal coefficient matrices are then multiplied and subjected to inverse-FFT to output a signal representing the received affected radio signal. A variety of channel scattering functions can be used to characterize the response of a transmitter-receiver system to such atmospheric effects.

Income inequality, disinvestment in health care and use of dental services.

PubMed

Bhandari, Bishal; Newton, Jonathan T; Bernabé, Eduardo

2015-01-01

To explore the interrelationships between income inequality, disinvestment in health care, and use of dental services at country level. This study pooled national estimates for use of dental services among adults aged 18 years or older from the 70 countries that participated in the World Health Survey from 2002 to 2004, together with aggregate data on national income (GDP per capita), income inequality (Gini coefficient), and disinvestment in health care (total health expenditure and dentist-to-population ratio) from various international sources. Use of dental services was defined as having had dental problems in the last 12 months and having received any treatment to address those needs. Associations between variables were explored using Pearson correlation coefficients and linear regression. Data from 63 countries representing the six WHO regions were analyzed. Use of dental services was negatively correlated with Gini coefficient (Pearson correlation coefficient -0.48, P < 0.001) and positively correlated with GDP per capita (0.40, P < 0.05), total health expenditure (0.45, P < 0.001), and dentist-to-population ratio (0.67, P < 0.001). The association between Gini coefficient and use of dental services was attenuated but remained significant after adjustments for GDP per capita, total health expenditure, and dentist-to-population ratio (regression coefficient -0.36; 95% CI -0.57, -0.15). This study shows an inverse relationship between income inequality and use of dental services. Of the two indicators of disinvestment in health care assessed, only dentist-to-population ratio was associated with income inequality and use of dental services. © 2014 American Association of Public Health Dentistry.

An infrared-visible image fusion scheme based on NSCT and compressed sensing

NASA Astrophysics Data System (ADS)

Zhang, Qiong; Maldague, Xavier

2015-05-01

Image fusion, as a research hot point nowadays in the field of infrared computer vision, has been developed utilizing different varieties of methods. Traditional image fusion algorithms are inclined to bring problems, such as data storage shortage and computational complexity increase, etc. Compressed sensing (CS) uses sparse sampling without knowing the priori knowledge and greatly reconstructs the image, which reduces the cost and complexity of image processing. In this paper, an advanced compressed sensing image fusion algorithm based on non-subsampled contourlet transform (NSCT) is proposed. NSCT provides better sparsity than the wavelet transform in image representation. Throughout the NSCT decomposition, the low-frequency and high-frequency coefficients can be obtained respectively. For the fusion processing of low-frequency coefficients of infrared and visible images , the adaptive regional energy weighting rule is utilized. Thus only the high-frequency coefficients are specially measured. Here we use sparse representation and random projection to obtain the required values of high-frequency coefficients, afterwards, the coefficients of each image block can be fused via the absolute maximum selection rule and/or the regional standard deviation rule. In the reconstruction of the compressive sampling results, a gradient-based iterative algorithm and the total variation (TV) method are employed to recover the high-frequency coefficients. Eventually, the fused image is recovered by inverse NSCT. Both the visual effects and the numerical computation results after experiments indicate that the presented approach achieves much higher quality of image fusion, accelerates the calculations, enhances various targets and extracts more useful information.

Fast downscaled inverses for images compressed with M-channel lapped transforms.

PubMed

de Queiroz, R L; Eschbach, R

1997-01-01

Compressed images may be decompressed and displayed or printed using different devices at different resolutions. Full decompression and rescaling in space domain is a very expensive method. We studied downscaled inverses where the image is decompressed partially, and a reduced inverse transform is used to recover the image. In this fashion, fewer transform coefficients are used and the synthesis process is simplified. We studied the design of fast inverses, for a given forward transform. General solutions are presented for M-channel finite impulse response (FIR) filterbanks, of which block and lapped transforms are a subset. Designs of faster inverses are presented for popular block and lapped transforms.

Monte Carlo calibration of avalanches described as Coulomb fluid flows.

PubMed

Ancey, Christophe

2005-07-15

The idea that snow avalanches might behave as granular flows, and thus be described as Coulomb fluid flows, came up very early in the scientific study of avalanches, but it is not until recently that field evidence has been provided that demonstrates the reliability of this idea. This paper aims to specify the bulk frictional behaviour of snow avalanches by seeking a universal friction law. Since the bulk friction coefficient cannot be measured directly in the field, the friction coefficient must be calibrated by adjusting the model outputs to closely match the recorded data. Field data are readily available but are of poor quality and accuracy. We used Bayesian inference techniques to specify the model uncertainty relative to data uncertainty and to robustly and efficiently solve the inverse problem. A sample of 173 events taken from seven paths in the French Alps was used. The first analysis showed that the friction coefficient behaved as a random variable with a smooth and bell-shaped empirical distribution function. Evidence was provided that the friction coefficient varied with the avalanche volume, but any attempt to adjust a one-to-one relationship relating friction to volume produced residual errors that could be as large as three times the maximum uncertainty of field data. A tentative universal friction law is proposed: the friction coefficient is a random variable, the distribution of which can be approximated by a normal distribution with a volume-dependent mean.

The solitary wave solution of coupled Klein-Gordon-Zakharov equations via two different numerical methods

NASA Astrophysics Data System (ADS)

Dehghan, Mehdi; Nikpour, Ahmad

2013-09-01

In this research, we propose two different methods to solve the coupled Klein-Gordon-Zakharov (KGZ) equations: the Differential Quadrature (DQ) and Globally Radial Basis Functions (GRBFs) methods. In the DQ method, the derivative value of a function with respect to a point is directly approximated by a linear combination of all functional values in the global domain. The principal work in this method is the determination of weight coefficients. We use two ways for obtaining these coefficients: cosine expansion (CDQ) and radial basis functions (RBFs-DQ), the former is a mesh-based method and the latter categorizes in the set of meshless methods. Unlike the DQ method, the GRBF method directly substitutes the expression of the function approximation by RBFs into the partial differential equation. The main problem in the GRBFs method is ill-conditioning of the interpolation matrix. Avoiding this problem, we study the bases introduced in Pazouki and Schaback (2011) [44]. Some examples are presented to compare the accuracy and easy implementation of the proposed methods. In numerical examples, we concentrate on Inverse Multiquadric (IMQ) and second-order Thin Plate Spline (TPS) radial basis functions. The variable shape parameter (exponentially and random) strategies are applied in the IMQ function and the results are compared with the constant shape parameter.

Dynamically consistent hydrography and absolute velocity in the eastern North Atlantic Ocean

NASA Technical Reports Server (NTRS)

Wunsch, Carl

1994-01-01

The problem of mapping a dynamically consistent hydrographic field and associated absolute geostrophic flow in the eastern North Atlantic between 24 deg and 36 deg N is related directly to the solution of the so-called thermocline equations. A nonlinear optimization problem involving Needler's P equation is solved to find the hydrography and resulting flow that minimizes the vertical mixing above about 1500 m in the ocean and is simultaneously consistent with the observations. A sharp minimum (at least in some dimensions) is found, apparently corresponding to a solution nearly conserving potential vorticity and with vertical eddy coefficient less than about 10(exp -5) sq m/s. Estimates of `residual' quantities such as eddy coefficients are extremely sensitive to slight modifications to the observed fields. Boundary conditions, vertical velocities, etc., are a product of the optimization and produce estimates differing quantitatively from prior ones relying directly upon observed hydrography. The results are generally insensitive to particular elements of the solution methodology, but many questions remain concerning the extent to which different synoptic sections can be asserted to represent the same ocean. The method can be regarded as a practical generalization of the beta spiral and geostrophic balance inverses for the estimate of absolute geostrophic flows. Numerous improvements to the methodology used in this preliminary attempt are possible.

The inverse problem of refraction travel times, part I: Types of Geophysical Nonuniqueness through Minimization

USGS Publications Warehouse

Ivanov, J.; Miller, R.D.; Xia, J.; Steeples, D.; Park, C.B.

2005-01-01

In a set of two papers we study the inverse problem of refraction travel times. The purpose of this work is to use the study as a basis for development of more sophisticated methods for finding more reliable solutions to the inverse problem of refraction travel times, which is known to be nonunique. The first paper, "Types of Geophysical Nonuniqueness through Minimization," emphasizes the existence of different forms of nonuniqueness in the realm of inverse geophysical problems. Each type of nonuniqueness requires a different type and amount of a priori information to acquire a reliable solution. Based on such coupling, a nonuniqueness classification is designed. Therefore, since most inverse geophysical problems are nonunique, each inverse problem must be studied to define what type of nonuniqueness it belongs to and thus determine what type of a priori information is necessary to find a realistic solution. The second paper, "Quantifying Refraction Nonuniqueness Using a Three-layer Model," serves as an example of such an approach. However, its main purpose is to provide a better understanding of the inverse refraction problem by studying the type of nonuniqueness it possesses. An approach for obtaining a realistic solution to the inverse refraction problem is planned to be offered in a third paper that is in preparation. The main goal of this paper is to redefine the existing generalized notion of nonuniqueness and a priori information by offering a classified, discriminate structure. Nonuniqueness is often encountered when trying to solve inverse problems. However, possible nonuniqueness diversity is typically neglected and nonuniqueness is regarded as a whole, as an unpleasant "black box" and is approached in the same manner by applying smoothing constraints, damping constraints with respect to the solution increment and, rarely, damping constraints with respect to some sparse reference information about the true parameters. In practice, when solving geophysical problems different types of nonuniqueness exist, and thus there are different ways to solve the problems. Nonuniqueness is usually regarded as due to data error, assuming the true geology is acceptably approximated by simple mathematical models. Compounding the nonlinear problems, geophysical applications routinely exhibit exact-data nonuniqueness even for models with very few parameters adding to the nonuniqueness due to data error. While nonuniqueness variations have been defined earlier, they have not been linked to specific use of a priori information necessary to resolve each case. Four types of nonuniqueness, typical for minimization problems are defined with the corresponding methods for inclusion of a priori information to find a realistic solution without resorting to a non-discriminative approach. The above-developed stand-alone classification is expected to be helpful when solving any geophysical inverse problems. ?? Birkha??user Verlag, Basel, 2005.

Computational methods for inverse problems in geophysics: inversion of travel time observations

USGS Publications Warehouse

Pereyra, V.; Keller, H.B.; Lee, W.H.K.

1980-01-01

General ways of solving various inverse problems are studied for given travel time observations between sources and receivers. These problems are separated into three components: (a) the representation of the unknown quantities appearing in the model; (b) the nonlinear least-squares problem; (c) the direct, two-point ray-tracing problem used to compute travel time once the model parameters are given. Novel software is described for (b) and (c), and some ideas given on (a). Numerical results obtained with artificial data and an implementation of the algorithm are also presented. ?? 1980.

A fixed energy fixed angle inverse scattering in interior transmission problem

NASA Astrophysics Data System (ADS)

Chen, Lung-Hui

2017-06-01

We study the inverse acoustic scattering problem in mathematical physics. The problem is to recover the index of refraction in an inhomogeneous medium by measuring the scattered wave fields in the far field. We transform the problem to the interior transmission problem in the study of the Helmholtz equation. We find an inverse uniqueness on the scatterer with a knowledge of a fixed interior transmission eigenvalue. By examining the solution in a series of spherical harmonics in the far field, we can determine uniquely the perturbation source for the radially symmetric perturbations.

Total-variation based velocity inversion with Bregmanized operator splitting algorithm

NASA Astrophysics Data System (ADS)

Zand, Toktam; Gholami, Ali

2018-04-01

Many problems in applied geophysics can be formulated as a linear inverse problem. The associated problems, however, are large-scale and ill-conditioned. Therefore, regularization techniques are needed to be employed for solving them and generating a stable and acceptable solution. We consider numerical methods for solving such problems in this paper. In order to tackle the ill-conditioning of the problem we use blockiness as a prior information of the subsurface parameters and formulate the problem as a constrained total variation (TV) regularization. The Bregmanized operator splitting (BOS) algorithm as a combination of the Bregman iteration and the proximal forward backward operator splitting method is developed to solve the arranged problem. Two main advantages of this new algorithm are that no matrix inversion is required and that a discrepancy stopping criterion is used to stop the iterations, which allow efficient solution of large-scale problems. The high performance of the proposed TV regularization method is demonstrated using two different experiments: 1) velocity inversion from (synthetic) seismic data which is based on Born approximation, 2) computing interval velocities from RMS velocities via Dix formula. Numerical examples are presented to verify the feasibility of the proposed method for high-resolution velocity inversion.

Analytical and numerical analysis of inverse optimization problems: conditions of uniqueness and computational methods

PubMed Central

Zatsiorsky, Vladimir M.

2011-01-01

One of the key problems of motor control is the redundancy problem, in particular how the central nervous system (CNS) chooses an action out of infinitely many possible. A promising way to address this question is to assume that the choice is made based on optimization of a certain cost function. A number of cost functions have been proposed in the literature to explain performance in different motor tasks: from force sharing in grasping to path planning in walking. However, the problem of uniqueness of the cost function(s) was not addressed until recently. In this article, we analyze two methods of finding additive cost functions in inverse optimization problems with linear constraints, so-called linear-additive inverse optimization problems. These methods are based on the Uniqueness Theorem for inverse optimization problems that we proved recently (Terekhov et al., J Math Biol 61(3):423–453, 2010). Using synthetic data, we show that both methods allow for determining the cost function. We analyze the influence of noise on the both methods. Finally, we show how a violation of the conditions of the Uniqueness Theorem may lead to incorrect solutions of the inverse optimization problem. PMID:21311907

The neural network approximation method for solving multidimensional nonlinear inverse problems of geophysics

NASA Astrophysics Data System (ADS)

Shimelevich, M. I.; Obornev, E. A.; Obornev, I. E.; Rodionov, E. A.

2017-07-01

The iterative approximation neural network method for solving conditionally well-posed nonlinear inverse problems of geophysics is presented. The method is based on the neural network approximation of the inverse operator. The inverse problem is solved in the class of grid (block) models of the medium on a regularized parameterization grid. The construction principle of this grid relies on using the calculated values of the continuity modulus of the inverse operator and its modifications determining the degree of ambiguity of the solutions. The method provides approximate solutions of inverse problems with the maximal degree of detail given the specified degree of ambiguity with the total number of the sought parameters n × 103 of the medium. The a priori and a posteriori estimates of the degree of ambiguity of the approximated solutions are calculated. The work of the method is illustrated by the example of the three-dimensional (3D) inversion of the synthesized 2D areal geoelectrical (audio magnetotelluric sounding, AMTS) data corresponding to the schematic model of a kimberlite pipe.

Geostatistical regularization operators for geophysical inverse problems on irregular meshes

NASA Astrophysics Data System (ADS)

Jordi, C.; Doetsch, J.; Günther, T.; Schmelzbach, C.; Robertsson, J. OA

2018-05-01

Irregular meshes allow to include complicated subsurface structures into geophysical modelling and inverse problems. The non-uniqueness of these inverse problems requires appropriate regularization that can incorporate a priori information. However, defining regularization operators for irregular discretizations is not trivial. Different schemes for calculating smoothness operators on irregular meshes have been proposed. In contrast to classical regularization constraints that are only defined using the nearest neighbours of a cell, geostatistical operators include a larger neighbourhood around a particular cell. A correlation model defines the extent of the neighbourhood and allows to incorporate information about geological structures. We propose an approach to calculate geostatistical operators for inverse problems on irregular meshes by eigendecomposition of a covariance matrix that contains the a priori geological information. Using our approach, the calculation of the operator matrix becomes tractable for 3-D inverse problems on irregular meshes. We tested the performance of the geostatistical regularization operators and compared them against the results of anisotropic smoothing in inversions of 2-D surface synthetic electrical resistivity tomography (ERT) data as well as in the inversion of a realistic 3-D cross-well synthetic ERT scenario. The inversions of 2-D ERT and seismic traveltime field data with geostatistical regularization provide results that are in good accordance with the expected geology and thus facilitate their interpretation. In particular, for layered structures the geostatistical regularization provides geologically more plausible results compared to the anisotropic smoothness constraints.

FOREWORD: 4th International Workshop on New Computational Methods for Inverse Problems (NCMIP2014)

NASA Astrophysics Data System (ADS)

2014-10-01

This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 4th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2014 (http://www.farman.ens-cachan.fr/NCMIP_2014.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 23, 2014. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/), and secondly at the initiative of Institut Farman, in May 2012 and May 2013, (http://www.farman.ens-cachan.fr/NCMIP_2012.html), (http://www.farman.ens-cachan.fr/NCMIP_2013.html). The New Computational Methods for Inverse Problems (NCMIP) Workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, Kernel methods, learning methods, convex optimization, free discontinuity problems, metamodels, proper orthogonal decomposition, reduced models for the inversion, non-linear inverse scattering, image reconstruction and restoration, and applications (bio-medical imaging, non-destructive evaluation...). NCMIP 2014 was a one-day workshop held in May 2014 which attracted around sixty attendees. Each of the submitted papers has been reviewed by two reviewers. There have been nine accepted papers. In addition, three international speakers were invited to present a longer talk. The workshop was supported by Institut Farman (ENS Cachan, CNRS) and endorsed by the following French research networks (GDR ISIS, GDR MIA, GDR MOA, GDR Ondes). The program committee acknowledges the following research laboratories: CMLA, LMT, LURPA, SATIE. Eric Vourc'h and Thomas Rodet

Test-retest reliability of sudden ankle inversion measurements in subjects with healthy ankle joints.

PubMed

Eechaute, Christophe; Vaes, Peter; Duquet, William; Van Gheluwe, Bart

2007-01-01

Sudden ankle inversion tests have been used to investigate whether the onset of peroneal muscle activity is delayed in patients with chronically unstable ankle joints. Before interpreting test results of latency times in patients with chronic ankle instability and healthy subjects, the reliability of these measures must be first demonstrated. To investigate the test-retest reliability of variables measured during a sudden ankle inversion movement in standing subjects with healthy ankle joints. Validation study. Research laboratory. 15 subjects with healthy ankle joints (30 ankles). Subjects stood on an ankle inversion platform with both feet tightly fixed to independently moveable trapdoors. An unexpected sudden ankle inversion of 50 degrees was imposed. We measured latency and motor response times and electromechanical delay of the peroneus longus muscle, along with the time and angular position of the first and second decelerating moments, the mean and maximum inversion speed, and the total inversion time. Correlation coefficients and standard error of measurements were calculated. Intraclass correlation coefficients ranged from 0.17 for the electromechanical delay of the peroneus longus muscle (standard error of measurement = 2.7 milliseconds) to 0.89 for the maximum inversion speed (standard error of measurement = 34.8 milliseconds). The reliability of the latency and motor response times of the peroneus longus muscle, the time of the first and second decelerating moments, and the mean and maximum inversion speed was acceptable in subjects with healthy ankle joints and supports the investigation of the reliability of these measures in subjects with chronic ankle instability. The lower reliability of the electromechanical delay of the peroneus longus muscle and the angular positions of both decelerating moments calls the use of these variables into question.

Bayesian Meta-Analysis of Coefficient Alpha

ERIC Educational Resources Information Center

Brannick, Michael T.; Zhang, Nanhua

2013-01-01

The current paper describes and illustrates a Bayesian approach to the meta-analysis of coefficient alpha. Alpha is the most commonly used estimate of the reliability or consistency (freedom from measurement error) for educational and psychological measures. The conventional approach to meta-analysis uses inverse variance weights to combine…

A study of the flow boiling heat transfer in a minichannel for a heated wall with surface texture produced by vibration-assisted laser machining

NASA Astrophysics Data System (ADS)

Piasecka, Magdalena; Strąk, Kinga; Maciejewska, Beata; Grabas, Bogusław

2016-09-01

The paper presents results concerning flow boiling heat transfer in a vertical minichannel with a depth of 1.7 mm and a width of 16 mm. The element responsible for heating FC-72, which flowed laminarly in the minichannel, was a plate with an enhanced surface. Two types of surface textures were considered. Both were produced by vibration-assisted laser machining. Infrared thermography was used to record changes in the temperature on the outer smooth side of the plate. Two-phase flow patterns were observed through a glass pane. The main aim of the study was to analyze how the two types of surface textures affect the heat transfer coefficient. A two-dimensional heat transfer approach was proposed to determine the local values of the heat transfer coefficient. The inverse problem for the heated wall was solved using a semi-analytical method based on the Trefftz functions. The results are presented as relationships between the heat transfer coefficient and the distance along the minichannel length and as boiling curves. The experimental data obtained for the two types of enhanced heated surfaces was compared with the results recorded for the smooth heated surface. The highest local values of the heat transfer coefficient were reported in the saturated boiling region for the plate with the type 1 texture produced by vibration-assisted laser machining.

Inverse problems in the design, modeling and testing of engineering systems

NASA Technical Reports Server (NTRS)

Alifanov, Oleg M.

1991-01-01

Formulations, classification, areas of application, and approaches to solving different inverse problems are considered for the design of structures, modeling, and experimental data processing. Problems in the practical implementation of theoretical-experimental methods based on solving inverse problems are analyzed in order to identify mathematical models of physical processes, aid in input data preparation for design parameter optimization, help in design parameter optimization itself, and to model experiments, large-scale tests, and real tests of engineering systems.

PHYSICAL EFFECTS OCCURRING DURING GENERATION AND AMPLIFICATION OF LASER RADIATION: Ultimate values of the gain of solid-state rod amplifiers operating under inversion storage conditions

NASA Astrophysics Data System (ADS)

Bayanov, V. I.; Vinokurov, G. N.; Zhulin, V. I.; Yashin, V. E.

1989-02-01

A numerical calculation is reported of an inversion conservation coefficient of cylindrical rod solid-state amplifiers with the active element diameter from 1.5 to 15 cm operated under continuous pumping conditions. It is shown that the ultimate gain, limited only by superluminescence, exceeds considerably the value usually obtained in experiments. Various methods of eliminating parasitic effects, which limit the gain of real amplifiers, are considered. The degree of influence of these effects on the inversion conservation coefficient is discussed. The results are given of an experimental determination of the gain close to the ultimate value (0.18 cm- 1 for an active element 3 cm in diameter). Calculations are reported of the angular distributions of superluminescence and parasitic modes demonstrating that the latter can be suppressed by spatial filtering.

Inverse problem to constrain the controlling parameters of large-scale heat transport processes: The Tiberias Basin example

NASA Astrophysics Data System (ADS)

Goretzki, Nora; Inbar, Nimrod; Siebert, Christian; Möller, Peter; Rosenthal, Eliyahu; Schneider, Michael; Magri, Fabien

2015-04-01

Salty and thermal springs exist along the lakeshore of the Sea of Galilee, which covers most of the Tiberias Basin (TB) in the northern Jordan- Dead Sea Transform, Israel/Jordan. As it is the only freshwater reservoir of the entire area, it is important to study the salinisation processes that pollute the lake. Simulations of thermohaline flow along a 35 km NW-SE profile show that meteoric and relic brines are flushed by the regional flow from the surrounding heights and thermally induced groundwater flow within the faults (Magri et al., 2015). Several model runs with trial and error were necessary to calibrate the hydraulic conductivity of both faults and major aquifers in order to fit temperature logs and spring salinity. It turned out that the hydraulic conductivity of the faults ranges between 30 and 140 m/yr whereas the hydraulic conductivity of the Upper Cenomanian aquifer is as high as 200 m/yr. However, large-scale transport processes are also dependent on other physical parameters such as thermal conductivity, porosity and fluid thermal expansion coefficient, which are hardly known. Here, inverse problems (IP) are solved along the NW-SE profile to better constrain the physical parameters (a) hydraulic conductivity, (b) thermal conductivity and (c) thermal expansion coefficient. The PEST code (Doherty, 2010) is applied via the graphical interface FePEST in FEFLOW (Diersch, 2014). The results show that both thermal and hydraulic conductivity are consistent with the values determined with the trial and error calibrations. Besides being an automatic approach that speeds up the calibration process, the IP allows to cover a wide range of parameter values, providing additional solutions not found with the trial and error method. Our study shows that geothermal systems like TB are more comprehensively understood when inverse models are applied to constrain coupled fluid flow processes over large spatial scales. References Diersch, H.-J.G., 2014. FEFLOW Finite Element Modeling of Flow, Mass and Heat Transport in Porous and Fractured Media. Springer- Verlag Berlin Heidelberg ,996p. Doherty J., 2010, PEST: Model-Independent Parameter Estimation. user manual 5th Edition. Watermark, Brisbane, Australia Magri, F., Inbar, N., Siebert C., Rosenthal, E., Guttman, J., Möller, P., 2015. Transient simulations of large-scale hydrogeological processes causing temperature and salinity anomalies in the Tiberias Basin. Journal of Hydrology, 520(0), 342-355.

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

NASA Astrophysics Data System (ADS)

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

2016-09-01

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace such that the dimensionality of the problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2-D and a random hydraulic conductivity field in 3-D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ˜101 to ˜102 in a multicore computational environment. Therefore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate to large-scale problems.

Solving geosteering inverse problems by stochastic Hybrid Monte Carlo method

DOE PAGES

Shen, Qiuyang; Wu, Xuqing; Chen, Jiefu; ...

2017-11-20

The inverse problems arise in almost all fields of science where the real-world parameters are extracted from a set of measured data. The geosteering inversion plays an essential role in the accurate prediction of oncoming strata as well as a reliable guidance to adjust the borehole position on the fly to reach one or more geological targets. This mathematical treatment is not easy to solve, which requires finding an optimum solution among a large solution space, especially when the problem is non-linear and non-convex. Nowadays, a new generation of logging-while-drilling (LWD) tools has emerged on the market. The so-called azimuthalmore » resistivity LWD tools have azimuthal sensitivity and a large depth of investigation. Hence, the associated inverse problems become much more difficult since the earth model to be inverted will have more detailed structures. The conventional deterministic methods are incapable to solve such a complicated inverse problem, where they suffer from the local minimum trap. Alternatively, stochastic optimizations are in general better at finding global optimal solutions and handling uncertainty quantification. In this article, we investigate the Hybrid Monte Carlo (HMC) based statistical inversion approach and suggest that HMC based inference is more efficient in dealing with the increased complexity and uncertainty faced by the geosteering problems.« less

Using a derivative-free optimization method for multiple solutions of inverse transport problems

DOE PAGES

Armstrong, Jerawan C.; Favorite, Jeffrey A.

2016-01-14

Identifying unknown components of an object that emits radiation is an important problem for national and global security. Radiation signatures measured from an object of interest can be used to infer object parameter values that are not known. This problem is called an inverse transport problem. An inverse transport problem may have multiple solutions and the most widely used approach for its solution is an iterative optimization method. This paper proposes a stochastic derivative-free global optimization algorithm to find multiple solutions of inverse transport problems. The algorithm is an extension of a multilevel single linkage (MLSL) method where a meshmore » adaptive direct search (MADS) algorithm is incorporated into the local phase. Furthermore, numerical test cases using uncollided fluxes of discrete gamma-ray lines are presented to show the performance of this new algorithm.« less

Frnakenstein: multiple target inverse RNA folding.

PubMed

Lyngsø, Rune B; Anderson, James W J; Sizikova, Elena; Badugu, Amarendra; Hyland, Tomas; Hein, Jotun

2012-10-09

RNA secondary structure prediction, or folding, is a classic problem in bioinformatics: given a sequence of nucleotides, the aim is to predict the base pairs formed in its three dimensional conformation. The inverse problem of designing a sequence folding into a particular target structure has only more recently received notable interest. With a growing appreciation and understanding of the functional and structural properties of RNA motifs, and a growing interest in utilising biomolecules in nano-scale designs, the interest in the inverse RNA folding problem is bound to increase. However, whereas the RNA folding problem from an algorithmic viewpoint has an elegant and efficient solution, the inverse RNA folding problem appears to be hard. In this paper we present a genetic algorithm approach to solve the inverse folding problem. The main aims of the development was to address the hitherto mostly ignored extension of solving the inverse folding problem, the multi-target inverse folding problem, while simultaneously designing a method with superior performance when measured on the quality of designed sequences. The genetic algorithm has been implemented as a Python program called Frnakenstein. It was benchmarked against four existing methods and several data sets totalling 769 real and predicted single structure targets, and on 292 two structure targets. It performed as well as or better at finding sequences which folded in silico into the target structure than all existing methods, without the heavy bias towards CG base pairs that was observed for all other top performing methods. On the two structure targets it also performed well, generating a perfect design for about 80% of the targets. Our method illustrates that successful designs for the inverse RNA folding problem does not necessarily have to rely on heavy biases in base pair and unpaired base distributions. The design problem seems to become more difficult on larger structures when the target structures are real structures, while no deterioration was observed for predicted structures. Design for two structure targets is considerably more difficult, but far from impossible, demonstrating the feasibility of automated design of artificial riboswitches. The Python implementation is available at http://www.stats.ox.ac.uk/research/genome/software/frnakenstein.

Frnakenstein: multiple target inverse RNA folding

PubMed Central

2012-01-01

Background RNA secondary structure prediction, or folding, is a classic problem in bioinformatics: given a sequence of nucleotides, the aim is to predict the base pairs formed in its three dimensional conformation. The inverse problem of designing a sequence folding into a particular target structure has only more recently received notable interest. With a growing appreciation and understanding of the functional and structural properties of RNA motifs, and a growing interest in utilising biomolecules in nano-scale designs, the interest in the inverse RNA folding problem is bound to increase. However, whereas the RNA folding problem from an algorithmic viewpoint has an elegant and efficient solution, the inverse RNA folding problem appears to be hard. Results In this paper we present a genetic algorithm approach to solve the inverse folding problem. The main aims of the development was to address the hitherto mostly ignored extension of solving the inverse folding problem, the multi-target inverse folding problem, while simultaneously designing a method with superior performance when measured on the quality of designed sequences. The genetic algorithm has been implemented as a Python program called Frnakenstein. It was benchmarked against four existing methods and several data sets totalling 769 real and predicted single structure targets, and on 292 two structure targets. It performed as well as or better at finding sequences which folded in silico into the target structure than all existing methods, without the heavy bias towards CG base pairs that was observed for all other top performing methods. On the two structure targets it also performed well, generating a perfect design for about 80% of the targets. Conclusions Our method illustrates that successful designs for the inverse RNA folding problem does not necessarily have to rely on heavy biases in base pair and unpaired base distributions. The design problem seems to become more difficult on larger structures when the target structures are real structures, while no deterioration was observed for predicted structures. Design for two structure targets is considerably more difficult, but far from impossible, demonstrating the feasibility of automated design of artificial riboswitches. The Python implementation is available at http://www.stats.ox.ac.uk/research/genome/software/frnakenstein. PMID:23043260

Regional recovery of the disturbing gravitational potential by inverting satellite gravitational gradients

NASA Astrophysics Data System (ADS)

Pitoňák, Martin; Šprlák, Michal; Hamáčková, Eliška; Novák, Pavel

2016-04-01

Regional recovery of the disturbing gravitational potential in the area of Central Europe from satellite gravitational gradients data is discussed in this contribution. The disturbing gravitational potential is obtained by inverting surface integral formulas which transform the disturbing gravitational potential onto disturbing gravitational gradients in the spherical local north-oriented frame. Two numerical approaches that solve the inverse problem are considered. In the first approach, the integral formulas are rigorously decomposed into two parts, that is, the effects of the gradient data within near and distant zones. While the effect of the near zone data is sought as an inverse problem, the effect of the distant zone data is synthesized from the global gravitational model GGM05S using spectral weights given by truncation error coefficients up to the degree 150. In the second approach, a reference gravitational field up to the degree 180 is applied to reduce and smooth measured gravitational gradients. In both cases we recovered the disturbing gravitational potential from each of the four well-measured gravitational gradients of the GOCE satellite separately as well as from their combination. Obtained results are compared with the EGM2008, DIR-r2, TIM-r2 and SPW-r2 global gravitational models. The best fit was achieved for EGM2008 and the second approach combining all four well-measured gravitational gradients with rms of 1.231 m2 s-2.

First Calderón Prize

NASA Astrophysics Data System (ADS)

Rundell, William; Somersalo, Erkki

2008-07-01

The Inverse Problems International Association (IPIA) awarded the first Calderón Prize to Matti Lassas for his outstanding contributions to the field of inverse problems, especially in geometric inverse problems. The Calderón Prize is given to a researcher under the age of 40 who has made distinguished contributions to the field of inverse problems broadly defined. The first Calderón Prize Committee consisted of Professors Adrian Nachman, Lassi Päivärinta, William Rundell (chair), and Michael Vogelius. William Rundell For the Calderón Prize Committee Prize ceremony The ceremony awarding the Calderón Prize. Matti Lassas is on the left. He and William Rundell are on the right. Photos by P Stefanov. Brief Biography of Matti Lassas Matti Lassas was born in 1969 in Helsinki, Finland, and studied at the University of Helsinki. He finished his Master's studies in 1992 in three years and earned his PhD in 1996. His PhD thesis, written under the supervision of Professor Erkki Somersalo was entitled `Non-selfadjoint inverse spectral problems and their applications to random bodies'. Already in his thesis, Matti demonstrated a remarkable command of different fields of mathematics, bringing together the spectral theory of operators, geometry of Riemannian surfaces, Maxwell's equations and stochastic analysis. He has continued to develop all of these branches in the framework of inverse problems, the most remarkable results perhaps being in the field of differential geometry and inverse problems. Matti has always been a very generous researcher, sharing his ideas with his numerous collaborators. He has authored over sixty scientific articles, among which a monograph on inverse boundary spectral problems with Alexander Kachalov and Yaroslav Kurylev and over forty articles in peer reviewed journals of the highest standards. To get an idea of the wide range of Matti's interests, it is enough to say that he also has three US patents on medical imaging applications. Matti is currently professor of mathematics at Helsinki University of Technology, where he has created his own line of research with young talented researchers around him. He is a central person in the Centre of Excellence in Inverse Problems Research of the Academy of Finland. Previously, Matti Lassas has won several awards in his home country, including the prestigious Vaisala price of the Finnish Academy of Science and Letters in 2004. He is a highly esteemed colleague, teacher and friend, and the Great Diving Beetle of the Finnish Inverse Problems Society (http://venda.uku.fi/research/FIPS/), an honorary title for a person who has no fear of the deep. Erkki Somersalo

Adaptive eigenspace method for inverse scattering problems in the frequency domain

NASA Astrophysics Data System (ADS)

Grote, Marcus J.; Kray, Marie; Nahum, Uri

2017-02-01

A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type iteration. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional basis of eigenfunctions, which is iteratively adapted during the optimization. Truncating the adaptive eigenspace (AE) basis at a (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Both analytical and numerical evidence underpins the accuracy of the AE representation. Numerical experiments demonstrate the efficiency and robustness to missing or noisy data of the resulting adaptive eigenspace inversion method.

Stochastic inversion of ocean color data using the cross-entropy method.

PubMed

Salama, Mhd Suhyb; Shen, Fang

2010-01-18

Improving the inversion of ocean color data is an ever continuing effort to increase the accuracy of derived inherent optical properties. In this paper we present a stochastic inversion algorithm to derive inherent optical properties from ocean color, ship and space borne data. The inversion algorithm is based on the cross-entropy method where sets of inherent optical properties are generated and converged to the optimal set using iterative process. The algorithm is validated against four data sets: simulated, noisy simulated in-situ measured and satellite match-up data sets. Statistical analysis of validation results is based on model-II regression using five goodness-of-fit indicators; only R2 and root mean square of error (RMSE) are mentioned hereafter. Accurate values of total absorption coefficient are derived with R2 > 0.91 and RMSE, of log transformed data, less than 0.55. Reliable values of the total backscattering coefficient are also obtained with R2 > 0.7 (after removing outliers) and RMSE < 0.37. The developed algorithm has the ability to derive reliable results from noisy data with R2 above 0.96 for the total absorption and above 0.84 for the backscattering coefficients. The algorithm is self contained and easy to implement and modify to derive the variability of chlorophyll-a absorption that may correspond to different phytoplankton species. It gives consistently accurate results and is therefore worth considering for ocean color global products.

Angular dependence of multiangle dynamic light scattering for particle size distribution inversion using a self-adapting regularization algorithm

NASA Astrophysics Data System (ADS)

Li, Lei; Yu, Long; Yang, Kecheng; Li, Wei; Li, Kai; Xia, Min

2018-04-01

The multiangle dynamic light scattering (MDLS) technique can better estimate particle size distributions (PSDs) than single-angle dynamic light scattering. However, determining the inversion range, angular weighting coefficients, and scattering angle combination is difficult but fundamental to the reconstruction for both unimodal and multimodal distributions. In this paper, we propose a self-adapting regularization method called the wavelet iterative recursion nonnegative Tikhonov-Phillips-Twomey (WIRNNT-PT) algorithm. This algorithm combines a wavelet multiscale strategy with an appropriate inversion method and could self-adaptively optimize several noteworthy issues containing the choices of the weighting coefficients, the inversion range and the optimal inversion method from two regularization algorithms for estimating the PSD from MDLS measurements. In addition, the angular dependence of the MDLS for estimating the PSDs of polymeric latexes is thoroughly analyzed. The dependence of the results on the number and range of measurement angles was analyzed in depth to identify the optimal scattering angle combination. Numerical simulations and experimental results for unimodal and multimodal distributions are presented to demonstrate both the validity of the WIRNNT-PT algorithm and the angular dependence of MDLS and show that the proposed algorithm with a six-angle analysis in the 30-130° range can be satisfactorily applied to retrieve PSDs from MDLS measurements.

Spectra of Particulate Backscattering in Natural Waters

NASA Technical Reports Server (NTRS)

Gordon, Howard, R.; Lewis, Marlon R.; McLean, Scott D.; Twardowski, Michael S.; Freeman, Scott A.; Voss, Kenneth J.; Boynton, Chris G.

2009-01-01

Hyperspectral profiles of downwelling irradiance and upwelling radiance in natural waters (oligotrophic and mesotrophic) are combined with inverse radiative transfer to obtain high resolution spectra of the absorption coefficient (a) and the backscattering coefficient (bb) of the water and its constituents. The absorption coefficient at the mesotrophic station clearly shows spectral absorption features attributable to several phytoplankton pigments (Chlorophyll a, b, c, and Carotenoids). The backscattering shows only weak spectral features and can be well represented by a power-law variation with wavelength (lambda): b(sub b) approx. Lambda(sup -n), where n is a constant between 0.4 and 1.0. However, the weak spectral features in b(sub b), suggest that it is depressed in spectral regions of strong particle absorption. The applicability of the present inverse radiative transfer algorithm, which omits the influence of Raman scattering, is limited to lambda < 490 nm in oligotrophic waters and lambda < 575 nm in mesotrophic waters.

PREFACE: Inverse Problems in Applied Sciences—towards breakthrough

NASA Astrophysics Data System (ADS)

Cheng, Jin; Iso, Yuusuke; Nakamura, Gen; Yamamoto, Masahiro

2007-06-01

These are the proceedings of the international conference `Inverse Problems in Applied Sciences—towards breakthrough' which was held at Hokkaido University, Sapporo, Japan on 3-7 July 2006 (http://coe.math.sci.hokudai.ac.jp/sympo/inverse/). There were 88 presentations and more than 100 participants, and we are proud to say that the conference was very successful. Nowadays, many new activities on inverse problems are flourishing at many centers of research around the world, and the conference has successfully gathered a world-wide variety of researchers. We believe that this volume contains not only main papers, but also conveys the general status of current research into inverse problems. This conference was the third biennial international conference on inverse problems, the core of which is the Pan-Pacific Asian area. The purpose of this series of conferences is to establish and develop constant international collaboration, especially among the Pan-Pacific Asian countries, and to lead the organization of activities concerning inverse problems centered in East Asia. The first conference was held at City University of Hong Kong in January 2002 and the second was held at Fudan University in June 2004. Following the preceding two successes, the third conference was organized in order to extend the scope of activities and build useful bridges to the next conference in Seoul in 2008. Therefore this third biennial conference was intended not only to establish collaboration and links between researchers in Asia and leading researchers worldwide in inverse problems but also to nurture interdisciplinary collaboration in theoretical fields such as mathematics, applied fields and evolving aspects of inverse problems. For these purposes, we organized tutorial lectures, serial lectures and a panel discussion as well as conference research presentations. This volume contains three lecture notes from the tutorial and serial lectures, and 22 papers. Especially at this flourishing time, it is necessary to carefully analyse the current status of inverse problems for further development. Thus we have opened with the panel discussion entitled `Future of Inverse Problems' with panelists: Professors J Cheng, H W Engl, V Isakov, R Kress, J-K Seo, G Uhlmann and the commentator: Elaine Longden-Chapman from IOP Publishing. The aims of the panel discussion were to examine the current research status from various viewpoints, to discuss how we can overcome any difficulties and how we can promote young researchers and open new possibilities for inverse problems such as industrial linkages. As one output, the panel discussion has triggered the organization of the Inverse Problems International Association (IPIA) which has led to its first international congress in the summer of 2007. Another remarkable outcome of the conference is, of course, the present volume: this is the very high quality online proceedings volume of Journal of Physics: Conference Series. Readers can see in these proceedings very well written tutorial lecture notes, and very high quality original research and review papers all of which show what was achieved by the time the conference was held. The electronic publication of the proceedings is a new way of publicizing the achievement of the conference. It has the advantage of wide circulation and cost reduction. We believe this is a most efficient method for our needs and purposes. We would like to take this opportunity to acknowledge all the people who helped to organize the conference. Guest Editors Jin Cheng, Fudan University, Shanghai, China Yuusuke Iso, Kyoto University, Kyoto, Japan Gen Nakamura, Hokkaido University, Sapporo, Japan Masahiro Yamamoto, University of Tokyo, Tokyo, Japan

The Relationship between Anxiety and Coping Strategies in Family Caregivers of Patients with Trauma.

PubMed

Rahnama, Mozhgan; Shahdadi, Hosien; Bagheri, Somyeh; Moghadam, Mahdieh Poodineh; Absalan, Ahmad

2017-04-01

Traumatic events are of high incidence and affect not only the patient but also their family members, causing psychological problems such as stress and anxiety for caregivers of these patients. Therefore, the application of appropriate coping strategies by them seems necessary in order to promote mental health. To study the relationship of anxiety with coping strategies in family caregivers of trauma patients. The present research was a descriptive-correlational study which was carried out on 127 family caregivers of patients with trauma in intensive care unit, surgery ward and emergency unit of Amir al-Mu'minin Hospital of Zabol, Sistan and Baluchestan Province. The respondents were selected based on the convenience sampling method. Demographics questionnaire, DASS-21, and Coping Strategies questionnaire were used for data collection. The obtained data were statistically analysed using descriptive statistics, Analysis of Variance (ANOVA), t-test, and Pearson correlation coefficient in statistical package for the Social Sciences (SPSS) version 21.0. Based on the results, 89.9% of family caregivers suffer from mild to severe anxiety. The most common type of coping strategy used by the respondents was emotion-focused. The results showed no relationship between anxiety and emotion-centrism, but an inverse relationship was found between problem-centrism and anxiety. The majority of family caregivers had anxiety. Given, the inverse relationship between the level of anxiety and the use of problem-based coping strategy, in addition to identifying and reducing the causes of anxiety in caregivers. It is recommended that appropriate coping strategies should be trained to them.

The Relationship between Anxiety and Coping Strategies in Family Caregivers of Patients with Trauma

PubMed Central

Rahnama, Mozhgan; Bagheri, Somyeh; Moghadam, Mahdieh Poodineh; Absalan, Ahmad

2017-01-01

Introduction Traumatic events are of high incidence and affect not only the patient but also their family members, causing psychological problems such as stress and anxiety for caregivers of these patients. Therefore, the application of appropriate coping strategies by them seems necessary in order to promote mental health. Aim To study the relationship of anxiety with coping strategies in family caregivers of trauma patients. Materials and Methods The present research was a descriptive-correlational study which was carried out on 127 family caregivers of patients with trauma in intensive care unit, surgery ward and emergency unit of Amir al-Mu’minin Hospital of Zabol, Sistan and Baluchestan Province. The respondents were selected based on the convenience sampling method. Demographics questionnaire, DASS-21, and Coping Strategies questionnaire were used for data collection. The obtained data were statistically analysed using descriptive statistics, Analysis of Variance (ANOVA), t-test, and Pearson correlation coefficient in statistical package for the Social Sciences (SPSS) version 21.0. Results Based on the results, 89.9% of family caregivers suffer from mild to severe anxiety. The most common type of coping strategy used by the respondents was emotion-focused. The results showed no relationship between anxiety and emotion-centrism, but an inverse relationship was found between problem-centrism and anxiety. Conclusion The majority of family caregivers had anxiety. Given, the inverse relationship between the level of anxiety and the use of problem-based coping strategy, in addition to identifying and reducing the causes of anxiety in caregivers. It is recommended that appropriate coping strategies should be trained to them. PMID:28571166

Solvability of the electrocardiology inverse problem for a moving dipole.

PubMed

Tolkachev, V; Bershadsky, B; Nemirko, A

1993-01-01

New formulations of the direct and inverse problems for the moving dipole are offered. It has been suggested to limit the study by a small area on the chest surface. This lowers the role of the medium inhomogeneity. When formulating the direct problem, irregular components are considered. The algorithm of simultaneous determination of the dipole and regular noise parameters has been described and analytically investigated. It is shown that temporal overdetermination of the equations offers a single solution of the inverse problem for the four leads.

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally-efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace, such that the dimensionality of themore » problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~10 1 to ~10 2 in a multi-core computational environment. Furthermore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.« less

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

DOE PAGES

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

2016-09-01

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally-efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace, such that the dimensionality of themore » problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~10 1 to ~10 2 in a multi-core computational environment. Furthermore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.« less

Using Directional Diffusion Coefficients for Nonlinear Diffusion Acceleration of the First Order SN Equations in Near-Void Regions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schunert, Sebastian; Hammer, Hans; Lou, Jijie

2016-11-01

The common definition of the diffusion coeffcient as the inverse of three times the transport cross section is not compat- ible with voids. Morel introduced a non-local tensor diffusion coeffcient that remains finite in voids[1]. It can be obtained by solving an auxiliary transport problem without scattering or fission. Larsen and Trahan successfully applied this diffusion coeffcient for enhancing the accuracy of diffusion solutions of very high temperature reactor (VHTR) problems that feature large, optically thin channels in the z-direction [2]. It is demonstrated that a significant reduction of error can be achieved in particular in the optically thin region.more » Along the same line of thought, non-local diffusion tensors are applied modeling the TREAT reactor confirming the findings of Larsen and Trahan [3]. Previous work of the authors have introduced a flexible Nonlinear-Diffusion Acceleration (NDA) method for the first order S N equations discretized with the discontinuous finite element method (DFEM), [4], [5], [6]. This NDA method uses a scalar diffusion coeffcient in the low-order system that is obtained as the flux weighted average of the inverse transport cross section. Hence, it su?ers from very large and potentially unbounded diffusion coeffcients in the low order problem. However, it was noted that the choice of the diffusion coeffcient does not influence consistency of the method at convergence and hence the di?usion coeffcient is essentially a free parameter. The choice of the di?usion coeffcient does, however, affect the convergence behavior of the nonlinear di?usion iterations. Within this work we use Morel’s non-local di?usion coef- ficient in the aforementioned NDA formulation in lieu of the flux weighted inverse of three times the transport cross section. The goal of this paper is to demonstrate that significant en- hancement of the spectral properties of NDA can be achieved in near void regions. For testing the spectral properties of the NDA with non-local diffusion coeffcients, the periodical horizontal interface problem is used [7]. This problem consists of alternating stripes of optically thin and thick materials both of which feature scattering ratios close to unity.« less

MAP Estimators for Piecewise Continuous Inversion

DTIC Science & Technology

2016-08-08

MAP estimators for piecewise continuous inversion M M Dunlop1 and A M Stuart Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK E...Published 8 August 2016 Abstract We study the inverse problem of estimating a field ua from data comprising a finite set of nonlinear functionals of ua...then natural to study maximum a posterior (MAP) estimators. Recently (Dashti et al 2013 Inverse Problems 29 095017) it has been shown that MAP

Time-domain full waveform inversion using instantaneous phase information with damping

NASA Astrophysics Data System (ADS)

Luo, Jingrui; Wu, Ru-Shan; Gao, Fuchun

2018-06-01

In time domain, the instantaneous phase can be obtained from the complex seismic trace using Hilbert transform. The instantaneous phase information has great potential in overcoming the local minima problem and improving the result of full waveform inversion. However, the phase wrapping problem, which comes from numerical calculation, prevents its application. In order to avoid the phase wrapping problem, we choose to use the exponential phase combined with the damping method, which gives instantaneous phase-based multi-stage inversion. We construct the objective functions based on the exponential instantaneous phase, and also derive the corresponding gradient operators. Conventional full waveform inversion and the instantaneous phase-based inversion are compared with numerical examples, which indicates that in the case without low frequency information in seismic data, our method is an effective and efficient approach for initial model construction for full waveform inversion.

Exploring SWOT discharge algorithm accuracy on the Sacramento River

NASA Astrophysics Data System (ADS)

Durand, M. T.; Yoon, Y.; Rodriguez, E.; Minear, J. T.; Andreadis, K.; Pavelsky, T. M.; Alsdorf, D. E.; Smith, L. C.; Bales, J. D.

2012-12-01

Scheduled for launch in 2019, the Surface Water and Ocean Topography (SWOT) satellite mission will utilize a Ka-band radar interferometer to measure river heights, widths, and slopes, globally, as well as characterize storage change in lakes and ocean surface dynamics with a spatial resolution ranging from 10 - 70 m, with temporal revisits on the order of a week. A discharge algorithm has been formulated to solve the inverse problem of characterizing river bathymetry and the roughness coefficient from SWOT observations. The algorithm uses a Bayesian Markov Chain estimation approach, treats rivers as sets of interconnected reaches (typically 5 km - 10 km in length), and produces best estimates of river bathymetry, roughness coefficient, and discharge, given SWOT observables. AirSWOT (the airborne version of SWOT) consists of a radar interferometer similar to SWOT, but mounted aboard an aircraft. AirSWOT spatial resolution will range from 1 - 35 m. In early 2013, AirSWOT will perform several flights over the Sacramento River, capturing river height, width, and slope at several different flow conditions. The Sacramento River presents an excellent target given that the river includes some stretches heavily affected by management (diversions, bypasses, etc.). AirSWOT measurements will be used to validate SWOT observation performance, but are also a unique opportunity for testing and demonstrating the capabilities and limitations of the discharge algorithm. This study uses HEC-RAS simulations of the Sacramento River to first, characterize expected discharge algorithm accuracy on the Sacramento River, and second to explore the required AirSWOT measurements needed to perform a successful inverse with the discharge algorithm. We focus on several specific research questions affecting algorithm performance: 1) To what extent do lateral inflows confound algorithm performance? We examine the ~100 km stretch of river from Colusa, CA to the Yolo Bypass, and investigate how the varying degrees of lateral flows affect algorithm performance. 2) To what extent does a simple slope-area method (i.e. Manning's equation) applied to river reaches accurately describe river discharge? 3) How accurately does the algorithm perform an inversion to accurately describe the river bathymetry and roughness coefficient? Finally, we explore the sensitivity of the algorithm to the number of AirSWOT flights and AirSWOT measurement precision for various river flow scenarios.

Development of an unsteady wake theory appropriate for aeroelastic analyses of rotors in hover and forward flight

NASA Technical Reports Server (NTRS)

Peters, David A.

1988-01-01

The purpose of this research is the development of an unsteady aerodynamic model for rotors such that it can be used in conventional aeroelastic analysis (e.g., eigenvalue determination and control system design). For this to happen, the model must be in a state-space formulation such that the states of the flow can be defined, calculated and identified as part of the analysis. The fluid mechanics of the problem is given by a closed-form inversion of an acceleration potential. The result is a set of first-order differential equations in time for the unknown flow coefficients. These equations are hierarchical in the sense that they may be truncated at any number of radial or azimuthal terms.

Solutions to inverse plume in a crosswind problem using a predictor - corrector method

NASA Astrophysics Data System (ADS)

Vanderveer, Joseph; Jaluria, Yogesh

2013-11-01

Investigation for minimalist solutions to the inverse convection problem of a plume in a crosswind has developed a predictor - corrector method. The inverse problem is to predict the strength and location of the plume with respect to a select few downstream sampling points. This is accomplished with the help of two numerical simulations of the domain at differing source strengths, allowing the generation of two inverse interpolation functions. These functions in turn are utilized by the predictor step to acquire the plume strength. Finally, the same interpolation functions with the corrections from the plume strength are used to solve for the plume location. Through optimization of the relative location of the sampling points, the minimum number of samples for accurate predictions is reduced to two for the plume strength and three for the plume location. After the optimization, the predictor-corrector method demonstrates global uniqueness of the inverse solution for all test cases. The solution error is less than 1% for both plume strength and plume location. The basic approach could be extended to other inverse convection transport problems, particularly those encountered in environmental flows.

Income Inequality and Use of Dental Services in 66 Countries.

PubMed

Bhandari, B; Newton, J T; Bernabé, E

2015-08-01

This study explored the association between income inequality and use of dental services and the role that investment in health care plays in explaining that association. We pooled individual-level data from 223,299 adults, 18 years or older, in 66 countries, who participated in the World Health Organization (WHO) World Health Surveys with country-level data from different international sources. Income inequality was measured at the national level using the Gini coefficient, and use of dental services was defined as having received treatment to address problems with mouth and/or teeth in the past year. The association between the Gini coefficient and use of dental services was examined in multilevel models controlling for a standard set of individual- and country-level confounders. The individual and joint contributions of 4 indicators of investment in health care were evaluated in sequential modeling. The Gini coefficient and use of dental services were inversely associated after adjustment for confounders. Every 10% increase in the Gini coefficient corresponded with a 15% lower odds of using dental services (odds ratio: 0.85; 95% confidence interval: 0.70-0.99). The association between the Gini coefficient and use of dental services was attenuated and became nonsignificant after individual adjustment for total health expenditure, public expenditure on health, health system responsiveness, or type of dental health system. The 4 indicators together explained 80% of the association between the Gini coefficient and use of dental services. This study suggests that more equal countries have greater use of dental services. It also supports the mediating role of investment in health care in explaining that association. © International & American Associations for Dental Research 2015.

Core flow inversion tested with numerical dynamo models

NASA Astrophysics Data System (ADS)

Rau, Steffen; Christensen, Ulrich; Jackson, Andrew; Wicht, Johannes

2000-05-01

We test inversion methods of geomagnetic secular variation data for the pattern of fluid flow near the surface of the core with synthetic data. These are taken from self-consistent 3-D models of convection-driven magnetohydrodynamic dynamos in rotating spherical shells, which generate dipole-dominated magnetic fields with an Earth-like morphology. We find that the frozen-flux approximation, which is fundamental to all inversion schemes, is satisfied to a fair degree in the models. In order to alleviate the non-uniqueness of the inversion, usually a priori conditions are imposed on the flow; for example, it is required to be purely toroidal or geostrophic. Either condition is nearly satisfied by our model flows near the outer surface. However, most of the surface velocity field lies in the nullspace of the inversion problem. Nonetheless, the a priori constraints reduce the nullspace, and by inverting the magnetic data with either one of them we recover a significant part of the flow. With the geostrophic condition the correlation coefficient between the inverted and the true velocity field can reach values of up to 0.65, depending on the choice of the damping parameter. The correlation is significant at the 95 per cent level for most spherical harmonic degrees up to l=26. However, it degrades substantially, even at long wavelengths, when we truncate the magnetic data sets to l <= 14, that is, to the resolution of core-field models. In some of the latter inversions prominent zonal currents, similar to those seen in core-flow models derived from geomagnetic data, occur in the equatorial region. However, the true flow does not contain this flow component. The results suggest that some meaningful information on the core-flow pattern can be retrieved from secular variation data, but also that the limited resolution of the magnetic core field could produce serious artefacts.

Acoustic Inversion in Optoacoustic Tomography: A Review

PubMed Central

Rosenthal, Amir; Ntziachristos, Vasilis; Razansky, Daniel

2013-01-01

Optoacoustic tomography enables volumetric imaging with optical contrast in biological tissue at depths beyond the optical mean free path by the use of optical excitation and acoustic detection. The hybrid nature of optoacoustic tomography gives rise to two distinct inverse problems: The optical inverse problem, related to the propagation of the excitation light in tissue, and the acoustic inverse problem, which deals with the propagation and detection of the generated acoustic waves. Since the two inverse problems have different physical underpinnings and are governed by different types of equations, they are often treated independently as unrelated problems. From an imaging standpoint, the acoustic inverse problem relates to forming an image from the measured acoustic data, whereas the optical inverse problem relates to quantifying the formed image. This review focuses on the acoustic aspects of optoacoustic tomography, specifically acoustic reconstruction algorithms and imaging-system practicalities. As these two aspects are intimately linked, and no silver bullet exists in the path towards high-performance imaging, we adopt a holistic approach in our review and discuss the many links between the two aspects. Four classes of reconstruction algorithms are reviewed: time-domain (so called back-projection) formulae, frequency-domain formulae, time-reversal algorithms, and model-based algorithms. These algorithms are discussed in the context of the various acoustic detectors and detection surfaces which are commonly used in experimental studies. We further discuss the effects of non-ideal imaging scenarios on the quality of reconstruction and review methods that can mitigate these effects. Namely, we consider the cases of finite detector aperture, limited-view tomography, spatial under-sampling of the acoustic signals, and acoustic heterogeneities and losses. PMID:24772060

Identification of material constants for piezoelectric transformers by three-dimensional, finite-element method and a design-sensitivity method.

PubMed

Joo, Hyun-Woo; Lee, Chang-Hwan; Rho, Jong-Seok; Jung, Hyun-Kyo

2003-08-01

In this paper, an inversion scheme for piezoelectric constants of piezoelectric transformers is proposed. The impedance of piezoelectric transducers is calculated using a three-dimensional finite element method. The validity of this is confirmed experimentally. The effects of material coefficients on piezoelectric transformers are investigated numerically. Six material coefficient variables for piezoelectric transformers were selected, and a design sensitivity method was adopted as an inversion scheme. The validity of the proposed method was confirmed by step-up ratio calculations. The proposed method is applied to the analysis of a sample piezoelectric transformer, and its resonance characteristics are obtained by numerically combined equivalent circuit method.

Photoacoustic optical properties at UV, VIS, and near IR wavelengths for laboratory generated and winter time ambient urban aerosols

NASA Astrophysics Data System (ADS)

Gyawali, M.; Arnott, W. P.; Zaveri, R. A.; Song, C.; Moosmüller, H.; Liu, L.; Mishchenko, M. I.; Chen, L.-W. A.; Green, M. C.; Watson, J. G.; Chow, J. C.

2011-09-01

We present the first laboratory and ambient photoacoustic (PA) measurement of aerosol light absorption coefficients at ultraviolet (UV) wavelength (i.e. 355 nm) and compare with measurements at 405, 532, 870, and 1047 nm. Simultaneous measurements of aerosol light scattering coefficients were achieved by the integrating reciprocal nephelometer within the PA';s acoustic resonator. Absorption and scattering measurements were carried out for various laboratory-generated aerosols, including salt, incense, and kerosene soot to evaluate the instrument calibration and gain insight on the spectral dependence of aerosol light absorption and scattering. Exact T-matrix method calculations were used to model the absorption and scattering characteristics of fractal-like agglomerates of different compactness and varying number of monomers. With these calculations, we attempted to estimate the number of monomers and fractal dimension of laboratory generated kerosene soot. Ambient measurements were obtained in Reno, Nevada, between 18 December 2009, and 18 January 2010. The measurement period included days with and without strong ground level temperature inversions, corresponding to highly polluted (freshly emitted aerosols) and relatively clean (aged aerosols) conditions. Particulate matter (PM) concentrations were measured and analyzed with other tracers of traffic emissions. The temperature inversion episodes caused very high concentration of PM2.5 and PM10 (particulate matter with aerodynamic diameters less than 2.5 μm and 10 μm, respectively) and gaseous pollutants: carbon monoxide (CO), nitric oxide (NO), and nitrogen dioxide (NO2). The diurnal change of absorption and scattering coefficients during the polluted (inversion) days increased approximately by a factor of two for all wavelengths compared to the clean days. The spectral variation in aerosol absorption coefficients indicated a significant amount of absorbing aerosol from traffic emissions and residential wood burning. The analysis of single scattering albedo (SSA), Ångström exponent of absorption (AEA), and Ångström exponent of scattering (AES) for clean and polluted days provides evidences that the aerosol aging and coating process is suppressed by strong temperature inversion under cloudy conditions. In general, measured UV absorption coefficients were found to be much larger for biomass burning aerosol than for typical ambient aerosols.

Review of the inverse scattering problem at fixed energy in quantum mechanics

NASA Technical Reports Server (NTRS)

Sabatier, P. C.

1972-01-01

Methods of solution of the inverse scattering problem at fixed energy in quantum mechanics are presented. Scattering experiments of a beam of particles at a nonrelativisitic energy by a target made up of particles are analyzed. The Schroedinger equation is used to develop the quantum mechanical description of the system and one of several functions depending on the relative distance of the particles. The inverse problem is the construction of the potentials from experimental measurements.

Rigorous theory of graded thermoelectric converters including finite heat transfer coefficients

NASA Astrophysics Data System (ADS)

Gerstenmaier, York Christian; Wachutka, Gerhard

2017-11-01

Maximization of thermoelectric (TE) converter performance with an inhomogeneous material and electric current distribution has been investigated in previous literature neglecting thermal contact resistances to the heat reservoirs. The heat transfer coefficients (HTCs), defined as inverse thermal contact resistances per unit area, are thus infinite, whereas in reality, always parasitic thermal resistances, i.e., finite HTCs, are present. Maximization of the generated electric power and of cooling power in the refrigerator mode with respect to Seebeck coefficients and heat conductivity for a given profile of the material's TE figure of merit Z are mathematically ill-posed problems in the presence of infinite HTCs. As will be shown in this work, a fully self consistent solution is possible for finite HTCs, and in many respects, the results are fundamentally different. A previous theory for 3D devices will be extended to include finite HTCs and is applied to 1D devices. For the heat conductivity profile, an infinite number of solutions exist leading to the same device performance. Cooling power maximization for finite HTCs in 1D will lead to a strongly enhanced corresponding efficiency (coefficient of performance), whereas results with infinite HTCs lead to a non-monotonous temperature profile and coefficient of performance tending to zero for the prescribed heat conductivities. For maximized generated electric power, the corresponding generator efficiency is nearly a constant independent from the finite HTC values. The maximized efficiencies in the generator and cooling mode are equal to the efficiencies for the infinite HTC, provided that the corresponding powers approach zero. These and more findings are condensed in 4 theorems in the conclusions.

Efficient Inversion of Mult-frequency and Multi-Source Electromagnetic Data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gary D. Egbert

2007-03-22

The project covered by this report focused on development of efficient but robust non-linear inversion algorithms for electromagnetic induction data, in particular for data collected with multiple receivers, and multiple transmitters, a situation extremely common in eophysical EM subsurface imaging methods. A key observation is that for such multi-transmitter problems each step in commonly used linearized iterative limited memory search schemes such as conjugate gradients (CG) requires solution of forward and adjoint EM problems for each of the N frequencies or sources, essentially generating data sensitivities for an N dimensional data-subspace. These multiple sensitivities allow a good approximation to themore » full Jacobian of the data mapping to be built up in many fewer search steps than would be required by application of textbook optimization methods, which take no account of the multiplicity of forward problems that must be solved for each search step. We have applied this idea to a develop a hybrid inversion scheme that combines features of the iterative limited memory type methods with a Newton-type approach using a partial calculation of the Jacobian. Initial tests on 2D problems show that the new approach produces results essentially identical to a Newton type Occam minimum structure inversion, while running more rapidly than an iterative (fixed regularization parameter) CG style inversion. Memory requirements, while greater than for something like CG, are modest enough that even in 3D the scheme should allow 3D inverse problems to be solved on a common desktop PC, at least for modest (~ 100 sites, 15-20 frequencies) data sets. A secondary focus of the research has been development of a modular system for EM inversion, using an object oriented approach. This system has proven useful for more rapid prototyping of inversion algorithms, in particular allowing initial development and testing to be conducted with two-dimensional example problems, before approaching more computationally cumbersome three-dimensional problems.« less

Definition and solution of a stochastic inverse problem for the Manning's n parameter field in hydrodynamic models.

PubMed

Butler, T; Graham, L; Estep, D; Dawson, C; Westerink, J J

2015-04-01

The uncertainty in spatially heterogeneous Manning's n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning's n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of "condition" for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning's n parameter and the effect on model predictions is analyzed.

Definition and solution of a stochastic inverse problem for the Manning's n parameter field in hydrodynamic models

NASA Astrophysics Data System (ADS)

Butler, T.; Graham, L.; Estep, D.; Dawson, C.; Westerink, J. J.

2015-04-01

The uncertainty in spatially heterogeneous Manning's n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning's n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of "condition" for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning's n parameter and the effect on model predictions is analyzed.

Inverse models: A necessary next step in ground-water modeling

USGS Publications Warehouse

Poeter, E.P.; Hill, M.C.

1997-01-01

Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares repression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares regression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.

Efficient Monte Carlo sampling of inverse problems using a neural network-based forward—applied to GPR crosshole traveltime inversion

NASA Astrophysics Data System (ADS)

Hansen, T. M.; Cordua, K. S.

2017-12-01

Probabilistically formulated inverse problems can be solved using Monte Carlo-based sampling methods. In principle, both advanced prior information, based on for example, complex geostatistical models and non-linear forward models can be considered using such methods. However, Monte Carlo methods may be associated with huge computational costs that, in practice, limit their application. This is not least due to the computational requirements related to solving the forward problem, where the physical forward response of some earth model has to be evaluated. Here, it is suggested to replace a numerical complex evaluation of the forward problem, with a trained neural network that can be evaluated very fast. This will introduce a modeling error that is quantified probabilistically such that it can be accounted for during inversion. This allows a very fast and efficient Monte Carlo sampling of the solution to an inverse problem. We demonstrate the methodology for first arrival traveltime inversion of crosshole ground penetrating radar data. An accurate forward model, based on 2-D full-waveform modeling followed by automatic traveltime picking, is replaced by a fast neural network. This provides a sampling algorithm three orders of magnitude faster than using the accurate and computationally expensive forward model, and also considerably faster and more accurate (i.e. with better resolution), than commonly used approximate forward models. The methodology has the potential to dramatically change the complexity of non-linear and non-Gaussian inverse problems that have to be solved using Monte Carlo sampling techniques.

Probabilistic estimation of splitting coefficients of normal modes of the Earth, and their uncertainties, using an autoregressive technique

NASA Astrophysics Data System (ADS)

Pachhai, S.; Masters, G.; Laske, G.

2017-12-01

Earth's normal-mode spectra are crucial to studying the long wavelength structure of the Earth. Such observations have been used extensively to estimate "splitting coefficients" which, in turn, can be used to determine the three-dimensional velocity and density structure. Most past studies apply a non-linear iterative inversion to estimate the splitting coefficients which requires that the earthquake source is known. However, it is challenging to know the source details, particularly for big events as used in normal-mode analyses. Additionally, the final solution of the non-linear inversion can depend on the choice of damping parameter and starting model. To circumvent the need to know the source, a two-step linear inversion has been developed and successfully applied to many mantle and core sensitive modes. The first step takes combinations of the data from a single event to produce spectra known as "receiver strips". The autoregressive nature of the receiver strips can then be used to estimate the structure coefficients without the need to know the source. Based on this approach, we recently employed a neighborhood algorithm to measure the splitting coefficients for an isolated inner-core sensitive mode (13S2). This approach explores the parameter space efficiently without any need of regularization and finds the structure coefficients which best fit the observed strips. Here, we implement a Bayesian approach to data collected for earthquakes from early 2000 and more recent. This approach combines the data (through likelihood) and prior information to provide rigorous parameter values and their uncertainties for both isolated and coupled modes. The likelihood function is derived from the inferred errors of the receiver strips which allows us to retrieve proper uncertainties. Finally, we apply model selection criteria that balance the trade-offs between fit (likelihood) and model complexity to investigate the degree and type of structure (elastic and anelastic) required to explain the data.

The incomplete inverse and its applications to the linear least squares problem

NASA Technical Reports Server (NTRS)

Morduch, G. E.

1977-01-01

A modified matrix product is explained, and it is shown that this product defiles a group whose inverse is called the incomplete inverse. It was proven that the incomplete inverse of an augmented normal matrix includes all the quantities associated with the least squares solution. An answer is provided to the problem that occurs when the data residuals are too large and when insufficient data to justify augmenting the model are available.

Analytic semigroups: Applications to inverse problems for flexible structures

NASA Technical Reports Server (NTRS)

Banks, H. T.; Rebnord, D. A.

1990-01-01

Convergence and stability results for least squares inverse problems involving systems described by analytic semigroups are presented. The practical importance of these results is demonstrated by application to several examples from problems of estimation of material parameters in flexible structures using accelerometer data.

Histogram analysis parameters of apparent diffusion coefficient reflect tumor cellularity and proliferation activity in head and neck squamous cell carcinoma

PubMed Central

Winter, Karsten; Richter, Cindy; Hoehn, Anna-Kathrin

2018-01-01

Our purpose was to analyze associations between apparent diffusion coefficient (ADC) histogram analysis parameters and histopathologicalfeatures in head and neck squamous cell carcinoma (HNSCC). The study involved 32 patients with primary HNSCC. For every tumor, the following histogram analysis parameters were calculated: ADCmean, ADCmax, ADCmin, ADCmedian, ADCmode, P10, P25, P75, P90, kurtosis, skewness, and entropy. Furthermore, proliferation index KI 67, cell count, total and average nucleic areas were estimated. Spearman's correlation coefficient (p) was used to analyze associations between investigated parameters. In overall sample, all ADC values showed moderate inverse correlations with KI 67. All ADC values except ADCmax correlated inversely with tumor cellularity. Slightly correlations were identified between total/average nucleic area and ADCmean, ADCmin, ADCmedian, and P25. In G1/2 tumors, only ADCmode correlated well with Ki67. No statistically significant correlations between ADC parameters and cellularity were found. In G3 tumors, Ki 67 correlated with all ADC parameters except ADCmode. Cell count correlated well with all ADC parameters except ADCmax. Total nucleic area correlated inversely with ADCmean, ADCmin, ADCmedian, P25, and P90. ADC histogram parameters reflect proliferation potential and cellularity in HNSCC. The associations between histopathology and imaging depend on tumor grading. PMID:29805759

A direct method for nonlinear ill-posed problems

NASA Astrophysics Data System (ADS)

Lakhal, A.

2018-02-01

We propose a direct method for solving nonlinear ill-posed problems in Banach-spaces. The method is based on a stable inversion formula we explicitly compute by applying techniques for analytic functions. Furthermore, we investigate the convergence and stability of the method and prove that the derived noniterative algorithm is a regularization. The inversion formula provides a systematic sensitivity analysis. The approach is applicable to a wide range of nonlinear ill-posed problems. We test the algorithm on a nonlinear problem of travel-time inversion in seismic tomography. Numerical results illustrate the robustness and efficiency of the algorithm.

A gradient based algorithm to solve inverse plane bimodular problems of identification

NASA Astrophysics Data System (ADS)

Ran, Chunjiang; Yang, Haitian; Zhang, Guoqing

2018-02-01

This paper presents a gradient based algorithm to solve inverse plane bimodular problems of identifying constitutive parameters, including tensile/compressive moduli and tensile/compressive Poisson's ratios. For the forward bimodular problem, a FE tangent stiffness matrix is derived facilitating the implementation of gradient based algorithms, for the inverse bimodular problem of identification, a two-level sensitivity analysis based strategy is proposed. Numerical verification in term of accuracy and efficiency is provided, and the impacts of initial guess, number of measurement points, regional inhomogeneity, and noisy data on the identification are taken into accounts.

Gravity inversion of a fault by Particle swarm optimization (PSO).

PubMed

Toushmalani, Reza

2013-01-01

Particle swarm optimization is a heuristic global optimization method and also an optimization algorithm, which is based on swarm intelligence. It comes from the research on the bird and fish flock movement behavior. In this paper we introduce and use this method in gravity inverse problem. We discuss the solution for the inverse problem of determining the shape of a fault whose gravity anomaly is known. Application of the proposed algorithm to this problem has proven its capability to deal with difficult optimization problems. The technique proved to work efficiently when tested to a number of models.

The Inverse Problem in Jet Acoustics

NASA Technical Reports Server (NTRS)

Wooddruff, S. L.; Hussaini, M. Y.

2001-01-01

The inverse problem for jet acoustics, or the determination of noise sources from far-field pressure information, is proposed as a tool for understanding the generation of noise by turbulence and for the improved prediction of jet noise. An idealized version of the problem is investigated first to establish the extent to which information about the noise sources may be determined from far-field pressure data and to determine how a well-posed inverse problem may be set up. Then a version of the industry-standard MGB code is used to predict a jet noise source spectrum from experimental noise data.

Alternatives to the stochastic "noise vector" approach

NASA Astrophysics Data System (ADS)

de Forcrand, Philippe; Jäger, Benjamin

2018-03-01

Several important observables, like the quark condensate and the Taylor coefficients of the expansion of the QCD pressure with respect to the chemical potential, are based on the trace of the inverse Dirac operator and of its powers. Such traces are traditionally estimated with "noise vectors" sandwiching the operator. We explore alternative approaches based on polynomial approximations of the inverse Dirac operator.

[Research on the method of interference correction for nondispersive infrared multi-component gas analysis].

PubMed

Sun, You-Wen; Liu, Wen-Qing; Wang, Shi-Mei; Huang, Shu-Hua; Yu, Xiao-Man

2011-10-01

A method of interference correction for nondispersive infrared multi-component gas analysis was described. According to the successive integral gas absorption models and methods, the influence of temperature and air pressure on the integral line strengths and linetype was considered, and based on Lorentz detuning linetypes, the absorption cross sections and response coefficients of H2O, CO2, CO, and NO on each filter channel were obtained. The four dimension linear regression equations for interference correction were established by response coefficients, the absorption cross interference was corrected by solving the multi-dimensional linear regression equations, and after interference correction, the pure absorbance signal on each filter channel was only controlled by the corresponding target gas concentration. When the sample cell was filled with gas mixture with a certain concentration proportion of CO, NO and CO2, the pure absorbance after interference correction was used for concentration inversion, the inversion concentration error for CO2 is 2.0%, the inversion concentration error for CO is 1.6%, and the inversion concentration error for NO is 1.7%. Both the theory and experiment prove that the interference correction method proposed for NDIR multi-component gas analysis is feasible.

A Parameterized Inversion Model for Soil Moisture and Biomass from Polarimetric Backscattering Coefficients

NASA Technical Reports Server (NTRS)

Truong-Loi, My-Linh; Saatchi, Sassan; Jaruwatanadilok, Sermsak

2012-01-01

A semi-empirical algorithm for the retrieval of soil moisture, root mean square (RMS) height and biomass from polarimetric SAR data is explained and analyzed in this paper. The algorithm is a simplification of the distorted Born model. It takes into account the physical scattering phenomenon and has three major components: volume, double-bounce and surface. This simplified model uses the three backscattering coefficients ( sigma HH, sigma HV and sigma vv) at low-frequency (P-band). The inversion process uses the Levenberg-Marquardt non-linear least-squares method to estimate the structural parameters. The estimation process is entirely explained in this paper, from initialization of the unknowns to retrievals. A sensitivity analysis is also done where the initial values in the inversion process are varying randomly. The results show that the inversion process is not really sensitive to initial values and a major part of the retrievals has a root-mean-square error lower than 5% for soil moisture, 24 Mg/ha for biomass and 0.49 cm for roughness, considering a soil moisture of 40%, roughness equal to 3cm and biomass varying from 0 to 500 Mg/ha with a mean of 161 Mg/ha

Estimating nanoparticle optical absorption with magnetic resonance temperature imaging and bioheat transfer simulation.

PubMed

MacLellan, Christopher J; Fuentes, David; Elliott, Andrew M; Schwartz, Jon; Hazle, John D; Stafford, R Jason

2014-02-01

Optically activated nanoparticle-mediated heating for thermal therapy applications is an area of intense research. The ability to characterise the spatio-temporal heating potential of these particles for use in modelling under various exposure conditions can aid in the exploration of new approaches for therapy as well as more quantitative prospective approaches to treatment planning. The purpose of this research was to investigate an inverse solution to the heat equation using magnetic resonance temperature imaging (MRTI) feedback, for providing optical characterisation of two types of nanoparticles (gold-silica nanoshells and gold nanorods). The optical absorption of homogeneous nanoparticle-agar mixtures was measured during exposure to an 808 nm laser using real-time MRTI. A coupled finite element solution of heat transfer was registered with the data and used to solve the inverse problem. The L2 norm of the difference between the temperature increase in the model and MRTI was minimised using a pattern search algorithm by varying the absorption coefficient of the mixture. Absorption fractions were within 10% of literature values for similar nanoparticles. Comparison of temporal and spatial profiles demonstrated good qualitative agreement between the model and the MRTI. The weighted root mean square error was <1.5 σMRTI and the average Dice similarity coefficient for ΔT = 5 °C isotherms was >0.9 over the measured time interval. This research demonstrates the feasibility of using an indirect method for making minimally invasive estimates of nanoparticle absorption that might be expanded to analyse a variety of geometries and particles of interest.

Inverse kinematics problem in robotics using neural networks

NASA Technical Reports Server (NTRS)

Choi, Benjamin B.; Lawrence, Charles

1992-01-01

In this paper, Multilayer Feedforward Networks are applied to the robot inverse kinematic problem. The networks are trained with endeffector position and joint angles. After training, performance is measured by having the network generate joint angles for arbitrary endeffector trajectories. A 3-degree-of-freedom (DOF) spatial manipulator is used for the study. It is found that neural networks provide a simple and effective way to both model the manipulator inverse kinematics and circumvent the problems associated with algorithmic solution methods.

Bayesian Inference in Satellite Gravity Inversion

NASA Technical Reports Server (NTRS)

Kis, K. I.; Taylor, Patrick T.; Wittmann, G.; Kim, Hyung Rae; Torony, B.; Mayer-Guerr, T.

2005-01-01

To solve a geophysical inverse problem means applying measurements to determine the parameters of the selected model. The inverse problem is formulated as the Bayesian inference. The Gaussian probability density functions are applied in the Bayes's equation. The CHAMP satellite gravity data are determined at the altitude of 400 kilometer altitude over the South part of the Pannonian basin. The model of interpretation is the right vertical cylinder. The parameters of the model are obtained from the minimum problem solved by the Simplex method.

EDITORIAL: Inverse Problems in Engineering

NASA Astrophysics Data System (ADS)

West, Robert M.; Lesnic, Daniel

2007-01-01

Presented here are 11 noteworthy papers selected from the Fifth International Conference on Inverse Problems in Engineering: Theory and Practice held in Cambridge, UK during 11-15 July 2005. The papers have been peer-reviewed to the usual high standards of this journal and the contributions of reviewers are much appreciated. The conference featured a good balance of the fundamental mathematical concepts of inverse problems with a diverse range of important and interesting applications, which are represented here by the selected papers. Aspects of finite-element modelling and the performance of inverse algorithms are investigated by Autrique et al and Leduc et al. Statistical aspects are considered by Emery et al and Watzenig et al with regard to Bayesian parameter estimation and inversion using particle filters. Electrostatic applications are demonstrated by van Berkel and Lionheart and also Nakatani et al. Contributions to the applications of electrical techniques and specifically electrical tomographies are provided by Wakatsuki and Kagawa, Kim et al and Kortschak et al. Aspects of inversion in optical tomography are investigated by Wright et al and Douiri et al. The authors are representative of the worldwide interest in inverse problems relating to engineering applications and their efforts in producing these excellent papers will be appreciated by many readers of this journal.

Inverse problem for multispecies ferromagneticlike mean-field models in phase space with many states

NASA Astrophysics Data System (ADS)

Fedele, Micaela; Vernia, Cecilia

2017-10-01

In this paper we solve the inverse problem for the Curie-Weiss model and its multispecies version when multiple thermodynamic states are present as in the low temperature phase where the phase space is clustered. The inverse problem consists of reconstructing the model parameters starting from configuration data generated according to the distribution of the model. We demonstrate that, without taking into account the presence of many states, the application of the inversion procedure produces very poor inference results. To overcome this problem, we use the clustering algorithm. When the system has two symmetric states of positive and negative magnetizations, the parameter reconstruction can also be obtained with smaller computational effort simply by flipping the sign of the magnetizations from positive to negative (or vice versa). The parameter reconstruction fails when the system undergoes a phase transition: In that case we give the correct inversion formulas for the Curie-Weiss model and we show that they can be used to measure how close the system gets to being critical.

Research on inverse, hybrid and optimization problems in engineering sciences with emphasis on turbomachine aerodynamics: Review of Chinese advances

NASA Technical Reports Server (NTRS)

Liu, Gao-Lian

1991-01-01

Advances in inverse design and optimization theory in engineering fields in China are presented. Two original approaches, the image-space approach and the variational approach, are discussed in terms of turbomachine aerodynamic inverse design. Other areas of research in turbomachine aerodynamic inverse design include the improved mean-streamline (stream surface) method and optimization theory based on optimal control. Among the additional engineering fields discussed are the following: the inverse problem of heat conduction, free-surface flow, variational cogeneration of optimal grid and flow field, and optimal meshing theory of gears.

Domain identification in impedance computed tomography by spline collocation method

NASA Technical Reports Server (NTRS)

Kojima, Fumio

1990-01-01

A method for estimating an unknown domain in elliptic boundary value problems is considered. The problem is formulated as an inverse problem of integral equations of the second kind. A computational method is developed using a splice collocation scheme. The results can be applied to the inverse problem of impedance computed tomography (ICT) for image reconstruction.

Relation of trihalomethane-formation potential to water-quality and physical characteristics of small water-supply lakes, eastern Kansas

USGS Publications Warehouse

Pope, L.M.; Arruda, J.A.; Fromm, C.H.

1988-01-01

The formation of carcinogenic trihalomethanes during the treatment of public surface water supplies has become a potentially serious problem. The U. S. Geological Survey, in cooperation with the Kansas Department of Health and Environment , investigated the potential for trihalomethane formation in water from 15 small, public water supply lakes in eastern Kansas from April 1984 through April 1986 in order to define the principal factors that affect or control the potential for trihalomethane formation during the water treatment process. Relations of mean concentrations of trihalomethane-formation potential to selected water quality and lake and watershed physical characteristics were investigated using correlation and regression analysis. Statistically significant, direct relations were developed between trihalomethanes produced in unfiltered and filtered lake water and mean concentrations of total and dissolved organic carbon. Correlation coefficients for these relations ranged from 0.86 to 0.93. Mean values of maximum depth of lake were shown to have statistically significant inverse relations to mean concentrations of trihalomethane-formation potential and total and dissolved organic carbon. Correlation coefficients for these relations ranged from -0.76 to -0.81. (USGS)

Viscoelastic response of the lateral side of the ankle to cyclic inversion: a time course analysis.

PubMed

Malmir, K; Olyaei, G R; Talebian, S; Jamshidi, A A

2014-12-01

Although important, viscoelastic behavior of the ankle's lateral side has rarely been studied. The present study assesses the viscoelastic behavior during cyclic inversions. Eighteen recreationally active healthy males underwent 40 passive cyclic inversions using a Biodex dynamometer at 5 °/s through 80% of maximum range of motion. Energy absorption and restitution and dissipation coefficient were calculated for each repetition. Changes in the mean of the dependent variables for repetitions 1 (R1 ), R5 , R10 , R15 , R20 , R25 , R30 , R35 and R40 were compared by three one-way analyses of variance with repeated measures. There was a significant difference between the means of energy absorption for the selected repetitions from R1 to R20 (P < 0.01), but there was no significant difference between them from R20 to R40 (P > 0.05). There was no significant difference between the means of energy restitution for the selected repetitions (P > 0.05). Whereas there was no significant difference consecutively between the means of dissipative coefficient for the selected repetitions (P > 0.05), there was a significant difference between the means of R30 or R40 relative to the baseline (P < 0.005). The decrease in the energy absorbed and the dissipation coefficient following repeated inversions may be due to the slippage of collagen fibers. The decrease in the shock absorbing ability of the tissues may expose them to injury. © 2014 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Computational structures for robotic computations

NASA Technical Reports Server (NTRS)

Lee, C. S. G.; Chang, P. R.

1987-01-01

The computational problem of inverse kinematics and inverse dynamics of robot manipulators by taking advantage of parallelism and pipelining architectures is discussed. For the computation of inverse kinematic position solution, a maximum pipelined CORDIC architecture has been designed based on a functional decomposition of the closed-form joint equations. For the inverse dynamics computation, an efficient p-fold parallel algorithm to overcome the recurrence problem of the Newton-Euler equations of motion to achieve the time lower bound of O(log sub 2 n) has also been developed.

A Toolkit for Forward/Inverse Problems in Electrocardiography within the SCIRun Problem Solving Environment

PubMed Central

Burton, Brett M; Tate, Jess D; Erem, Burak; Swenson, Darrell J; Wang, Dafang F; Steffen, Michael; Brooks, Dana H; van Dam, Peter M; Macleod, Rob S

2012-01-01

Computational modeling in electrocardiography often requires the examination of cardiac forward and inverse problems in order to non-invasively analyze physiological events that are otherwise inaccessible or unethical to explore. The study of these models can be performed in the open-source SCIRun problem solving environment developed at the Center for Integrative Biomedical Computing (CIBC). A new toolkit within SCIRun provides researchers with essential frameworks for constructing and manipulating electrocardiographic forward and inverse models in a highly efficient and interactive way. The toolkit contains sample networks, tutorials and documentation which direct users through SCIRun-specific approaches in the assembly and execution of these specific problems. PMID:22254301

An inverse moisture diffusion algorithm for the determination of diffusion coefficient

Treesearch

Jen Y. Liu; William T. Simpson; Steve P. Verrill

2000-01-01

The finite difference approximation is applied to estimate the moisture-dependent diffusion coefficient by utilizing test data of isothermal moisture desorption in northern red oak (Quercus rubra). The test data contain moisture distributions at discrete locations across the thickness of specimens, which coincides with the radial direction of northern red oak, and at...

An inverse moisture diffusion algorithm for the determination of diffusion coefficient

Treesearch

Jen Y. Liu; William T. Simpson; Steve P. Verrill

2001-01-01

The finite difference approximation is applied to estimate the moisture-dependent diffusion coefficient by utilizing test data of isothermal moisture desorption in northern red oak (Quercus rubra). The test data contain moisture distributions at discrete locations across the thickness of specimens, which coincides with the radial direction of northern red oak, and at...

The Form of the Solutions of the Linear Integro-Differential Equations of Subsonic Aeroelasticity.

DTIC Science & Technology

1979-09-01

coefficients w (0) are given in Table 3; it V follows that, for T > 0 and (E - K v2) non-singular, the inverse transform of M- ) has the form, using (B-I) V...degree of freedom system by expanding )M- I in the form of equation (35), obtaining its inverse transform using the v -1results of Appendix A and hence...obtaining the inverse transform of M- l . The two-dimensional case, when the characteristic equation has a zero root, is not as simple. * Assuming all

This is SPIRAL-TAP: Sparse Poisson Intensity Reconstruction ALgorithms--theory and practice.

PubMed

Harmany, Zachary T; Marcia, Roummel F; Willett, Rebecca M

2012-03-01

Observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model. As a result, accurate reconstruction of a spatially or temporally distributed phenomenon (f*) from Poisson data (y) cannot be effectively accomplished by minimizing a conventional penalized least-squares objective function. The problem addressed in this paper is the estimation of f* from y in an inverse problem setting, where the number of unknowns may potentially be larger than the number of observations and f* admits sparse approximation. The optimization formulation considered in this paper uses a penalized negative Poisson log-likelihood objective function with nonnegativity constraints (since Poisson intensities are naturally nonnegative). In particular, the proposed approach incorporates key ideas of using separable quadratic approximations to the objective function at each iteration and penalization terms related to l1 norms of coefficient vectors, total variation seminorms, and partition-based multiscale estimation methods.

The role of simulated small-scale ocean variability in inverse computations for ocean acoustic tomography.

PubMed

Dushaw, Brian D; Sagen, Hanne

2017-12-01

Ocean acoustic tomography depends on a suitable reference ocean environment with which to set the basic parameters of the inverse problem. Some inverse problems may require a reference ocean that includes the small-scale variations from internal waves, small mesoscale, or spice. Tomographic inversions that employ data of stable shadow zone arrivals, such as those that have been observed in the North Pacific and Canary Basin, are an example. Estimating temperature from the unique acoustic data that have been obtained in Fram Strait is another example. The addition of small-scale variability to augment a smooth reference ocean is essential to understanding the acoustic forward problem in these cases. Rather than a hindrance, the stochastic influences of the small scale can be exploited to obtain accurate inverse estimates. Inverse solutions are readily obtained, and they give computed arrival patterns that matched the observations. The approach is not ad hoc, but universal, and it has allowed inverse estimates for ocean temperature variations in Fram Strait to be readily computed on several acoustic paths for which tomographic data were obtained.

Joint Geophysical Inversion With Multi-Objective Global Optimization Methods

NASA Astrophysics Data System (ADS)

Lelievre, P. G.; Bijani, R.; Farquharson, C. G.

2015-12-01

Pareto multi-objective global optimization (PMOGO) methods generate a suite of solutions that minimize multiple objectives (e.g. data misfits and regularization terms) in a Pareto-optimal sense. Providing a suite of models, as opposed to a single model that minimizes a weighted sum of objectives, allows a more complete assessment of the possibilities and avoids the often difficult choice of how to weight each objective. We are applying PMOGO methods to three classes of inverse problems. The first class are standard mesh-based problems where the physical property values in each cell are treated as continuous variables. The second class of problems are also mesh-based but cells can only take discrete physical property values corresponding to known or assumed rock units. In the third class we consider a fundamentally different type of inversion in which a model comprises wireframe surfaces representing contacts between rock units; the physical properties of each rock unit remain fixed while the inversion controls the position of the contact surfaces via control nodes. This third class of problem is essentially a geometry inversion, which can be used to recover the unknown geometry of a target body or to investigate the viability of a proposed Earth model. Joint inversion is greatly simplified for the latter two problem classes because no additional mathematical coupling measure is required in the objective function. PMOGO methods can solve numerically complicated problems that could not be solved with standard descent-based local minimization methods. This includes the latter two classes of problems mentioned above. There are significant increases in the computational requirements when PMOGO methods are used but these can be ameliorated using parallelization and problem dimension reduction strategies.

An inverse dynamics approach to trajectory optimization and guidance for an aerospace plane

NASA Technical Reports Server (NTRS)

Lu, Ping

1992-01-01

The optimal ascent problem for an aerospace planes is formulated as an optimal inverse dynamic problem. Both minimum-fuel and minimax type of performance indices are considered. Some important features of the optimal trajectory and controls are used to construct a nonlinear feedback midcourse controller, which not only greatly simplifies the difficult constrained optimization problem and yields improved solutions, but is also suited for onboard implementation. Robust ascent guidance is obtained by using combination of feedback compensation and onboard generation of control through the inverse dynamics approach. Accurate orbital insertion can be achieved with near-optimal control of the rocket through inverse dynamics even in the presence of disturbances.

Time-reversal and Bayesian inversion

NASA Astrophysics Data System (ADS)

Debski, Wojciech

2017-04-01

Probabilistic inversion technique is superior to the classical optimization-based approach in all but one aspects. It requires quite exhaustive computations which prohibit its use in huge size inverse problems like global seismic tomography or waveform inversion to name a few. The advantages of the approach are, however, so appealing that there is an ongoing continuous afford to make the large inverse task as mentioned above manageable with the probabilistic inverse approach. One of the perspective possibility to achieve this goal relays on exploring the internal symmetry of the seismological modeling problems in hand - a time reversal and reciprocity invariance. This two basic properties of the elastic wave equation when incorporating into the probabilistic inversion schemata open a new horizons for Bayesian inversion. In this presentation we discuss the time reversal symmetry property, its mathematical aspects and propose how to combine it with the probabilistic inverse theory into a compact, fast inversion algorithm. We illustrate the proposed idea with the newly developed location algorithm TRMLOC and discuss its efficiency when applied to mining induced seismic data.

Joint Inversion of Body-Wave Arrival Times and Surface-Wave Dispersion Data in the Wavelet Domain Constrained by Sparsity Regularization

NASA Astrophysics Data System (ADS)

Zhang, H.; Fang, H.; Yao, H.; Maceira, M.; van der Hilst, R. D.

2014-12-01

Recently, Zhang et al. (2014, Pure and Appiled Geophysics) have developed a joint inversion code incorporating body-wave arrival times and surface-wave dispersion data. The joint inversion code was based on the regional-scale version of the double-difference tomography algorithm tomoDD. The surface-wave inversion part uses the propagator matrix solver in the algorithm DISPER80 (Saito, 1988) for forward calculation of dispersion curves from layered velocity models and the related sensitivities. The application of the joint inversion code to the SAFOD site in central California shows that the fault structure is better imaged in the new model, which is able to fit both the body-wave and surface-wave observations adequately. Here we present a new joint inversion method that solves the model in the wavelet domain constrained by sparsity regularization. Compared to the previous method, it has the following advantages: (1) The method is both data- and model-adaptive. For the velocity model, it can be represented by different wavelet coefficients at different scales, which are generally sparse. By constraining the model wavelet coefficients to be sparse, the inversion in the wavelet domain can inherently adapt to the data distribution so that the model has higher spatial resolution in the good data coverage zone. Fang and Zhang (2014, Geophysical Journal International) have showed the superior performance of the wavelet-based double-difference seismic tomography method compared to the conventional method. (2) For the surface wave inversion, the joint inversion code takes advantage of the recent development of direct inversion of surface wave dispersion data for 3-D variations of shear wave velocity without the intermediate step of phase or group velocity maps (Fang et al., 2014, Geophysical Journal International). A fast marching method is used to compute, at each period, surface wave traveltimes and ray paths between sources and receivers. We will test the new joint inversion code at the SAFOD site to compare its performance over the previous code. We will also select another fault zone such as the San Jacinto Fault Zone to better image its structure.

Inverse random source scattering for the Helmholtz equation in inhomogeneous media

NASA Astrophysics Data System (ADS)

Li, Ming; Chen, Chuchu; Li, Peijun

2018-01-01

This paper is concerned with an inverse random source scattering problem in an inhomogeneous background medium. The wave propagation is modeled by the stochastic Helmholtz equation with the source driven by additive white noise. The goal is to reconstruct the statistical properties of the random source such as the mean and variance from the boundary measurement of the radiated random wave field at multiple frequencies. Both the direct and inverse problems are considered. We show that the direct problem has a unique mild solution by a constructive proof. For the inverse problem, we derive Fredholm integral equations, which connect the boundary measurement of the radiated wave field with the unknown source function. A regularized block Kaczmarz method is developed to solve the ill-posed integral equations. Numerical experiments are included to demonstrate the effectiveness of the proposed method.

Rapid processing of data based on high-performance algorithms for solving inverse problems and 3D-simulation of the tsunami and earthquakes

NASA Astrophysics Data System (ADS)

Marinin, I. V.; Kabanikhin, S. I.; Krivorotko, O. I.; Karas, A.; Khidasheli, D. G.

2012-04-01

We consider new techniques and methods for earthquake and tsunami related problems, particularly - inverse problems for the determination of tsunami source parameters, numerical simulation of long wave propagation in soil and water and tsunami risk estimations. In addition, we will touch upon the issue of database management and destruction scenario visualization. New approaches and strategies, as well as mathematical tools and software are to be shown. The long joint investigations by researchers of the Institute of Mathematical Geophysics and Computational Mathematics SB RAS and specialists from WAPMERR and Informap have produced special theoretical approaches, numerical methods, and software tsunami and earthquake modeling (modeling of propagation and run-up of tsunami waves on coastal areas), visualization, risk estimation of tsunami, and earthquakes. Algorithms are developed for the operational definition of the origin and forms of the tsunami source. The system TSS numerically simulates the source of tsunami and/or earthquakes and includes the possibility to solve the direct and the inverse problem. It becomes possible to involve advanced mathematical results to improve models and to increase the resolution of inverse problems. Via TSS one can construct maps of risks, the online scenario of disasters, estimation of potential damage to buildings and roads. One of the main tools for the numerical modeling is the finite volume method (FVM), which allows us to achieve stability with respect to possible input errors, as well as to achieve optimum computing speed. Our approach to the inverse problem of tsunami and earthquake determination is based on recent theoretical results concerning the Dirichlet problem for the wave equation. This problem is intrinsically ill-posed. We use the optimization approach to solve this problem and SVD-analysis to estimate the degree of ill-posedness and to find the quasi-solution. The software system we developed is intended to create technology «no frost», realizing a steady stream of direct and inverse problems: solving the direct problem, the visualization and comparison with observed data, to solve the inverse problem (correction of the model parameters). The main objective of further work is the creation of a workstation operating emergency tool that could be used by an emergency duty person in real time.

PREFACE: First International Congress of the International Association of Inverse Problems (IPIA): Applied Inverse Problems 2007: Theoretical and Computational Aspects

NASA Astrophysics Data System (ADS)

Uhlmann, Gunther

2008-07-01

This volume represents the proceedings of the fourth Applied Inverse Problems (AIP) international conference and the first congress of the Inverse Problems International Association (IPIA) which was held in Vancouver, Canada, June 25 29, 2007. The organizing committee was formed by Uri Ascher, University of British Columbia, Richard Froese, University of British Columbia, Gary Margrave, University of Calgary, and Gunther Uhlmann, University of Washington, chair. The conference was part of the activities of the Pacific Institute of Mathematical Sciences (PIMS) Collaborative Research Group on inverse problems (http://www.pims.math.ca/scientific/collaborative-research-groups/past-crgs). This event was also supported by grants from NSF and MITACS. Inverse Problems (IP) are problems where causes for a desired or an observed effect are to be determined. They lie at the heart of scientific inquiry and technological development. The enormous increase in computing power and the development of powerful algorithms have made it possible to apply the techniques of IP to real-world problems of growing complexity. Applications include a number of medical as well as other imaging techniques, location of oil and mineral deposits in the earth's substructure, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes and, more recently, modelling in the life sciences. The series of Applied Inverse Problems (AIP) Conferences aims to provide a primary international forum for academic and industrial researchers working on all aspects of inverse problems, such as mathematical modelling, functional analytic methods, computational approaches, numerical algorithms etc. The steering committee of the AIP conferences consists of Heinz Engl (Johannes Kepler Universität, Austria), Joyce McLaughlin (RPI, USA), William Rundell (Texas A&M, USA), Erkki Somersalo (Helsinki University of Technology, Finland), Masahiro Yamamoto (University of Tokyo, Japan), Gunther Uhlmann (University of Washington) and Jun Zou (Chinese University of Hong Kong). IPIA is a recently formed organization that intends to promote the field of inverse problem at all levels. See http://www.inverse-problems.net/. IPIA awarded the first Calderón prize at the opening of the conference to Matti Lassas (see first article in the Proceedings). There was also a general meeting of IPIA during the workshop. This was probably the largest conference ever on IP with 350 registered participants. The program consisted of 18 invited speakers and the Calderón Prize Lecture given by Matti Lassas. Another integral part of the program was the more than 60 mini-symposia that covered a broad spectrum of the theory and applications of inverse problems, focusing on recent developments in medical imaging, seismic exploration, remote sensing, industrial applications, numerical and regularization methods in inverse problems. Another important related topic was image processing in particular the advances which have allowed for significant enhancement of widely used imaging techniques. For more details on the program see the web page: http://www.pims.math.ca/science/2007/07aip. These proceedings reflect the broad spectrum of topics covered in AIP 2007. The conference and these proceedings would not have happened without the contributions of many people. I thank all my fellow organizers, the invited speakers, the speakers and organizers of mini-symposia for making this an exciting and vibrant event. I also thank PIMS, NSF and MITACS for their generous financial support. I take this opportunity to thank the PIMS staff, particularly Ken Leung, for making the local arrangements. Also thanks are due to Stephen McDowall for his help in preparing the schedule of the conference and Xiaosheng Li for the help in preparing these proceedings. I also would like to thank the contributors of this volume and the referees. Finally, many thanks are due to Graham Douglas and Elaine Longden-Chapman for suggesting publication in Journal of Physics: Conference Series.

Modular Approaches to Earth Science Scientific Computing: 3D Electromagnetic Induction Modeling as an Example

NASA Astrophysics Data System (ADS)

Tandon, K.; Egbert, G.; Siripunvaraporn, W.

2003-12-01

We are developing a modular system for three-dimensional inversion of electromagnetic (EM) induction data, using an object oriented programming approach. This approach allows us to modify the individual components of the inversion scheme proposed, and also reuse the components for variety of problems in earth science computing howsoever diverse they might be. In particular, the modularity allows us to (a) change modeling codes independently of inversion algorithm details; (b) experiment with new inversion algorithms; and (c) modify the way prior information is imposed in the inversion to test competing hypothesis and techniques required to solve an earth science problem. Our initial code development is for EM induction equations on a staggered grid, using iterative solution techniques in 3D. An example illustrated here is an experiment with the sensitivity of 3D magnetotelluric inversion to uncertainties in the boundary conditions required for regional induction problems. These boundary conditions should reflect the large-scale geoelectric structure of the study area, which is usually poorly constrained. In general for inversion of MT data, one fixes boundary conditions at the edge of the model domain, and adjusts the earth?s conductivity structure within the modeling domain. Allowing for errors in specification of the open boundary values is simple in principle, but no existing inversion codes that we are aware of have this feature. Adding a feature such as this is straightforward within the context of the modular approach. More generally, a modular approach provides an efficient methodology for setting up earth science computing problems to test various ideas. As a concrete illustration relevant to EM induction problems, we investigate the sensitivity of MT data near San Andreas Fault at Parkfield (California) to uncertainties in the regional geoelectric structure.

Definition and solution of a stochastic inverse problem for the Manning’s n parameter field in hydrodynamic models

DOE PAGES

Butler, Troy; Graham, L.; Estep, D.; ...

2015-02-03

The uncertainty in spatially heterogeneous Manning’s n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented in this paper. Technical details that arise in practice by applying the framework to determine the Manning’s n parameter field in amore » shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of “condition” for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. Finally, this notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning’s n parameter and the effect on model predictions is analyzed.« less

Improved definition of crustal anomalies for Magsat data

NASA Technical Reports Server (NTRS)

1981-01-01

A scheme was developed for separating the portions of the magnetic field measured by the Magsat 1 satellite that arise from internal and external sources. To test this method, a set of sample coefficients were used to compute the field values along a simulated satellite orbit. This data was then used to try to recover the original coefficients. Matrix inversion and recursive least squares methods were used to solve for the input coefficients. The accuracy of the two methods are compared.

A Riemann-Hilbert approach to the inverse problem for the Stark operator on the line

NASA Astrophysics Data System (ADS)

Its, A.; Sukhanov, V.

2016-05-01

The paper is concerned with the inverse scattering problem for the Stark operator on the line with a potential from the Schwartz class. In our study of the inverse problem, we use the Riemann-Hilbert formalism. This allows us to overcome the principal technical difficulties which arise in the more traditional approaches based on the Gel’fand-Levitan-Marchenko equations, and indeed solve the problem. We also produce a complete description of the relevant scattering data (which have not been obtained in the previous works on the Stark operator) and establish the bijection between the Schwartz class potentials and the scattering data.

Approximation Of Multi-Valued Inverse Functions Using Clustering And Sugeno Fuzzy Inference

NASA Technical Reports Server (NTRS)

Walden, Maria A.; Bikdash, Marwan; Homaifar, Abdollah

1998-01-01

Finding the inverse of a continuous function can be challenging and computationally expensive when the inverse function is multi-valued. Difficulties may be compounded when the function itself is difficult to evaluate. We show that we can use fuzzy-logic approximators such as Sugeno inference systems to compute the inverse on-line. To do so, a fuzzy clustering algorithm can be used in conjunction with a discriminating function to split the function data into branches for the different values of the forward function. These data sets are then fed into a recursive least-squares learning algorithm that finds the proper coefficients of the Sugeno approximators; each Sugeno approximator finds one value of the inverse function. Discussions about the accuracy of the approximation will be included.

Development of a Preventive HIV Vaccine Requires Solving Inverse Problems Which Is Unattainable by Rational Vaccine Design

PubMed Central

Van Regenmortel, Marc H. V.

2018-01-01

Hypotheses and theories are essential constituents of the scientific method. Many vaccinologists are unaware that the problems they try to solve are mostly inverse problems that consist in imagining what could bring about a desired outcome. An inverse problem starts with the result and tries to guess what are the multiple causes that could have produced it. Compared to the usual direct scientific problems that start with the causes and derive or calculate the results using deductive reasoning and known mechanisms, solving an inverse problem uses a less reliable inductive approach and requires the development of a theoretical model that may have different solutions or none at all. Unsuccessful attempts to solve inverse problems in HIV vaccinology by reductionist methods, systems biology and structure-based reverse vaccinology are described. The popular strategy known as rational vaccine design is unable to solve the multiple inverse problems faced by HIV vaccine developers. The term “rational” is derived from “rational drug design” which uses the 3D structure of a biological target for designing molecules that will selectively bind to it and inhibit its biological activity. In vaccine design, however, the word “rational” simply means that the investigator is concentrating on parts of the system for which molecular information is available. The economist and Nobel laureate Herbert Simon introduced the concept of “bounded rationality” to explain why the complexity of the world economic system makes it impossible, for instance, to predict an event like the financial crash of 2007–2008. Humans always operate under unavoidable constraints such as insufficient information, a limited capacity to process huge amounts of data and a limited amount of time available to reach a decision. Such limitations always prevent us from achieving the complete understanding and optimization of a complex system that would be needed to achieve a truly rational design process. This is why the complexity of the human immune system prevents us from rationally designing an HIV vaccine by solving inverse problems. PMID:29387066

The importance of coherence in inverse problems in optics

NASA Astrophysics Data System (ADS)

Ferwerda, H. A.; Baltes, H. P.; Glass, A. S.; Steinle, B.

1981-12-01

Current inverse problems of statistical optics are presented with a guide to relevant literature. The inverse problems are categorized into four groups, and the Van Cittert-Zernike theorem and its generalization are discussed. The retrieval of structural information from the far-zone degree of coherence and the time-averaged intensity distribution of radiation scattered by a superposition of random and periodic scatterers are also discussed. In addition, formulas for the calculation of far-zone properties are derived within the framework of scalar optics, and results are applied to two examples.

FOREWORD: Tackling inverse problems in a Banach space environment: from theory to applications Tackling inverse problems in a Banach space environment: from theory to applications

NASA Astrophysics Data System (ADS)

Schuster, Thomas; Hofmann, Bernd; Kaltenbacher, Barbara

2012-10-01

Inverse problems can usually be modelled as operator equations in infinite-dimensional spaces with a forward operator acting between Hilbert or Banach spaces—a formulation which quite often also serves as the basis for defining and analyzing solution methods. The additional amount of structure and geometric interpretability provided by the concept of an inner product has rendered these methods amenable to a convergence analysis, a fact which has led to a rigorous and comprehensive study of regularization methods in Hilbert spaces over the last three decades. However, for numerous problems such as x-ray diffractometry, certain inverse scattering problems and a number of parameter identification problems in PDEs, the reasons for using a Hilbert space setting seem to be based on conventions rather than an appropriate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, non-Hilbertian regularization and data fidelity terms incorporating a priori information on solution and noise, such as general Lp-norms, TV-type norms, or the Kullback-Leibler divergence, have recently become very popular. These facts have motivated intensive investigations on regularization methods in Banach spaces, a topic which has emerged as a highly active research field within the area of inverse problems. Meanwhile some of the most well-known regularization approaches, such as Tikhonov-type methods requiring the solution of extremal problems, and iterative ones like the Landweber method, the Gauss-Newton method, as well as the approximate inverse method, have been investigated for linear and nonlinear operator equations in Banach spaces. Convergence with rates has been proven and conditions on the solution smoothness and on the structure of nonlinearity have been formulated. Still, beyond the existing results a large number of challenging open questions have arisen, due to the more involved handling of general Banach spaces and the larger variety of concrete instances with special properties. The aim of this special section is to provide a forum for highly topical ongoing work in the area of regularization in Banach spaces, its numerics and its applications. Indeed, we have been lucky enough to obtain a number of excellent papers both from colleagues who have previously been contributing to this topic and from researchers entering the field due to its relevance in practical inverse problems. We would like to thank all contributers for enabling us to present a high quality collection of papers on topics ranging from various aspects of regularization via efficient numerical solution to applications in PDE models. We give a brief overview of the contributions included in this issue (here ordered alphabetically by first author). In their paper, Iterative regularization with general penalty term—theory and application to L1 and TV regularization, Radu Bot and Torsten Hein provide an extension of the Landweber iteration for linear operator equations in Banach space to general operators in place of the inverse duality mapping, which corresponds to the use of general regularization functionals in variational regularization. The L∞ topology in data space corresponds to the frequently occuring situation of uniformly distributed data noise. A numerically efficient solution of the resulting Tikhonov regularization problem via a Moreau-Yosida appriximation and a semismooth Newton method, along with a δ-free regularization parameter choice rule, is the topic of the paper L∞ fitting for inverse problems with uniform noise by Christian Clason. Extension of convergence rates results from classical source conditions to their generalization via variational inequalities with a priori and a posteriori stopping rules is the main contribution of the paper Regularization of linear ill-posed problems by the augmented Lagrangian method and variational inequalities by Klaus Frick and Markus Grasmair, again in the context of some iterative method. A powerful tool for proving convergence rates of Tikhonov type but also other regularization methods in Banach spaces are assumptions of the type of variational inequalities that combine conditions on solution smoothness (i.e., source conditions in the Hilbert space case) and nonlinearity of the forward operator. In Parameter choice in Banach space regularization under variational inequalities, Bernd Hofmann and Peter Mathé provide results with general error measures and especially study the question of regularization parameter choice. Daijun Jiang, Hui Feng, and Jun Zou consider an application of Banach space ideas in the context of an application problem in their paper Convergence rates of Tikhonov regularizations for parameter identifiation in a parabolic-elliptic system, namely the identification of a distributed diffusion coefficient in a coupled elliptic-parabolic system. In particular, they show convergence rates of Lp-H1 (variational) regularization for the application under consideration via the use and verification of certain source and nonlinearity conditions. In computational practice, the Lp norm with p close to one is often used as a substitute for the actually sparsity promoting L1 norm. In Norm sensitivity of sparsity regularization with respect to p, Kamil S Kazimierski, Peter Maass and Robin Strehlow consider the question of how sensitive the Tikhonov regularized solution is with respect to p. They do so by computing the derivative via the implicit function theorem, particularly at the crucial value, p=1. Another iterative regularization method in Banach space is considered by Qinian Jin and Linda Stals in Nonstationary iterated Tikhonov regularization for ill-posed problems in Banach spaces. Using a variational formulation and under some smoothness and convexity assumption on the preimage space, they extend the convergence analysis of the well-known iterative Tikhonov method for linear problems in Hilbert space to a more general Banach space framework. Systems of linear or nonlinear operators can be efficiently treated by cyclic iterations, thus several variants of gradient and Newton-type Kaczmarz methods have already been studied in the Hilbert space setting. Antonio Leitão and M Marques Alves in their paper On Landweber---Kaczmarz methods for regularizing systems of ill-posed equations in Banach spaces carry out an extension to Banach spaces for the fundamental Landweber version. The impact of perturbations in the evaluation of the forward operator and its derivative on the convergence behaviour of regularization methods is a practically and highly relevant issue. It is treated in the paper Convergence rates analysis of Tikhonov regularization for nonlinear ill-posed problems with noisy operators by Shuai Lu and Jens Flemming for variational regularization of nonlinear problems in Banach spaces. In The approximate inverse in action: IV. Semi-discrete equations in a Banach space setting, Thomas Schuster, Andreas Rieder and Frank Schöpfer extend the concept of approximate inverse to the practically and highly relevant situation of finitely many measurements and a general smooth and convex Banach space as preimage space. They devise two approaches for computing the reconstruction kernels required in the method and provide convergence and regularization results. Frank Werner and Thorsten Hohage in Convergence rates in expectation for Tikhonov-type regularization of inverse problems with Poisson data prove convergence rates results for variational regularization with general convex regularization term and the Kullback-Leibler distance as data fidelity term by combining a new result on Poisson distributed data with a deterministic rates analysis. Finally, we would like to thank the Inverse Problems team, especially Joanna Evangelides and Chris Wileman, for their extraordinary smooth and productive cooperation, as well as Alfred K Louis for his kind support of our initiative.

Comparison of iterative inverse coarse-graining methods

NASA Astrophysics Data System (ADS)

Rosenberger, David; Hanke, Martin; van der Vegt, Nico F. A.

2016-10-01

Deriving potentials for coarse-grained Molecular Dynamics (MD) simulations is frequently done by solving an inverse problem. Methods like Iterative Boltzmann Inversion (IBI) or Inverse Monte Carlo (IMC) have been widely used to solve this problem. The solution obtained by application of these methods guarantees a match in the radial distribution function (RDF) between the underlying fine-grained system and the derived coarse-grained system. However, these methods often fail in reproducing thermodynamic properties. To overcome this deficiency, additional thermodynamic constraints such as pressure or Kirkwood-Buff integrals (KBI) may be added to these methods. In this communication we test the ability of these methods to converge to a known solution of the inverse problem. With this goal in mind we have studied a binary mixture of two simple Lennard-Jones (LJ) fluids, in which no actual coarse-graining is performed. We further discuss whether full convergence is actually needed to achieve thermodynamic representability.

Atmospheric inverse modeling via sparse reconstruction

NASA Astrophysics Data System (ADS)

Hase, Nils; Miller, Scot M.; Maaß, Peter; Notholt, Justus; Palm, Mathias; Warneke, Thorsten

2017-10-01

Many applications in atmospheric science involve ill-posed inverse problems. A crucial component of many inverse problems is the proper formulation of a priori knowledge about the unknown parameters. In most cases, this knowledge is expressed as a Gaussian prior. This formulation often performs well at capturing smoothed, large-scale processes but is often ill equipped to capture localized structures like large point sources or localized hot spots. Over the last decade, scientists from a diverse array of applied mathematics and engineering fields have developed sparse reconstruction techniques to identify localized structures. In this study, we present a new regularization approach for ill-posed inverse problems in atmospheric science. It is based on Tikhonov regularization with sparsity constraint and allows bounds on the parameters. We enforce sparsity using a dictionary representation system. We analyze its performance in an atmospheric inverse modeling scenario by estimating anthropogenic US methane (CH4) emissions from simulated atmospheric measurements. Different measures indicate that our sparse reconstruction approach is better able to capture large point sources or localized hot spots than other methods commonly used in atmospheric inversions. It captures the overall signal equally well but adds details on the grid scale. This feature can be of value for any inverse problem with point or spatially discrete sources. We show an example for source estimation of synthetic methane emissions from the Barnett shale formation.

Variable-permittivity linear inverse problem for the H(sub z)-polarized case

NASA Technical Reports Server (NTRS)

Moghaddam, M.; Chew, W. C.

1993-01-01

The H(sub z)-polarized inverse problem has rarely been studied before due to the complicated way in which the unknown permittivity appears in the wave equation. This problem is equivalent to the acoustic inverse problem with variable density. We have recently reported the solution to the nonlinear variable-permittivity H(sub z)-polarized inverse problem using the Born iterative method. Here, the linear inverse problem is solved for permittivity (epsilon) and permeability (mu) using a different approach which is an extension of the basic ideas of diffraction tomography (DT). The key to solving this problem is to utilize frequency diversity to obtain the required independent measurements. The receivers are assumed to be in the far field of the object, and plane wave incidence is also assumed. It is assumed that the scatterer is weak, so that the Born approximation can be used to arrive at a relationship between the measured pressure field and two terms related to the spatial Fourier transform of the two unknowns, epsilon and mu. The term involving permeability corresponds to monopole scattering and that for permittivity to dipole scattering. Measurements at several frequencies are used and a least squares problem is solved to reconstruct epsilon and mu. It is observed that the low spatial frequencies in the spectra of epsilon and mu produce inaccuracies in the results. Hence, a regularization method is devised to remove this problem. Several results are shown. Low contrast objects for which the above analysis holds are used to show that good reconstructions are obtained for both permittivity and permeability after regularization is applied.

On computational experiments in some inverse problems of heat and mass transfer

NASA Astrophysics Data System (ADS)

Bilchenko, G. G.; Bilchenko, N. G.

2016-11-01

The results of mathematical modeling of effective heat and mass transfer on hypersonic aircraft permeable surfaces are considered. The physic-chemical processes (the dissociation and the ionization) in laminar boundary layer of compressible gas are appreciated. Some algorithms of control restoration are suggested for the interpolation and approximation statements of heat and mass transfer inverse problems. The differences between the methods applied for the problem solutions search for these statements are discussed. Both the algorithms are realized as programs. Many computational experiments were accomplished with the use of these programs. The parameters of boundary layer obtained by means of the A.A.Dorodnicyn's generalized integral relations method from solving the direct problems have been used to obtain the inverse problems solutions. Two types of blowing laws restoration for the inverse problem in interpolation statement are presented as the examples. The influence of the temperature factor on the blowing restoration is investigated. The different character of sensitivity of controllable parameters (the local heat flow and local tangent friction) respectively to step (discrete) changing of control (the blowing) and the switching point position is studied.

Design and test of a natural laminar flow/large Reynolds number airfoil with a high design cruise lift coefficient

NASA Technical Reports Server (NTRS)

Kolesar, C. E.

1987-01-01

Research activity on an airfoil designed for a large airplane capable of very long endurance times at a low Mach number of 0.22 is examined. Airplane mission objectives and design optimization resulted in requirements for a very high design lift coefficient and a large amount of laminar flow at high Reynolds number to increase the lift/drag ratio and reduce the loiter lift coefficient. Natural laminar flow was selected instead of distributed mechanical suction for the measurement technique. A design lift coefficient of 1.5 was identified as the highest which could be achieved with a large extent of laminar flow. A single element airfoil was designed using an inverse boundary layer solution and inverse airfoil design computer codes to create an airfoil section that would achieve performance goals. The design process and results, including airfoil shape, pressure distributions, and aerodynamic characteristics are presented. A two dimensional wind tunnel model was constructed and tested in a NASA Low Turbulence Pressure Tunnel which enabled testing at full scale design Reynolds number. A comparison is made between theoretical and measured results to establish accuracy and quality of the airfoil design technique.

Filtering techniques for efficient inversion of two-dimensional Nuclear Magnetic Resonance data

NASA Astrophysics Data System (ADS)

Bortolotti, V.; Brizi, L.; Fantazzini, P.; Landi, G.; Zama, F.

2017-10-01

The inversion of two-dimensional Nuclear Magnetic Resonance (NMR) data requires the solution of a first kind Fredholm integral equation with a two-dimensional tensor product kernel and lower bound constraints. For the solution of this ill-posed inverse problem, the recently presented 2DUPEN algorithm [V. Bortolotti et al., Inverse Problems, 33(1), 2016] uses multiparameter Tikhonov regularization with automatic choice of the regularization parameters. In this work, I2DUPEN, an improved version of 2DUPEN that implements Mean Windowing and Singular Value Decomposition filters, is deeply tested. The reconstruction problem with filtered data is formulated as a compressed weighted least squares problem with multi-parameter Tikhonov regularization. Results on synthetic and real 2D NMR data are presented with the main purpose to deeper analyze the separate and combined effects of these filtering techniques on the reconstructed 2D distribution.

Regularization Reconstruction Method for Imaging Problems in Electrical Capacitance Tomography

NASA Astrophysics Data System (ADS)

Chu, Pan; Lei, Jing

2017-11-01

The electrical capacitance tomography (ECT) is deemed to be a powerful visualization measurement technique for the parametric measurement in a multiphase flow system. The inversion task in the ECT technology is an ill-posed inverse problem, and seeking for an efficient numerical method to improve the precision of the reconstruction images is important for practical measurements. By the introduction of the Tikhonov regularization (TR) methodology, in this paper a loss function that emphasizes the robustness of the estimation and the low rank property of the imaging targets is put forward to convert the solution of the inverse problem in the ECT reconstruction task into a minimization problem. Inspired by the split Bregman (SB) algorithm, an iteration scheme is developed for solving the proposed loss function. Numerical experiment results validate that the proposed inversion method not only reconstructs the fine structures of the imaging targets, but also improves the robustness.

Termination Proofs for String Rewriting Systems via Inverse Match-Bounds

NASA Technical Reports Server (NTRS)

Butler, Ricky (Technical Monitor); Geser, Alfons; Hofbauer, Dieter; Waldmann, Johannes

2004-01-01

Annotating a letter by a number, one can record information about its history during a reduction. A string rewriting system is called match-bounded if there is a global upper bound to these numbers. In earlier papers we established match-boundedness as a strong sufficient criterion for both termination and preservation of regular languages. We show now that the string rewriting system whose inverse (left and right hand sides exchanged) is match-bounded, also have exceptional properties, but slightly different ones. Inverse match-bounded systems effectively preserve context-free languages; their sets of normalized strings and their sets of immortal strings are effectively regular. These sets of strings can be used to decide the normalization, the termination and the uniform termination problems of inverse match-bounded systems. We also show that the termination problem is decidable in linear time, and that a certain strong reachability problem is deciable, thus solving two open problems of McNaughton's.

The inverse Wiener polarity index problem for chemical trees.

PubMed

Du, Zhibin; Ali, Akbar

2018-01-01

The Wiener polarity number (which, nowadays, known as the Wiener polarity index and usually denoted by Wp) was devised by the chemist Harold Wiener, for predicting the boiling points of alkanes. The index Wp of chemical trees (chemical graphs representing alkanes) is defined as the number of unordered pairs of vertices (carbon atoms) at distance 3. The inverse problems based on some well-known topological indices have already been addressed in the literature. The solution of such inverse problems may be helpful in speeding up the discovery of lead compounds having the desired properties. This paper is devoted to solving a stronger version of the inverse problem based on Wiener polarity index for chemical trees. More precisely, it is proved that for every integer t ∈ {n - 3, n - 2,…,3n - 16, 3n - 15}, n ≥ 6, there exists an n-vertex chemical tree T such that Wp(T) = t.

Assimilating data into open ocean tidal models

NASA Astrophysics Data System (ADS)

Kivman, Gennady A.

The problem of deriving tidal fields from observations by reason of incompleteness and imperfectness of every data set practically available has an infinitely large number of allowable solutions fitting the data within measurement errors and hence can be treated as ill-posed. Therefore, interpolating the data always relies on some a priori assumptions concerning the tides, which provide a rule of sampling or, in other words, a regularization of the ill-posed problem. Data assimilation procedures used in large scale tide modeling are viewed in a common mathematical framework as such regularizations. It is shown that they all (basis functions expansion, parameter estimation, nudging, objective analysis, general inversion, and extended general inversion), including those (objective analysis and general inversion) originally formulated in stochastic terms, may be considered as utilizations of one of the three general methods suggested by the theory of ill-posed problems. The problem of grid refinement critical for inverse methods and nudging is discussed.

Fast and robust estimation of ophthalmic wavefront aberrations

NASA Astrophysics Data System (ADS)

Dillon, Keith

2016-12-01

Rapidly rising levels of myopia, particularly in the developing world, have led to an increased need for inexpensive and automated approaches to optometry. A simple and robust technique is provided for estimating major ophthalmic aberrations using a gradient-based wavefront sensor. The approach is based on the use of numerical calculations to produce diverse combinations of phase components, followed by Fourier transforms to calculate the coefficients. The approach does not utilize phase unwrapping nor iterative solution of inverse problems. This makes the method very fast and tolerant to image artifacts, which do not need to be detected and masked or interpolated as is needed in other techniques. These features make it a promising algorithm on which to base low-cost devices for applications that may have limited access to expert maintenance and operation.

Density-to-Potential Inversions to Guide Development of Exchange-Correlation Approximations at Finite Temperature

NASA Astrophysics Data System (ADS)

Jensen, Daniel; Wasserman, Adam; Baczewski, Andrew

The construction of approximations to the exchange-correlation potential for warm dense matter (WDM) is a topic of significant recent interest. In this work, we study the inverse problem of Kohn-Sham (KS) DFT as a means of guiding functional design at zero temperature and in WDM. Whereas the forward problem solves the KS equations to produce a density from a specified exchange-correlation potential, the inverse problem seeks to construct the exchange-correlation potential from specified densities. These two problems require different computational methods and convergence criteria despite sharing the same mathematical equations. We present two new inversion methods based on constrained variational and PDE-constrained optimization methods. We adapt these methods to finite temperature calculations to reveal the exchange-correlation potential's temperature dependence in WDM-relevant conditions. The different inversion methods presented are applied to both non-interacting and interacting model systems for comparison. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Security Administration under contract DE-AC04-94.

Particle tracking by using single coefficient of Wigner-Ville distribution

NASA Astrophysics Data System (ADS)

Widjaja, J.; Dawprateep, S.; Chuamchaitrakool, P.; Meemon, P.

2016-11-01

A new method for extracting information from particle holograms by using a single coefficient of Wigner-Ville distribution (WVD) is proposed to obviate drawbacks of conventional numerical reconstructions. Our previous study found that analysis of the holograms by using the WVD gives output coefficients which are mainly confined along a diagonal direction intercepted at the origin of the WVD plane. The slope of this diagonal direction is inversely proportional to the particle position. One of these coefficients always has minimum amplitude, regardless of the particle position. By detecting position of the coefficient with minimum amplitude in the WVD plane, the particle position can be accurately measured. The proposed method is verified through computer simulations.

Performance impact of mutation operators of a subpopulation-based genetic algorithm for multi-robot task allocation problems.

PubMed

Liu, Chun; Kroll, Andreas

2016-01-01

Multi-robot task allocation determines the task sequence and distribution for a group of robots in multi-robot systems, which is one of constrained combinatorial optimization problems and more complex in case of cooperative tasks because they introduce additional spatial and temporal constraints. To solve multi-robot task allocation problems with cooperative tasks efficiently, a subpopulation-based genetic algorithm, a crossover-free genetic algorithm employing mutation operators and elitism selection in each subpopulation, is developed in this paper. Moreover, the impact of mutation operators (swap, insertion, inversion, displacement, and their various combinations) is analyzed when solving several industrial plant inspection problems. The experimental results show that: (1) the proposed genetic algorithm can obtain better solutions than the tested binary tournament genetic algorithm with partially mapped crossover; (2) inversion mutation performs better than other tested mutation operators when solving problems without cooperative tasks, and the swap-inversion combination performs better than other tested mutation operators/combinations when solving problems with cooperative tasks. As it is difficult to produce all desired effects with a single mutation operator, using multiple mutation operators (including both inversion and swap) is suggested when solving similar combinatorial optimization problems.

A function space framework for structural total variation regularization with applications in inverse problems

NASA Astrophysics Data System (ADS)

Hintermüller, Michael; Holler, Martin; Papafitsoros, Kostas

2018-06-01

In this work, we introduce a function space setting for a wide class of structural/weighted total variation (TV) regularization methods motivated by their applications in inverse problems. In particular, we consider a regularizer that is the appropriate lower semi-continuous envelope (relaxation) of a suitable TV type functional initially defined for sufficiently smooth functions. We study examples where this relaxation can be expressed explicitly, and we also provide refinements for weighted TV for a wide range of weights. Since an integral characterization of the relaxation in function space is, in general, not always available, we show that, for a rather general linear inverse problems setting, instead of the classical Tikhonov regularization problem, one can equivalently solve a saddle-point problem where no a priori knowledge of an explicit formulation of the structural TV functional is needed. In particular, motivated by concrete applications, we deduce corresponding results for linear inverse problems with norm and Poisson log-likelihood data discrepancy terms. Finally, we provide proof-of-concept numerical examples where we solve the saddle-point problem for weighted TV denoising as well as for MR guided PET image reconstruction.

Convex blind image deconvolution with inverse filtering

NASA Astrophysics Data System (ADS)

Lv, Xiao-Guang; Li, Fang; Zeng, Tieyong

2018-03-01

Blind image deconvolution is the process of estimating both the original image and the blur kernel from the degraded image with only partial or no information about degradation and the imaging system. It is a bilinear ill-posed inverse problem corresponding to the direct problem of convolution. Regularization methods are used to handle the ill-posedness of blind deconvolution and get meaningful solutions. In this paper, we investigate a convex regularized inverse filtering method for blind deconvolution of images. We assume that the support region of the blur object is known, as has been done in a few existing works. By studying the inverse filters of signal and image restoration problems, we observe the oscillation structure of the inverse filters. Inspired by the oscillation structure of the inverse filters, we propose to use the star norm to regularize the inverse filter. Meanwhile, we use the total variation to regularize the resulting image obtained by convolving the inverse filter with the degraded image. The proposed minimization model is shown to be convex. We employ the first-order primal-dual method for the solution of the proposed minimization model. Numerical examples for blind image restoration are given to show that the proposed method outperforms some existing methods in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), visual quality and time consumption.

Parana Basin Structure from Multi-Objective Inversion of Surface Wave and Receiver Function by Competent Genetic Algorithm

NASA Astrophysics Data System (ADS)

An, M.; Assumpcao, M.

2003-12-01

The joint inversion of receiver function and surface wave is an effective way to diminish the influences of the strong tradeoff among parameters and the different sensitivity to the model parameters in their respective inversions, but the inversion problem becomes more complex. Multi-objective problems can be much more complicated than single-objective inversion in the model selection and optimization. If objectives are involved and conflicting, models can be ordered only partially. In this case, Pareto-optimal preference should be used to select solutions. On the other hand, the inversion to get only a few optimal solutions can not deal properly with the strong tradeoff between parameters, the uncertainties in the observation, the geophysical complexities and even the incompetency of the inversion technique. The effective way is to retrieve the geophysical information statistically from many acceptable solutions, which requires more competent global algorithms. Competent genetic algorithms recently proposed are far superior to the conventional genetic algorithm and can solve hard problems quickly, reliably and accurately. In this work we used one of competent genetic algorithms, Bayesian Optimization Algorithm as the main inverse procedure. This algorithm uses Bayesian networks to draw out inherited information and can use Pareto-optimal preference in the inversion. With this algorithm, the lithospheric structure of Paran"› basin is inverted to fit both the observations of inter-station surface wave dispersion and receiver function.

Wavelet-based localization of oscillatory sources from magnetoencephalography data.

PubMed

Lina, J M; Chowdhury, R; Lemay, E; Kobayashi, E; Grova, C

2014-08-01

Transient brain oscillatory activities recorded with Eelectroencephalography (EEG) or magnetoencephalography (MEG) are characteristic features in physiological and pathological processes. This study is aimed at describing, evaluating, and illustrating with clinical data a new method for localizing the sources of oscillatory cortical activity recorded by MEG. The method combines time-frequency representation and an entropic regularization technique in a common framework, assuming that brain activity is sparse in time and space. Spatial sparsity relies on the assumption that brain activity is organized among cortical parcels. Sparsity in time is achieved by transposing the inverse problem in the wavelet representation, for both data and sources. We propose an estimator of the wavelet coefficients of the sources based on the maximum entropy on the mean (MEM) principle. The full dynamics of the sources is obtained from the inverse wavelet transform, and principal component analysis of the reconstructed time courses is applied to extract oscillatory components. This methodology is evaluated using realistic simulations of single-trial signals, combining fast and sudden discharges (spike) along with bursts of oscillating activity. The method is finally illustrated with a clinical application using MEG data acquired on a patient with a right orbitofrontal epilepsy.

Estimation of biological parameters of marine organisms using linear and nonlinear acoustic scattering model-based inversion methods.

PubMed

Chu, Dezhang; Lawson, Gareth L; Wiebe, Peter H

2016-05-01

The linear inversion commonly used in fisheries and zooplankton acoustics assumes a constant inversion kernel and ignores the uncertainties associated with the shape and behavior of the scattering targets, as well as other relevant animal parameters. Here, errors of the linear inversion due to uncertainty associated with the inversion kernel are quantified. A scattering model-based nonlinear inversion method is presented that takes into account the nonlinearity of the inverse problem and is able to estimate simultaneously animal abundance and the parameters associated with the scattering model inherent to the kernel. It uses sophisticated scattering models to estimate first, the abundance, and second, the relevant shape and behavioral parameters of the target organisms. Numerical simulations demonstrate that the abundance, size, and behavior (tilt angle) parameters of marine animals (fish or zooplankton) can be accurately inferred from the inversion by using multi-frequency acoustic data. The influence of the singularity and uncertainty in the inversion kernel on the inversion results can be mitigated by examining the singular values for linear inverse problems and employing a non-linear inversion involving a scattering model-based kernel.

An ambiguity of information content and error in an ill-posed satellite inversion

NASA Astrophysics Data System (ADS)

Koner, Prabhat

According to Rodgers (2000, stochastic approach), the averaging kernel (AK) is the representational matrix to understand the information content in a scholastic inversion. On the other hand, in deterministic approach this is referred to as model resolution matrix (MRM, Menke 1989). The analysis of AK/MRM can only give some understanding of how much regularization is imposed on the inverse problem. The trace of the AK/MRM matrix, which is the so-called degree of freedom from signal (DFS; stochastic) or degree of freedom in retrieval (DFR; deterministic). There are no physical/mathematical explanations in the literature: why the trace of the matrix is a valid form to calculate this quantity? We will present an ambiguity between information and error using a real life problem of SST retrieval from GOES13. The stochastic information content calculation is based on the linear assumption. The validity of such mathematics in satellite inversion will be questioned because it is based on the nonlinear radiative transfer and ill-conditioned inverse problems. References: Menke, W., 1989: Geophysical data analysis: discrete inverse theory. San Diego academic press. Rodgers, C.D., 2000: Inverse methods for atmospheric soundings: theory and practice. Singapore :World Scientific.

The inverse electroencephalography pipeline

NASA Astrophysics Data System (ADS)

Weinstein, David Michael

The inverse electroencephalography (EEG) problem is defined as determining which regions of the brain are active based on remote measurements recorded with scalp EEG electrodes. An accurate solution to this problem would benefit both fundamental neuroscience research and clinical neuroscience applications. However, constructing accurate patient-specific inverse EEG solutions requires complex modeling, simulation, and visualization algorithms, and to date only a few systems have been developed that provide such capabilities. In this dissertation, a computational system for generating and investigating patient-specific inverse EEG solutions is introduced, and the requirements for each stage of this Inverse EEG Pipeline are defined and discussed. While the requirements of many of the stages are satisfied with existing algorithms, others have motivated research into novel modeling and simulation methods. The principal technical results of this work include novel surface-based volume modeling techniques, an efficient construction for the EEG lead field, and the Open Source release of the Inverse EEG Pipeline software for use by the bioelectric field research community. In this work, the Inverse EEG Pipeline is applied to three research problems in neurology: comparing focal and distributed source imaging algorithms; separating measurements into independent activation components for multifocal epilepsy; and localizing the cortical activity that produces the P300 effect in schizophrenia.

IPDO-2007: Inverse Problems, Design and Optimization Symposium

DTIC Science & Technology

2007-08-01

Kanevce, G. H., Kanevce, Lj. P., and Mitrevski , V. B.), International Symposium on Inverse Problems, Design and Optimization (IPDO-2007), (eds...107 Gligor Kanevce Ljubica Kanevce Vangelce Mitrevski George Dulikravich 108 Gligor Kanevce Ljubica Kanevce Igor Andreevski George Dulikravich

Histogram analysis parameters of apparent diffusion coefficient reflect tumor cellularity and proliferation activity in head and neck squamous cell carcinoma.

PubMed

Surov, Alexey; Meyer, Hans Jonas; Winter, Karsten; Richter, Cindy; Hoehn, Anna-Kathrin

2018-05-04

Our purpose was to analyze associations between apparent diffusion coefficient (ADC) histogram analysis parameters and histopathologicalfeatures in head and neck squamous cell carcinoma (HNSCC). The study involved 32 patients with primary HNSCC. For every tumor, the following histogram analysis parameters were calculated: ADCmean, ADCmax, ADC min , ADC median , ADC mode , P10, P25, P75, P90, kurtosis, skewness, and entropy. Furthermore, proliferation index KI 67, cell count, total and average nucleic areas were estimated. Spearman's correlation coefficient (p) was used to analyze associations between investigated parameters. In overall sample, all ADC values showed moderate inverse correlations with KI 67. All ADC values except ADCmax correlated inversely with tumor cellularity. Slightly correlations were identified between total/average nucleic area and ADC mean , ADC min , ADC median , and P25. In G1/2 tumors, only ADCmode correlated well with Ki67. No statistically significant correlations between ADC parameters and cellularity were found. In G3 tumors, Ki 67 correlated with all ADC parameters except ADCmode. Cell count correlated well with all ADC parameters except ADCmax. Total nucleic area correlated inversely with ADC mean , ADC min , ADC median , P25, and P90. ADC histogram parameters reflect proliferation potential and cellularity in HNSCC. The associations between histopathology and imaging depend on tumor grading.

Enhance field water-color measurements with a Secchi disk and its implication for fusion of active and passive ocean-color remote sensing.

PubMed

Lee, Zhongping; Shang, Shaoling; Du, Keping; Liu, Bingyi; Lin, Gong; Wei, Jianwei; Li, Xiaolong

2018-05-01

Inversion of the total absorption (a) and backscattering coefficients of bulk water through a fusion of remote sensing reflectance (R rs ) and Secchi disk depth (Z SD ) is developed. An application of such a system to a synthesized wide-range dataset shows a reduction of ∼3 folds in the uncertainties of inverted a(λ) (in a range of ∼0.01-6.8  m -1 ) from R rs (λ) for the 350-560 nm range. Such a fusion is further proposed to process concurrent active (ocean LiDAR) and passive (ocean-color) measurements, which can lead to nearly "exact" analytical inversion of an R rs spectrum. With such a fusion, it is found that the uncertainty in the inverted total a in the 350-560 nm range could be reduced to ∼2% for the synthesized data, which can thus significantly improve the derivation of a coefficients of other varying components. Although the inclusion of Z SD places an extra constraint in the inversion of R rs , no apparent improvement over the quasi-analytical algorithm (QAA) was found when the fusion of Z SD and R rs was applied to a field dataset, which calls for more accurate determination of the absorption coefficients from water samples.

A preprocessing strategy for helioseismic inversions

NASA Astrophysics Data System (ADS)

Christensen-Dalsgaard, J.; Thompson, M. J.

1993-05-01

Helioseismic inversion in general involves considerable computational expense, due to the large number of modes that is typically considered. This is true in particular of the widely used optimally localized averages (OLA) inversion methods, which require the inversion of one or more matrices whose order is the number of modes in the set. However, the number of practically independent pieces of information that a large helioseismic mode set contains is very much less than the number of modes, suggesting that the set might first be reduced before the expensive inversion is performed. We demonstrate with a model problem that by first performing a singular value decomposition the original problem may be transformed into a much smaller one, reducing considerably the cost of the OLA inversion and with no significant loss of information.

Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations

NASA Astrophysics Data System (ADS)

Jiang, Daijun; Li, Zhiyuan; Liu, Yikan; Yamamoto, Masahiro

2017-05-01

In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic equations. The result is weaker than its parabolic counterpart in the sense that we additionally impose the homogeneous boundary condition. As a direct application, we prove the uniqueness for an inverse problem on determining the spatial component in the source term by interior measurements. Numerically, we reformulate our inverse source problem as an optimization problem, and propose an iterative thresholding algorithm. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

Viscoelastic property identification from waveform reconstruction

NASA Astrophysics Data System (ADS)

Leymarie, N.; Aristégui, C.; Audoin, B.; Baste, S.

2002-05-01

An inverse method is proposed for the determination of the viscoelastic properties of material plates from the plane-wave transmitted acoustic field. Innovations lie in a two-step inversion scheme based on the well-known maximum-likelihood principle with an analytic signal formulation. In addition, establishing the analytical formulations of the plate transmission coefficient we implement an efficient and slightly noise-sensitive process suited to both very thin plates and strongly dispersive media.

Comparing multiple statistical methods for inverse prediction in nuclear forensics applications

DOE PAGES

Lewis, John R.; Zhang, Adah; Anderson-Cook, Christine Michaela

2017-10-29

Forensic science seeks to predict source characteristics using measured observables. Statistically, this objective can be thought of as an inverse problem where interest is in the unknown source characteristics or factors ( X) of some underlying causal model producing the observables or responses (Y = g ( X) + error). Here, this paper reviews several statistical methods for use in inverse problems and demonstrates that comparing results from multiple methods can be used to assess predictive capability. Motivation for assessing inverse predictions comes from the desired application to historical and future experiments involving nuclear material production for forensics research inmore » which inverse predictions, along with an assessment of predictive capability, are desired.« less

Comparing multiple statistical methods for inverse prediction in nuclear forensics applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lewis, John R.; Zhang, Adah; Anderson-Cook, Christine Michaela

Forensic science seeks to predict source characteristics using measured observables. Statistically, this objective can be thought of as an inverse problem where interest is in the unknown source characteristics or factors ( X) of some underlying causal model producing the observables or responses (Y = g ( X) + error). Here, this paper reviews several statistical methods for use in inverse problems and demonstrates that comparing results from multiple methods can be used to assess predictive capability. Motivation for assessing inverse predictions comes from the desired application to historical and future experiments involving nuclear material production for forensics research inmore » which inverse predictions, along with an assessment of predictive capability, are desired.« less

Final Report: Resolving and Discriminating Overlapping Anomalies from Multiple Objects in Cluttered Environments

DTIC Science & Technology

2015-12-15

UXO community . NAME Total Number: PERCENT_SUPPORTEDNAME FTE Equivalent: Total Number: Irma Shamatava 0.50 0.50 1 Resolving and Discriminating...Distinguishing an object of interest from innocuous items is the main problem that the UXO community is facing currently. This inverse problem...innocuous items is the main problem that the UXO community is facing currently. This inverse problem demands fast and accurate representation of

IMPROVED SEARCH OF PRINCIPAL COMPONENT ANALYSIS DATABASES FOR SPECTRO-POLARIMETRIC INVERSION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Casini, R.; Lites, B. W.; Ramos, A. Asensio

2013-08-20

We describe a simple technique for the acceleration of spectro-polarimetric inversions based on principal component analysis (PCA) of Stokes profiles. This technique involves the indexing of the database models based on the sign of the projections (PCA coefficients) of the first few relevant orders of principal components of the four Stokes parameters. In this way, each model in the database can be attributed a distinctive binary number of 2{sup 4n} bits, where n is the number of PCA orders used for the indexing. Each of these binary numbers (indices) identifies a group of ''compatible'' models for the inversion of amore » given set of observed Stokes profiles sharing the same index. The complete set of the binary numbers so constructed evidently determines a partition of the database. The search of the database for the PCA inversion of spectro-polarimetric data can profit greatly from this indexing. In practical cases it becomes possible to approach the ideal acceleration factor of 2{sup 4n} as compared to the systematic search of a non-indexed database for a traditional PCA inversion. This indexing method relies on the existence of a physical meaning in the sign of the PCA coefficients of a model. For this reason, the presence of model ambiguities and of spectro-polarimetric noise in the observations limits in practice the number n of relevant PCA orders that can be used for the indexing.« less

Cross hole GPR traveltime inversion using a fast and accurate neural network as a forward model

NASA Astrophysics Data System (ADS)

Mejer Hansen, Thomas

2017-04-01

Probabilistic formulated inverse problems can be solved using Monte Carlo based sampling methods. In principle both advanced prior information, such as based on geostatistics, and complex non-linear forward physical models can be considered. However, in practice these methods can be associated with huge computational costs that in practice limit their application. This is not least due to the computational requirements related to solving the forward problem, where the physical response of some earth model has to be evaluated. Here, it is suggested to replace a numerical complex evaluation of the forward problem, with a trained neural network that can be evaluated very fast. This will introduce a modeling error, that is quantified probabilistically such that it can be accounted for during inversion. This allows a very fast and efficient Monte Carlo sampling of the solution to an inverse problem. We demonstrate the methodology for first arrival travel time inversion of cross hole ground-penetrating radar (GPR) data. An accurate forward model, based on 2D full-waveform modeling followed by automatic travel time picking, is replaced by a fast neural network. This provides a sampling algorithm three orders of magnitude faster than using the full forward model, and considerably faster, and more accurate, than commonly used approximate forward models. The methodology has the potential to dramatically change the complexity of the types of inverse problems that can be solved using non-linear Monte Carlo sampling techniques.

Fast calculation of tissue optical properties using MC and the experimental evaluation for diagnosis of cervical cancer

NASA Astrophysics Data System (ADS)

Zhang, Shuying; Zhou, Xiaoqing; Qin, Zhuanping; Zhao, Huijuan

2011-02-01

This article aims at the development of the fast inverse Monte Carlo (MC) simulation for the reconstruction of optical properties (absorption coefficient μs and scattering coefficient μs) of cylindrical tissue, such as a cervix, from the measurement of near infrared diffuse light on frequency domain. Frequency domain information (amplitude and phase) is extracted from the time domain MC with a modified method. To shorten the computation time in reconstruction of optical properties, efficient and fast forward MC has to be achieved. To do this, firstly, databases of the frequency-domain information under a range of μa and μs were pre-built by combining MC simulation with Lambert-Beer's law. Then, a double polynomial model was adopted to quickly obtain the frequency-domain information in any optical properties. Based on the fast forward MC, the optical properties can be quickly obtained in a nonlinear optimization scheme. Reconstruction resulting from simulated data showed that the developed inverse MC method has the advantages in both the reconstruction accuracy and computation time. The relative errors in reconstruction of the μs and μs are less than +/-6% and +/-12% respectively, while another coefficient (μs or μs) is in a fixed value. When both μs and μs are unknown, the relative errors in reconstruction of the reduced scattering coefficient and absorption coefficient are mainly less than +/-10% in range of 45< μs <80 cm-1 and 0.25< a μ <0.55 cm-1. With the rapid reconstruction strategy developed in this article the computation time for reconstructing one set of the optical properties is less than 0.5 second. Endoscopic measurement on two tubular solid phantoms were also carried out to evaluate the system and the inversion scheme. The results demonstrated that less than 20% relative error can be achieved.

Accurate reconstruction of the optical parameter distribution in participating medium based on the frequency-domain radiative transfer equation

NASA Astrophysics Data System (ADS)

Qiao, Yao-Bin; Qi, Hong; Zhao, Fang-Zhou; Ruan, Li-Ming

2016-12-01

Reconstructing the distribution of optical parameters in the participating medium based on the frequency-domain radiative transfer equation (FD-RTE) to probe the internal structure of the medium is investigated in the present work. The forward model of FD-RTE is solved via the finite volume method (FVM). The regularization term formatted by the generalized Gaussian Markov random field model is used in the objective function to overcome the ill-posed nature of the inverse problem. The multi-start conjugate gradient (MCG) method is employed to search the minimum of the objective function and increase the efficiency of convergence. A modified adjoint differentiation technique using the collimated radiative intensity is developed to calculate the gradient of the objective function with respect to the optical parameters. All simulation results show that the proposed reconstruction algorithm based on FD-RTE can obtain the accurate distributions of absorption and scattering coefficients. The reconstructed images of the scattering coefficient have less errors than those of the absorption coefficient, which indicates the former are more suitable to probing the inner structure. Project supported by the National Natural Science Foundation of China (Grant No. 51476043), the Major National Scientific Instruments and Equipment Development Special Foundation of China (Grant No. 51327803), and the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 51121004).

A multi-frequency iterative imaging method for discontinuous inverse medium problem

NASA Astrophysics Data System (ADS)

Zhang, Lei; Feng, Lixin

2018-06-01

The inverse medium problem with discontinuous refractive index is a kind of challenging inverse problem. We employ the primal dual theory and fast solution of integral equations, and propose a new iterative imaging method. The selection criteria of regularization parameter is given by the method of generalized cross-validation. Based on multi-frequency measurements of the scattered field, a recursive linearization algorithm has been presented with respect to the frequency from low to high. We also discuss the initial guess selection strategy by semi-analytical approaches. Numerical experiments are presented to show the effectiveness of the proposed method.

Effective one-dimensional approach to the source reconstruction problem of three-dimensional inverse optoacoustics

NASA Astrophysics Data System (ADS)

Stritzel, J.; Melchert, O.; Wollweber, M.; Roth, B.

2017-09-01

The direct problem of optoacoustic signal generation in biological media consists of solving an inhomogeneous three-dimensional (3D) wave equation for an initial acoustic stress profile. In contrast, the more defiant inverse problem requires the reconstruction of the initial stress profile from a proper set of observed signals. In this article, we consider an effectively 1D approach, based on the assumption of a Gaussian transverse irradiation source profile and plane acoustic waves, in which the effects of acoustic diffraction are described in terms of a linear integral equation. The respective inverse problem along the beam axis can be cast into a Volterra integral equation of the second kind for which we explore here efficient numerical schemes in order to reconstruct initial stress profiles from observed signals, constituting a methodical progress of computational aspects of optoacoustics. In this regard, we explore the validity as well as the limits of the inversion scheme via numerical experiments, with parameters geared toward actual optoacoustic problem instances. The considered inversion input consists of synthetic data, obtained in terms of the effectively 1D approach, and, more generally, a solution of the 3D optoacoustic wave equation. Finally, we also analyze the effect of noise and different detector-to-sample distances on the optoacoustic signal and the reconstructed pressure profiles.

The inverse problem of sensing the mass and force induced by an adsorbate on a beam nanomechanical resonator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Yun; Zhang, Yin

2016-06-08

The mass sensing superiority of a micro/nanomechanical resonator sensor over conventional mass spectrometry has been, or at least, is being firmly established. Because the sensing mechanism of a mechanical resonator sensor is the shifts of resonant frequencies, how to link the shifts of resonant frequencies with the material properties of an analyte formulates an inverse problem. Besides the analyte/adsorbate mass, many other factors such as position and axial force can also cause the shifts of resonant frequencies. The in-situ measurement of the adsorbate position and axial force is extremely difficult if not impossible, especially when an adsorbate is as smallmore » as a molecule or an atom. Extra instruments are also required. In this study, an inverse problem of using three resonant frequencies to determine the mass, position and axial force is formulated and solved. The accuracy of the inverse problem solving method is demonstrated and how the method can be used in the real application of a nanomechanical resonator is also discussed. Solving the inverse problem is helpful to the development and application of mechanical resonator sensor on two things: reducing extra experimental equipments and achieving better mass sensing by considering more factors.« less

Distorted Born iterative T-matrix method for inversion of CSEM data in anisotropic media

NASA Astrophysics Data System (ADS)

Jakobsen, Morten; Tveit, Svenn

2018-05-01

We present a direct iterative solutions to the nonlinear controlled-source electromagnetic (CSEM) inversion problem in the frequency domain, which is based on a volume integral equation formulation of the forward modelling problem in anisotropic conductive media. Our vectorial nonlinear inverse scattering approach effectively replaces an ill-posed nonlinear inverse problem with a series of linear ill-posed inverse problems, for which there already exist efficient (regularized) solution methods. The solution update the dyadic Green's function's from the source to the scattering-volume and from the scattering-volume to the receivers, after each iteration. The T-matrix approach of multiple scattering theory is used for efficient updating of all dyadic Green's functions after each linearized inversion step. This means that we have developed a T-matrix variant of the Distorted Born Iterative (DBI) method, which is often used in the acoustic and electromagnetic (medical) imaging communities as an alternative to contrast-source inversion. The main advantage of using the T-matrix approach in this context, is that it eliminates the need to perform a full forward simulation at each iteration of the DBI method, which is known to be consistent with the Gauss-Newton method. The T-matrix allows for a natural domain decomposition, since in the sense that a large model can be decomposed into an arbitrary number of domains that can be treated independently and in parallel. The T-matrix we use for efficient model updating is also independent of the source-receiver configuration, which could be an advantage when performing fast-repeat modelling and time-lapse inversion. The T-matrix is also compatible with the use of modern renormalization methods that can potentially help us to reduce the sensitivity of the CSEM inversion results on the starting model. To illustrate the performance and potential of our T-matrix variant of the DBI method for CSEM inversion, we performed a numerical experiments based on synthetic CSEM data associated with 2D VTI and 3D orthorombic model inversions. The results of our numerical experiment suggest that the DBIT method for inversion of CSEM data in anisotropic media is both accurate and efficient.

Formation of stable inverse sheath in ion–ion plasma by strong negative ion emission

NASA Astrophysics Data System (ADS)

Zhang, Zhe; Wu, Bang; Yang, Shali; Zhang, Ya; Chen, Dezhi; Fan, Mingwu; Jiang, Wei

2018-06-01

The effect of strong charged particle emission on plasma–wall interactions is a classical, yet unresolved question in plasma physics. Previous studies on secondary electron emission have shown that with different emission coefficients, there are classical, space-charge-limited, and inverse sheaths. In this letter, we demonstrate that a stable ion–ion inverse sheath and ion–ion plasma are formed with strong surface emission of negative ions. The continuous space-charge-limited to inverse ion–ion sheath transition is observed, and the plasma near the surface consequently transforms into pure ion–ion plasma. The results may explain the long-puzzled experimental observation that the density of negative ions depends on only charge not mass in negative ion sources.

Polarization lidar for atmospheric monitoring

NASA Astrophysics Data System (ADS)

Liu, Qiaojun; Wu, Chengxuan; Yuk Sun Cheng, Andrew; Wang, Zhangjun; Meng, Xiangqian; Chen, Chao; Li, Xianxin; Liu, Xingtao; Zhang, Hao; Zong, Fangyi

2018-04-01

Aerosol plays an important role in global climate and weather changes. Polarization lidar captures parallel and perpendicular signals from atmosphere to research aerosols. The lidar system we used has three emission wavelengths and could obtain the atmospheric aerosol extinction coefficient, backscattering coefficient and depolarization ratio. In this paper, the design of the lidar is described. The methods of data acquisition and inversion are given. Some recent results are presented.

Gravitational Collapse of Magnetized Clouds. II. The Role of Ohmic Dissipation

NASA Astrophysics Data System (ADS)

Shu, Frank H.; Galli, Daniele; Lizano, Susana; Cai, Mike

2006-08-01

We formulate the problem of magnetic field dissipation during the accretion phase of low-mass star formation, and we carry out the first step of an iterative solution procedure by assuming that the gas is in free fall along radial field lines. This so-called ``kinematic approximation'' ignores the back reaction of the Lorentz force on the accretion flow. In quasi-steady state and assuming the resistivity coefficient to be spatially uniform, the problem is analytically soluble in terms of Legendre's polynomials and hypergeometric confluent functions. The dissipation of the magnetic field occurs inside a region of radius inversely proportional to the mass of the central star (the ``Ohm radius''), where the magnetic field becomes asymptotically straight and uniform. In our solution the magnetic flux problem of star formation is avoided because the magnetic flux dragged in the accreting protostar is always zero. Our results imply that the effective resistivity of the infalling gas must be higher by at least 1 order of magnitude than the microscopic electric resistivity, to avoid conflict with measurements of paleomagnetism in meteorites and with the observed luminosity of regions of low-mass star formation.

Evaluation of Contact Heat Transfer Coefficient and Phase Transformation during Hot Stamping of a Hat-Type Part

PubMed Central

Kim, Heung-Kyu; Lee, Seong Hyeon; Choi, Hyunjoo

2015-01-01

Using an inverse analysis technique, the heat transfer coefficient on the die-workpiece contact surface of a hot stamping process was evaluated as a power law function of contact pressure. This evaluation was to determine whether the heat transfer coefficient on the contact surface could be used for finite element analysis of the entire hot stamping process. By comparing results of the finite element analysis and experimental measurements of the phase transformation, an evaluation was performed to determine whether the obtained heat transfer coefficient function could provide reasonable finite element prediction for workpiece properties affected by the hot stamping process. PMID:28788046

Partial F-tests with multiply imputed data in the linear regression framework via coefficient of determination.

PubMed

Chaurasia, Ashok; Harel, Ofer

2015-02-10

Tests for regression coefficients such as global, local, and partial F-tests are common in applied research. In the framework of multiple imputation, there are several papers addressing tests for regression coefficients. However, for simultaneous hypothesis testing, the existing methods are computationally intensive because they involve calculation with vectors and (inversion of) matrices. In this paper, we propose a simple method based on the scalar entity, coefficient of determination, to perform (global, local, and partial) F-tests with multiply imputed data. The proposed method is evaluated using simulated data and applied to suicide prevention data. Copyright © 2014 John Wiley & Sons, Ltd.

Study of Parameters And Methods of LL-Ⅳ Distributed Hydrological Model in DMIP2

NASA Astrophysics Data System (ADS)

Li, L.; Wu, J.; Wang, X.; Yang, C.; Zhao, Y.; Zhou, H.

2008-05-01

: The Physics-based distributed hydrological model is considered as an important developing period from the traditional experience-hydrology to the physical hydrology. The Hydrology Laboratory of the NOAA National Weather Service proposes the first and second phase of the Distributed Model Intercomparison Project (DMIP)，that it is a great epoch-making work. LL distributed hydrological model has been developed to the fourth generation since it was established in 1997 on the Fengman-I district reservoir area (11000 km2).The LL-I distributed hydrological model was born with the applications of flood control system in the Fengman-I in China. LL-II was developed under the DMIP-I support, it is combined with GIS, RS, GPS, radar rainfall measurement.LL-III was established along with Applications of LL Distributed Model on Water Resources which was supported by the 973-projects of The Ministry of Science and Technology of the People's Republic of China. LL-Ⅳ was developed to face China's water problem. Combined with Blue River and the Baron Fork River basin of DMIP-II, the convection-diffusion equation of non-saturated and saturated seepage was derived from the soil water dynamics and continuous equation. In view of the technical characteristics of the model, the advantage of using convection-diffusion equation to compute confluence overall is longer period of predictable, saving memory space, fast budgeting, clear physical concepts, etc. The determination of parameters of hydrological model is the key, including experience coefficients and parameters of physical parameters. There are methods of experience, inversion, and the optimization to determine the model parameters, and each has advantages and disadvantages. This paper briefly introduces the LL-Ⅳ distribution hydrological model equations, and particularly introduces methods of parameters determination and simulation results on Blue River and Baron Fork River basin for DMIP-II. The soil moisture diffusion coefficient and coefficient of hydraulic conductivity are involved all through the LL-Ⅳ distribution of runoff and slope convergence model, used mainly empirical formula to determine. It's used optimization methods to calculate the two parameters of evaporation capacity (coefficient of bare land and vegetation land), two parameters of interception and wave velocity of Overland Flow, interflow and groundwater. The approach of determining wave velocity of River Network confluence and diffusion coefficient is: 1. Estimate roughness based mainly on digital information such as land use, soil texture, etc. 2.Establish the empirical formula. Another method is called convection-diffusion numerical inversion.

Viscoelastic material inversion using Sierra-SD and ROL

DOE Office of Scientific and Technical Information (OSTI.GOV)

Walsh, Timothy; Aquino, Wilkins; Ridzal, Denis

2014-11-01

In this report we derive frequency-domain methods for inverse characterization of the constitutive parameters of viscoelastic materials. The inverse problem is cast in a PDE-constrained optimization framework with efficient computation of gradients and Hessian vector products through matrix free operations. The abstract optimization operators for first and second derivatives are derived from first principles. Various methods from the Rapid Optimization Library (ROL) are tested on the viscoelastic inversion problem. The methods described herein are applied to compute the viscoelastic bulk and shear moduli of a foam block model, which was recently used in experimental testing for viscoelastic property characterization.

Two-level image authentication by two-step phase-shifting interferometry and compressive sensing

NASA Astrophysics Data System (ADS)

Zhang, Xue; Meng, Xiangfeng; Yin, Yongkai; Yang, Xiulun; Wang, Yurong; Li, Xianye; Peng, Xiang; He, Wenqi; Dong, Guoyan; Chen, Hongyi

2018-01-01

A two-level image authentication method is proposed; the method is based on two-step phase-shifting interferometry, double random phase encoding, and compressive sensing (CS) theory, by which the certification image can be encoded into two interferograms. Through discrete wavelet transform (DWT), sparseness processing, Arnold transform, and data compression, two compressed signals can be generated and delivered to two different participants of the authentication system. Only the participant who possesses the first compressed signal attempts to pass the low-level authentication. The application of Orthogonal Match Pursuit CS algorithm reconstruction, inverse Arnold transform, inverse DWT, two-step phase-shifting wavefront reconstruction, and inverse Fresnel transform can result in the output of a remarkable peak in the central location of the nonlinear correlation coefficient distributions of the recovered image and the standard certification image. Then, the other participant, who possesses the second compressed signal, is authorized to carry out the high-level authentication. Therefore, both compressed signals are collected to reconstruct the original meaningful certification image with a high correlation coefficient. Theoretical analysis and numerical simulations verify the feasibility of the proposed method.

Experimental extractions of particle position from inline holograms using single coefficient of Wigner-Ville analysis

NASA Astrophysics Data System (ADS)

Widjaja, Joewono; Dawprateep, Saowaros; Chuamchaitrakool, Porntip

2017-07-01

Extractions of particle positions from inline holograms using a single coefficient of Wigner-Ville distribution (WVD) are experimentally verified. WVD analysis of holograms gives local variation of fringe frequency. Regardless of an axial position of particles, one of the WVD coefficients has the unique characteristics of having the lowest amplitude and being located on a line with a slope inversely proportional to the particle position. Experimental results obtained using two image sensors with different resolutions verify the feasibility of the present method.

Optical properties of an anterior lamellar human cornea model based on fibrin-agarose

NASA Astrophysics Data System (ADS)

Ionescu, Ana M.; Cardona, Juan de la Cruz; Ghinea, Razvan; Garzón, Ingrid; González-Andrades, Miguel; Alaminos, Miguel; Pérez, Maria del Mar

2017-08-01

The optical evaluation carried out using the Inverse Adding-Doubling (IAD) method to determine the scattering and the absorption coefficients of the bioengineered human corneal stromas showed that this type of artificial biomaterials shared many similarities with native control cornea after four weeks of development in culture. Their absorption and reduced scattering coefficients values were higher than the ones of the control cornea, but their spectral behaviors of both coefficients were similar. Time of development in culture was an influencing factor on the results.

Complete Sets of Radiating and Nonradiating Parts of a Source and Their Fields with Applications in Inverse Scattering Limited-Angle Problems

PubMed Central

Louis, A. K.

2006-01-01

Many algorithms applied in inverse scattering problems use source-field systems instead of the direct computation of the unknown scatterer. It is well known that the resulting source problem does not have a unique solution, since certain parts of the source totally vanish outside of the reconstruction area. This paper provides for the two-dimensional case special sets of functions, which include all radiating and all nonradiating parts of the source. These sets are used to solve an acoustic inverse problem in two steps. The problem under discussion consists of determining an inhomogeneous obstacle supported in a part of a disc, from data, known for a subset of a two-dimensional circle. In a first step, the radiating parts are computed by solving a linear problem. The second step is nonlinear and consists of determining the nonradiating parts. PMID:23165060

Reconstruction of local perturbations in periodic surfaces

NASA Astrophysics Data System (ADS)

Lechleiter, Armin; Zhang, Ruming

2018-03-01

This paper concerns the inverse scattering problem to reconstruct a local perturbation in a periodic structure. Unlike the periodic problems, the periodicity for the scattered field no longer holds, thus classical methods, which reduce quasi-periodic fields in one periodic cell, are no longer available. Based on the Floquet-Bloch transform, a numerical method has been developed to solve the direct problem, that leads to a possibility to design an algorithm for the inverse problem. The numerical method introduced in this paper contains two steps. The first step is initialization, that is to locate the support of the perturbation by a simple method. This step reduces the inverse problem in an infinite domain into one periodic cell. The second step is to apply the Newton-CG method to solve the associated optimization problem. The perturbation is then approximated by a finite spline basis. Numerical examples are given at the end of this paper, showing the efficiency of the numerical method.

Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

ERIC Educational Resources Information Center

El-Gebeily, M.; Yushau, B.

2008-01-01

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

Frechet derivatives for shallow water ocean acoustic inverse problems

NASA Astrophysics Data System (ADS)

Odom, Robert I.

2003-04-01

For any inverse problem, finding a model fitting the data is only half the problem. Most inverse problems of interest in ocean acoustics yield nonunique model solutions, and involve inevitable trade-offs between model and data resolution and variance. Problems of uniqueness and resolution and variance trade-offs can be addressed by examining the Frechet derivatives of the model-data functional with respect to the model variables. Tarantola [Inverse Problem Theory (Elsevier, Amsterdam, 1987), p. 613] published analytical formulas for the basic derivatives, e.g., derivatives of pressure with respect to elastic moduli and density. Other derivatives of interest, such as the derivative of transmission loss with respect to attenuation, can be easily constructed using the chain rule. For a range independent medium the analytical formulas involve only the Green's function and the vertical derivative of the Green's function for the medium. A crucial advantage of the analytical formulas for the Frechet derivatives over numerical differencing is that they can be computed with a single pass of any program which supplies the Green's function. Various derivatives of interest in shallow water ocean acoustics are presented and illustrated by an application to the sensitivity of measured pressure to shallow water sediment properties. [Work supported by ONR.

Accounting for model error in Bayesian solutions to hydrogeophysical inverse problems using a local basis approach

NASA Astrophysics Data System (ADS)

Irving, J.; Koepke, C.; Elsheikh, A. H.

2017-12-01

Bayesian solutions to geophysical and hydrological inverse problems are dependent upon a forward process model linking subsurface parameters to measured data, which is typically assumed to be known perfectly in the inversion procedure. However, in order to make the stochastic solution of the inverse problem computationally tractable using, for example, Markov-chain-Monte-Carlo (MCMC) methods, fast approximations of the forward model are commonly employed. This introduces model error into the problem, which has the potential to significantly bias posterior statistics and hamper data integration efforts if not properly accounted for. Here, we present a new methodology for addressing the issue of model error in Bayesian solutions to hydrogeophysical inverse problems that is geared towards the common case where these errors cannot be effectively characterized globally through some parametric statistical distribution or locally based on interpolation between a small number of computed realizations. Rather than focusing on the construction of a global or local error model, we instead work towards identification of the model-error component of the residual through a projection-based approach. In this regard, pairs of approximate and detailed model runs are stored in a dictionary that grows at a specified rate during the MCMC inversion procedure. At each iteration, a local model-error basis is constructed for the current test set of model parameters using the K-nearest neighbour entries in the dictionary, which is then used to separate the model error from the other error sources before computing the likelihood of the proposed set of model parameters. We demonstrate the performance of our technique on the inversion of synthetic crosshole ground-penetrating radar traveltime data for three different subsurface parameterizations of varying complexity. The synthetic data are generated using the eikonal equation, whereas a straight-ray forward model is assumed in the inversion procedure. In each case, the developed model-error approach enables to remove posterior bias and obtain a more realistic characterization of uncertainty.

Identification of groundwater flow parameters using reciprocal data from hydraulic interference tests

NASA Astrophysics Data System (ADS)

Marinoni, Marianna; Delay, Frederick; Ackerer, Philippe; Riva, Monica; Guadagnini, Alberto

2016-08-01

We investigate the effect of considering reciprocal drawdown curves for the characterization of hydraulic properties of aquifer systems through inverse modeling based on interference well testing. Reciprocity implies that drawdown observed in a well B when pumping takes place from well A should strictly coincide with the drawdown observed in A when pumping in B with the same flow rate as in A. In this context, a critical point related to applications of hydraulic tomography is the assessment of the number of available independent drawdown data and their impact on the solution of the inverse problem. The issue arises when inverse modeling relies upon mathematical formulations of the classical single-continuum approach to flow in porous media grounded on Darcy's law. In these cases, introducing reciprocal drawdown curves in the database of an inverse problem is equivalent to duplicate some information, to a certain extent. We present a theoretical analysis of the way a Least-Square objective function and a Levenberg-Marquardt minimization algorithm are affected by the introduction of reciprocal information in the inverse problem. We also investigate the way these reciprocal data, eventually corrupted by measurement errors, influence model parameter identification in terms of: (a) the convergence of the inverse model, (b) the optimal values of parameter estimates, and (c) the associated estimation uncertainty. Our theoretical findings are exemplified through a suite of computational examples focused on block-heterogeneous systems with increased complexity level. We find that the introduction of noisy reciprocal information in the objective function of the inverse problem has a very limited influence on the optimal parameter estimates. Convergence of the inverse problem improves when adding diverse (nonreciprocal) drawdown series, but does not improve when reciprocal information is added to condition the flow model. The uncertainty on optimal parameter estimates is influenced by the strength of measurement errors and it is not significantly diminished or increased by adding noisy reciprocal information.

A methodology to determine boundary conditions from forced convection experiments using liquid crystal thermography

NASA Astrophysics Data System (ADS)

Jakkareddy, Pradeep S.; Balaji, C.

2017-02-01

This paper reports the results of an experimental study to estimate the heat flux and convective heat transfer coefficient using liquid crystal thermography and Bayesian inference in a heat generating sphere, enclosed in a cubical Teflon block. The geometry considered for the experiments comprises a heater inserted in a hollow hemispherical aluminium ball, resulting in a volumetric heat generation source that is placed at the center of the Teflon block. Calibrated thermochromic liquid crystal sheets are used to capture the temperature distribution at the front face of the Teflon block. The forward model is the three dimensional conduction equation which is solved within the Teflon block to obtain steady state temperatures, using COMSOL. Match up experiments are carried out for various velocities by minimizing the residual between TLC and simulated temperatures for every assumed loss coefficient, to obtain a correlation of average Nusselt number against Reynolds number. This is used for prescribing the boundary condition for the solution to the forward model. A surrogate model obtained by artificial neural network built upon the data from COMSOL simulations is used to drive a Markov Chain Monte Carlo based Metropolis Hastings algorithm to generate the samples. Bayesian inference is adopted to solve the inverse problem for determination of heat flux and heat transfer coefficient from the measured temperature field. Point estimates of the posterior like the mean, maximum a posteriori and standard deviation of the retrieved heat flux and convective heat transfer coefficient are reported. Additionally the effect of number of samples on the performance of the estimation process has been investigated.

An approach to quantum-computational hydrologic inverse analysis

DOE PAGES

O'Malley, Daniel

2018-05-02

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealermore » to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.« less

An approach to quantum-computational hydrologic inverse analysis.

PubMed

O'Malley, Daniel

2018-05-02

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealer to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.

Coupling of Large Amplitude Inversion with Other States

NASA Astrophysics Data System (ADS)

Pearson, John; Yu, Shanshan

2016-06-01

The coupling of a large amplitude motion with a small amplitude vibration remains one of the least well characterized problems in molecular physics. Molecular inversion poses a few unique and not intuitively obvious challenges to the large amplitude motion problem. In spite of several decades of theoretical work numerous challenges in calculation of transition frequencies and more importantly intensities persist. The most challenging aspect of this problem is that the inversion coordinate is a unique function of the overall vibrational state including both the large and small amplitude modes. As a result, the r-axis system and the meaning of the K-quantum number in the rotational basis set are unique to each vibrational state of large or small amplitude motion. This unfortunate reality has profound consequences to calculation of intensities and the coupling of nearly degenerate vibrational states. The case of NH3 inversion and inversion through a plane of symmetry in alcohols will be examined to find a general path forward.

An approach to quantum-computational hydrologic inverse analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

O'Malley, Daniel

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealermore » to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.« less

Mixed linear-non-linear inversion of crustal deformation data: Bayesian inference of model, weighting and regularization parameters

NASA Astrophysics Data System (ADS)

Fukuda, Jun'ichi; Johnson, Kaj M.

2010-06-01

We present a unified theoretical framework and solution method for probabilistic, Bayesian inversions of crustal deformation data. The inversions involve multiple data sets with unknown relative weights, model parameters that are related linearly or non-linearly through theoretic models to observations, prior information on model parameters and regularization priors to stabilize underdetermined problems. To efficiently handle non-linear inversions in which some of the model parameters are linearly related to the observations, this method combines both analytical least-squares solutions and a Monte Carlo sampling technique. In this method, model parameters that are linearly and non-linearly related to observations, relative weights of multiple data sets and relative weights of prior information and regularization priors are determined in a unified Bayesian framework. In this paper, we define the mixed linear-non-linear inverse problem, outline the theoretical basis for the method, provide a step-by-step algorithm for the inversion, validate the inversion method using synthetic data and apply the method to two real data sets. We apply the method to inversions of multiple geodetic data sets with unknown relative data weights for interseismic fault slip and locking depth. We also apply the method to the problem of estimating the spatial distribution of coseismic slip on faults with unknown fault geometry, relative data weights and smoothing regularization weight.

A two-step combination of top-down and bottom-up fire emission estimates at regional and global scales: strengths and main uncertainties

NASA Astrophysics Data System (ADS)

Sofiev, Mikhail; Soares, Joana; Kouznetsov, Rostislav; Vira, Julius; Prank, Marje

2016-04-01

Top-down emission estimation via inverse dispersion modelling is used for various problems, where bottom-up approaches are difficult or highly uncertain. One of such areas is the estimation of emission from wild-land fires. In combination with dispersion modelling, satellite and/or in-situ observations can, in principle, be used to efficiently constrain the emission values. This is the main strength of the approach: the a-priori values of the emission factors (based on laboratory studies) are refined for real-life situations using the inverse-modelling technique. However, the approach also has major uncertainties, which are illustrated here with a few examples of the Integrated System for wild-land Fires (IS4FIRES). IS4FIRES generates the smoke emission and injection profile from MODIS and SEVIRI active-fire radiative energy observations. The emission calculation includes two steps: (i) initial top-down calibration of emission factors via inverse dispersion problem solution that is made once using training dataset from the past, (ii) application of the obtained emission coefficients to individual-fire radiative energy observations, thus leading to bottom-up emission compilation. For such a procedure, the major classes of uncertainties include: (i) imperfect information on fires, (ii) simplifications in the fire description, (iii) inaccuracies in the smoke observations and modelling, (iv) inaccuracies of the inverse problem solution. Using examples of the fire seasons 2010 in Russia, 2012 in Eurasia, 2007 in Australia, etc, it is pointed out that the top-down system calibration performed for a limited number of comparatively moderate cases (often the best-observed ones) may lead to errors in application to extreme events. For instance, the total emission of 2010 Russian fires is likely to be over-estimated by up to 50% if the calibration is based on the season 2006 and fire description is simplified. Longer calibration period and more sophisticated parameterization (including the smoke injection model and distinguishing all relevant vegetation types) can improve the predictions. The other significant parameter, so far weakly addressed in fire emission inventories, is the size spectrum of the emitted aerosols. Direct size-resolving measurements showed, for instance, that smoke from smouldering fires has smaller particles as compares with smoke from flaming fires. Due to dependence of the smoke optical thickness on the size distribution, such variability can lead to significant changes in the top-down calibration step. Experiments with IS4FIRES-SILAM system manifested up to a factor of two difference in AOD, depending on the assumption on particle spectrum.

Direct and inverse problems of studying the properties of multilayer nanostructures based on a two-dimensional model of X-ray reflection and scattering

NASA Astrophysics Data System (ADS)

Khachaturov, R. V.

2014-06-01

A mathematical model of X-ray reflection and scattering by multilayered nanostructures in the quasi-optical approximation is proposed. X-ray propagation and the electric field distribution inside the multilayered structure are considered with allowance for refraction, which is taken into account via the second derivative with respect to the depth of the structure. This model is used to demonstrate the possibility of solving inverse problems in order to determine the characteristics of irregularities not only over the depth (as in the one-dimensional problem) but also over the length of the structure. An approximate combinatorial method for system decomposition and composition is proposed for solving the inverse problems.

Application of Vorob'ev's asymptotic solution to retrieval of the structural characteristics Cn2 from BSA-lidar data

NASA Astrophysics Data System (ADS)

Razenkov, I. A.

2017-11-01

Micro pulse lasers have allowed solution of some technical problems and design of a specialized aerosol lidar capable of recording backscattering amplification (BSA) in a turbulent atmosphere (2014) by now. The BSA-lidar has two receiving channels, one of which is affected by a turbulence. The measurement result is the ratio of echo signals, i.e., the coefficient of backscattering amplification. The problem of lidar data inversion and retrieval of "optical" turbulence parameters was recently solved by V.V. Vorob'ev theoretically (2016). A lidar experiment was organized for testing the solution, and the asymptotic solution was applied to echo signals, which allowed estimating the daily behavior of the structural characteristics Cn 2 along a horizontal 2-km path. The experiment was accompanied by parallel independent measurements of Cn 2 by an image jitter sensor along the same path. It was shown experimentally that the Vorob'ev solution is applicable to Cn 2 retrieval from BSA-lidar data if β0 2<=3 for β0 2>3, the saturation of the amplification effect and a decrease in the experimental data with respect to calculation results are observed. The coefficient of correlation between the retrieved structural characteristics Cn 2 of the lidar and jitter sensor is 0.8-0.9. The Cn 2 values retrieved from lidar signals turned out to be 20-40% lower than the Cn 2 values of the image jitter sensor.

a Novel Discrete Optimal Transport Method for Bayesian Inverse Problems

NASA Astrophysics Data System (ADS)

Bui-Thanh, T.; Myers, A.; Wang, K.; Thiery, A.

2017-12-01

We present the Augmented Ensemble Transform (AET) method for generating approximate samples from a high-dimensional posterior distribution as a solution to Bayesian inverse problems. Solving large-scale inverse problems is critical for some of the most relevant and impactful scientific endeavors of our time. Therefore, constructing novel methods for solving the Bayesian inverse problem in more computationally efficient ways can have a profound impact on the science community. This research derives the novel AET method for exploring a posterior by solving a sequence of linear programming problems, resulting in a series of transport maps which map prior samples to posterior samples, allowing for the computation of moments of the posterior. We show both theoretical and numerical results, indicating this method can offer superior computational efficiency when compared to other SMC methods. Most of this efficiency is derived from matrix scaling methods to solve the linear programming problem and derivative-free optimization for particle movement. We use this method to determine inter-well connectivity in a reservoir and the associated uncertainty related to certain parameters. The attached file shows the difference between the true parameter and the AET parameter in an example 3D reservoir problem. The error is within the Morozov discrepancy allowance with lower computational cost than other particle methods.

Seismic waveform inversion best practices: regional, global and exploration test cases

NASA Astrophysics Data System (ADS)

Modrak, Ryan; Tromp, Jeroen

2016-09-01

Reaching the global minimum of a waveform misfit function requires careful choices about the nonlinear optimization, preconditioning and regularization methods underlying an inversion. Because waveform inversion problems are susceptible to erratic convergence associated with strong nonlinearity, one or two test cases are not enough to reliably inform such decisions. We identify best practices, instead, using four seismic near-surface problems, one regional problem and two global problems. To make meaningful quantitative comparisons between methods, we carry out hundreds of inversions, varying one aspect of the implementation at a time. Comparing nonlinear optimization algorithms, we find that limited-memory BFGS provides computational savings over nonlinear conjugate gradient methods in a wide range of test cases. Comparing preconditioners, we show that a new diagonal scaling derived from the adjoint of the forward operator provides better performance than two conventional preconditioning schemes. Comparing regularization strategies, we find that projection, convolution, Tikhonov regularization and total variation regularization are effective in different contexts. Besides questions of one strategy or another, reliability and efficiency in waveform inversion depend on close numerical attention and care. Implementation details involving the line search and restart conditions have a strong effect on computational cost, regardless of the chosen nonlinear optimization algorithm.

Inverse modeling of BTEX dissolution and biodegradation at the Bemidji, MN crude-oil spill site

USGS Publications Warehouse

Essaid, H.I.; Cozzarelli, I.M.; Eganhouse, R.P.; Herkelrath, W.N.; Bekins, B.A.; Delin, G.N.

2003-01-01

The U.S. Geological Survey (USGS) solute transport and biodegradation code BIOMOC was used in conjunction with the USGS universal inverse modeling code UCODE to quantify field-scale hydrocarbon dissolution and biodegradation at the USGS Toxic Substances Hydrology Program crude-oil spill research site located near Bemidji, MN. This inverse modeling effort used the extensive historical data compiled at the Bemidji site from 1986 to 1997 and incorporated a multicomponent transport and biodegradation model. Inverse modeling was successful when coupled transport and degradation processes were incorporated into the model and a single dissolution rate coefficient was used for all BTEX components. Assuming a stationary oil body, we simulated benzene, toluene, ethylbenzene, m,p-xylene, and o-xylene (BTEX) concentrations in the oil and ground water, respectively, as well as dissolved oxygen. Dissolution from the oil phase and aerobic and anaerobic degradation processes were represented. The parameters estimated were the recharge rate, hydraulic conductivity, dissolution rate coefficient, individual first-order BTEX anaerobic degradation rates, and transverse dispersivity. Results were similar for simulations obtained using several alternative conceptual models of the hydrologic system and biodegradation processes. The dissolved BTEX concentration data were not sufficient to discriminate between these conceptual models. The calibrated simulations reproduced the general large-scale evolution of the plume, but did not reproduce the observed small-scale spatial and temporal variability in concentrations. The estimated anaerobic biodegradation rates for toluene and o-xylene were greater than the dissolution rate coefficient. However, the estimated anaerobic biodegradation rates for benzene, ethylbenzene, and m,p-xylene were less than the dissolution rate coefficient. The calibrated model was used to determine the BTEX mass balance in the oil body and groundwater plume. Dissolution from the oil body was greatest for compounds with large effective solubilities (benzene) and with large degradation rates (toluene and o-xylene). Anaerobic degradation removed 77% of the BTEX that dissolved into the water phase and aerobic degradation removed 17%. Although goodness-of-fit measures for the alternative conceptual models were not significantly different, predictions made with the models were quite variable. ?? 2003 Elsevier Science B.V. All rights reserved.

Accounting for model error in Bayesian solutions to hydrogeophysical inverse problems using a local basis approach

NASA Astrophysics Data System (ADS)

Köpke, Corinna; Irving, James; Elsheikh, Ahmed H.

2018-06-01

Bayesian solutions to geophysical and hydrological inverse problems are dependent upon a forward model linking subsurface physical properties to measured data, which is typically assumed to be perfectly known in the inversion procedure. However, to make the stochastic solution of the inverse problem computationally tractable using methods such as Markov-chain-Monte-Carlo (MCMC), fast approximations of the forward model are commonly employed. This gives rise to model error, which has the potential to significantly bias posterior statistics if not properly accounted for. Here, we present a new methodology for dealing with the model error arising from the use of approximate forward solvers in Bayesian solutions to hydrogeophysical inverse problems. Our approach is geared towards the common case where this error cannot be (i) effectively characterized through some parametric statistical distribution; or (ii) estimated by interpolating between a small number of computed model-error realizations. To this end, we focus on identification and removal of the model-error component of the residual during MCMC using a projection-based approach, whereby the orthogonal basis employed for the projection is derived in each iteration from the K-nearest-neighboring entries in a model-error dictionary. The latter is constructed during the inversion and grows at a specified rate as the iterations proceed. We demonstrate the performance of our technique on the inversion of synthetic crosshole ground-penetrating radar travel-time data considering three different subsurface parameterizations of varying complexity. Synthetic data are generated using the eikonal equation, whereas a straight-ray forward model is assumed for their inversion. In each case, our developed approach enables us to remove posterior bias and obtain a more realistic characterization of uncertainty.

Control and System Theory, Optimization, Inverse and Ill-Posed Problems

DTIC Science & Technology

1988-09-14

Justlfleatlen Distribut ion/ Availability Codes # AFOSR-87-0350 Avat’ and/or1987-1988 Dist Special *CONTROL AND SYSTEM THEORY , ~ * OPTIMIZATION, * INVERSE...considerable va- riety of research investigations within the grant areas (Control and system theory , Optimization, and Ill-posed problems]. The

Construction of Joule Thomson inversion curves for mixtures using equation of state

NASA Astrophysics Data System (ADS)

Patankar, A. S.; Atrey, M. D.

2017-02-01

The Joule-Thomson effect is at the heart of Joule-Thomson cryocoolers and gas liquefaction cycles. The effective harnessing of this phenomenon necessitates the knowledge of Joule-Thomson coefficient and the inversion curve. When the working fluid is a mixture, (in mix refrigerant Joule-Thomson cryocooler, MRJT) the phase diagrams, equations of state and inversion curves of multi-component systems become important. The lowest temperature attainable by such a cryocooler depends on the inversion characteristics of the mixture used. In this work the construction of differential Joule-Thomson inversion curves of mixtures using Redlich-Kwong, Soave-Redlich-Kwong and Peng-Robinson equations of state is investigated assuming single phase. It is demonstrated that inversion curves constructed for pure fluids can be improved by choosing an appropriate value of acentric factor. Inversion curves are used to predict maximum inversion temperatures of multicomponent systems. An application where this information is critical is a two-stage J-T cryocooler using a mixture as the working fluid, especially for the second stage. The pre-cooling temperature that the first stage is required to generate depends on the maximum inversion temperature of the second stage working fluid.

Towards adjoint-based inversion for rheological parameters in nonlinear viscous mantle flow

NASA Astrophysics Data System (ADS)

Worthen, Jennifer; Stadler, Georg; Petra, Noemi; Gurnis, Michael; Ghattas, Omar

2014-09-01

We address the problem of inferring mantle rheological parameter fields from surface velocity observations and instantaneous nonlinear mantle flow models. We formulate this inverse problem as an infinite-dimensional nonlinear least squares optimization problem governed by nonlinear Stokes equations. We provide expressions for the gradient of the cost functional of this optimization problem with respect to two spatially-varying rheological parameter fields: the viscosity prefactor and the exponent of the second invariant of the strain rate tensor. Adjoint (linearized) Stokes equations, which are characterized by a 4th order anisotropic viscosity tensor, facilitates efficient computation of the gradient. A quasi-Newton method for the solution of this optimization problem is presented, which requires the repeated solution of both nonlinear forward Stokes and linearized adjoint Stokes equations. For the solution of the nonlinear Stokes equations, we find that Newton’s method is significantly more efficient than a Picard fixed point method. Spectral analysis of the inverse operator given by the Hessian of the optimization problem reveals that the numerical eigenvalues collapse rapidly to zero, suggesting a high degree of ill-posedness of the inverse problem. To overcome this ill-posedness, we employ Tikhonov regularization (favoring smooth parameter fields) or total variation (TV) regularization (favoring piecewise-smooth parameter fields). Solution of two- and three-dimensional finite element-based model inverse problems show that a constant parameter in the constitutive law can be recovered well from surface velocity observations. Inverting for a spatially-varying parameter field leads to its reasonable recovery, in particular close to the surface. When inferring two spatially varying parameter fields, only an effective viscosity field and the total viscous dissipation are recoverable. Finally, a model of a subducting plate shows that a localized weak zone at the plate boundary can be partially recovered, especially with TV regularization.

Deconvolution using a neural network

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lehman, S.K.

1990-11-15

Viewing one dimensional deconvolution as a matrix inversion problem, we compare a neural network backpropagation matrix inverse with LMS, and pseudo-inverse. This is a largely an exercise in understanding how our neural network code works. 1 ref.

Genetics Home Reference: Koolen-de Vries syndrome

MedlinePlus

... of Koolen-de Vries syndrome , has undergone an inversion . An inversion involves two breaks in a chromosome; the resulting ... lineage have no health problems related to the inversion. However, genetic material can be lost or duplicated ...

Three-dimensional inversion of multisource array electromagnetic data

NASA Astrophysics Data System (ADS)

Tartaras, Efthimios

Three-dimensional (3-D) inversion is increasingly important for the correct interpretation of geophysical data sets in complex environments. To this effect, several approximate solutions have been developed that allow the construction of relatively fast inversion schemes. One such method that is fast and provides satisfactory accuracy is the quasi-linear (QL) approximation. It has, however, the drawback that it is source-dependent and, therefore, impractical in situations where multiple transmitters in different positions are employed. I have, therefore, developed a localized form of the QL approximation that is source-independent. This so-called localized quasi-linear (LQL) approximation can have a scalar, a diagonal, or a full tensor form. Numerical examples of its comparison with the full integral equation solution, the Born approximation, and the original QL approximation are given. The objective behind developing this approximation is to use it in a fast 3-D inversion scheme appropriate for multisource array data such as those collected in airborne surveys, cross-well logging, and other similar geophysical applications. I have developed such an inversion scheme using the scalar and diagonal LQL approximation. It reduces the original nonlinear inverse electromagnetic (EM) problem to three linear inverse problems. The first of these problems is solved using a weighted regularized linear conjugate gradient method, whereas the last two are solved in the least squares sense. The algorithm I developed provides the option of obtaining either smooth or focused inversion images. I have applied the 3-D LQL inversion to synthetic 3-D EM data that simulate a helicopter-borne survey over different earth models. The results demonstrate the stability and efficiency of the method and show that the LQL approximation can be a practical solution to the problem of 3-D inversion of multisource array frequency-domain EM data. I have also applied the method to helicopter-borne EM data collected by INCO Exploration over the Voisey's Bay area in Labrador, Canada. The results of the 3-D inversion successfully delineate the shallow massive sulfides and show that the method can produce reasonable results even in areas of complex geology and large resistivity contrasts.

Sensitivity computation of the ell1 minimization problem and its application to dictionary design of ill-posed problems

NASA Astrophysics Data System (ADS)

Horesh, L.; Haber, E.

2009-09-01

The ell1 minimization problem has been studied extensively in the past few years. Recently, there has been a growing interest in its application for inverse problems. Most studies have concentrated in devising ways for sparse representation of a solution using a given prototype dictionary. Very few studies have addressed the more challenging problem of optimal dictionary construction, and even these were primarily devoted to the simplistic sparse coding application. In this paper, sensitivity analysis of the inverse solution with respect to the dictionary is presented. This analysis reveals some of the salient features and intrinsic difficulties which are associated with the dictionary design problem. Equipped with these insights, we propose an optimization strategy that alleviates these hurdles while utilizing the derived sensitivity relations for the design of a locally optimal dictionary. Our optimality criterion is based on local minimization of the Bayesian risk, given a set of training models. We present a mathematical formulation and an algorithmic framework to achieve this goal. The proposed framework offers the design of dictionaries for inverse problems that incorporate non-trivial, non-injective observation operators, where the data and the recovered parameters may reside in different spaces. We test our algorithm and show that it yields improved dictionaries for a diverse set of inverse problems in geophysics and medical imaging.

Inverse scattering transform and soliton classification of the coupled modified Korteweg-de Vries equation

NASA Astrophysics Data System (ADS)

Wu, Jianping; Geng, Xianguo

2017-12-01

The inverse scattering transform of the coupled modified Korteweg-de Vries equation is studied by the Riemann-Hilbert approach. In the direct scattering process, the spectral analysis of the Lax pair is performed, from which a Riemann-Hilbert problem is established for the equation. In the inverse scattering process, by solving Riemann-Hilbert problems corresponding to the reflectionless cases, three types of multi-soliton solutions are obtained. The multi-soliton classification is based on the zero structures of the Riemann-Hilbert problem. In addition, some figures are given to illustrate the soliton characteristics of the coupled modified Korteweg-de Vries equation.

Time domain analysis of thin-wire antennas over lossy ground using the reflection-coefficient approximation

NASA Astrophysics Data System (ADS)

FernáNdez Pantoja, M.; Yarovoy, A. G.; Rubio Bretones, A.; GonzáLez GarcíA, S.

2009-12-01

This paper presents a procedure to extend the methods of moments in time domain for the transient analysis of thin-wire antennas to include those cases where the antennas are located over a lossy half-space. This extended technique is based on the reflection coefficient (RC) approach, which approximates the fields incident on the ground interface as plane waves and calculates the time domain RC using the inverse Fourier transform of Fresnel equations. The implementation presented in this paper uses general expressions for the RC which extend its range of applicability to lossy grounds, and is proven to be accurate and fast for antennas located not too near to the ground. The resulting general purpose procedure, able to treat arbitrarily oriented thin-wire antennas, is appropriate for all kind of half-spaces, including lossy cases, and it has turned out to be as computationally fast solving the problem of an arbitrary ground as dealing with a perfect electric conductor ground plane. Results show a numerical validation of the method for different half-spaces, paying special attention to the influence of the antenna to ground distance in the accuracy of the results.

Individual differences in children's understanding of inversion and arithmetical skill.

PubMed

Gilmore, Camilla K; Bryant, Peter

2006-06-01

Background and aims. In order to develop arithmetic expertise, children must understand arithmetic principles, such as the inverse relationship between addition and subtraction, in addition to learning calculation skills. We report two experiments that investigate children's understanding of the principle of inversion and the relationship between their conceptual understanding and arithmetical skills. A group of 127 children from primary schools took part in the study. The children were from 2 age groups (6-7 and 8-9 years). Children's accuracy on inverse and control problems in a variety of presentation formats and in canonical and non-canonical forms was measured. Tests of general arithmetic ability were also administered. Children consistently performed better on inverse than control problems, which indicates that they could make use of the inverse principle. Presentation format affected performance: picture presentation allowed children to apply their conceptual understanding flexibly regardless of the problem type, while word problems restricted their ability to use their conceptual knowledge. Cluster analyses revealed three subgroups with different profiles of conceptual understanding and arithmetical skill. Children in the 'high ability' and 'low ability' groups showed conceptual understanding that was in-line with their arithmetical skill, whilst a 3rd group of children had more advanced conceptual understanding than arithmetical skill. The three subgroups may represent different points along a single developmental path or distinct developmental paths. The discovery of the existence of the three groups has important consequences for education. It demonstrates the importance of considering the pattern of individual children's conceptual understanding and problem-solving skills.

Automated Carrier Landing of an Unmanned Combat Aerial Vehicle Using Dynamic Inversion

DTIC Science & Technology

2007-06-01

17 CN normal force coefficient . . . . . . . . . . . . . . . . . . . . 17 CA axial force coefficient...slug·ft2 Ixzb 0 slug·ft2 The aircraft has a single engine inlet for a single, centerline mounted turbofan engine. For purposes of this research, the...assumed to remain constant for each simulation run and were based on an assumed 10% fuel load with full weapons [2]. The rest of these values were

Remote Sensing Image Fusion Method Based on Nonsubsampled Shearlet Transform and Sparse Representation

NASA Astrophysics Data System (ADS)

Moonon, Altan-Ulzii; Hu, Jianwen; Li, Shutao

2015-12-01

The remote sensing image fusion is an important preprocessing technique in remote sensing image processing. In this paper, a remote sensing image fusion method based on the nonsubsampled shearlet transform (NSST) with sparse representation (SR) is proposed. Firstly, the low resolution multispectral (MS) image is upsampled and color space is transformed from Red-Green-Blue (RGB) to Intensity-Hue-Saturation (IHS). Then, the high resolution panchromatic (PAN) image and intensity component of MS image are decomposed by NSST to high and low frequency coefficients. The low frequency coefficients of PAN and the intensity component are fused by the SR with the learned dictionary. The high frequency coefficients of intensity component and PAN image are fused by local energy based fusion rule. Finally, the fused result is obtained by performing inverse NSST and inverse IHS transform. The experimental results on IKONOS and QuickBird satellites demonstrate that the proposed method provides better spectral quality and superior spatial information in the fused image than other remote sensing image fusion methods both in visual effect and object evaluation.

Effects of molecular size and structure on self-diffusion coefficient and viscosity for saturated hydrocarbons having six carbon atoms.

PubMed

Iwahashi, Makio; Kasahara, Yasutoshi

2007-01-01

Self-diffusion coefficients and viscosities for the saturated hydrocarbons having six carbon atoms such as hexane, 2-methylpentane (2MP), 3-methylpentane (3MP), 2,2-dimethylbutane (22DMB), 2,3-dimethylbutane (23DMB), methylcyclopentane (McP) and cyclohexane (cH) were measured at various constant temperatures; obtained results were discussed in connection with their molar volumes, molecular structures and thermodynamic properties. The values of self-diffusion coefficients as the microscopic property were inversely proportional to those of viscosities as the macroscopic property. The order of their viscosities was almost same to those of their melting temperatures and enthalpies of fusion, which reflect the attractive interactions among their molecules. On the other hand, the order of the self-diffusion coefficients inversely related to the order of the melting temperatures and the enthalpies of the fusion. Namely, the compound having the larger attractive interaction mostly shows the less mobility in its liquid state, e.g., cyclohexane (cH), having the largest attractive interaction and the smallest molar volume exhibits an extremely large viscosity and small self-diffusion coefficient comparing with other hydrocarbons. However, a significant exception was 22DMB, being most close to a sphere: In spite of the smallest attractive interaction and the largest molar volume of 22DMB in the all samples, it has the thirdly larger viscosity and the thirdly smaller self-diffusion coefficient. Consequently, the dynamical properties such as self-diffusion and viscosity for the saturated hydrocarbons are determined not only by their attractive interactions but also by their molecular structures.

THE SUCCESSIVE LINEAR ESTIMATOR: A REVISIT. (R827114)

EPA Science Inventory

This paper examines the theoretical basis of the successive linear estimator (SLE) that has been developed for the inverse problem in subsurface hydrology. We show that the SLE algorithm is a non-linear iterative estimator to the inverse problem. The weights used in the SLE al...

ON THE GEOSTATISTICAL APPROACH TO THE INVERSE PROBLEM. (R825689C037)

EPA Science Inventory

Abstract

The geostatistical approach to the inverse problem is discussed with emphasis on the importance of structural analysis. Although the geostatistical approach is occasionally misconstrued as mere cokriging, in fact it consists of two steps: estimation of statist...

On a local solvability and stability of the inverse transmission eigenvalue problem

NASA Astrophysics Data System (ADS)

Bondarenko, Natalia; Buterin, Sergey

2017-11-01

We prove a local solvability and stability of the inverse transmission eigenvalue problem posed by McLaughlin and Polyakov (1994 J. Diff. Equ. 107 351-82). In particular, this result establishes the minimality of the data used therein. The proof is constructive.

NLSE: Parameter-Based Inversion Algorithm

NASA Astrophysics Data System (ADS)

Sabbagh, Harold A.; Murphy, R. Kim; Sabbagh, Elias H.; Aldrin, John C.; Knopp, Jeremy S.

Chapter 11 introduced us to the notion of an inverse problem and gave us some examples of the value of this idea to the solution of realistic industrial problems. The basic inversion algorithm described in Chap. 11 was based upon the Gauss-Newton theory of nonlinear least-squares estimation and is called NLSE in this book. In this chapter we will develop the mathematical background of this theory more fully, because this algorithm will be the foundation of inverse methods and their applications during the remainder of this book. We hope, thereby, to introduce the reader to the application of sophisticated mathematical concepts to engineering practice without introducing excessive mathematical sophistication.

Solution of some types of differential equations: operational calculus and inverse differential operators.

PubMed

Zhukovsky, K

2014-01-01

We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated.

Multi-Focus Image Fusion Based on NSCT and NSST

NASA Astrophysics Data System (ADS)

Moonon, Altan-Ulzii; Hu, Jianwen

2015-12-01

In this paper, a multi-focus image fusion algorithm based on the nonsubsampled contourlet transform (NSCT) and the nonsubsampled shearlet transform (NSST) is proposed. The source images are first decomposed by the NSCT and NSST into low frequency coefficients and high frequency coefficients. Then, the average method is used to fuse low frequency coefficient of the NSCT. To obtain more accurate salience measurement, the high frequency coefficients of the NSST and NSCT are combined to measure salience. The high frequency coefficients of the NSCT with larger salience are selected as fused high frequency coefficients. Finally, the fused image is reconstructed by the inverse NSCT. We adopt three metrics (Q AB/F , Q e and Q w ) to evaluate the quality of fused images. The experimental results demonstrate that the proposed method outperforms other methods. It retains highly detailed edges and contours.

Invertible flexible matrices

NASA Astrophysics Data System (ADS)

Justino, Júlia

2017-06-01

Matrices with coefficients having uncertainties of type o (.) or O (.), called flexible matrices, are studied from the point of view of nonstandard analysis. The uncertainties of the afore-mentioned kind will be given in the form of the so-called neutrices, for instance the set of all infinitesimals. Since flexible matrices have uncertainties in their coefficients, it is not possible to define the identity matrix in an unique way and so the notion of spectral identity matrix arises. Not all nonsingular flexible matrices can be turned into a spectral identity matrix using Gauss-Jordan elimination method, implying that that not all nonsingular flexible matrices have the inverse matrix. Under certain conditions upon the size of the uncertainties appearing in a nonsingular flexible matrix, a general theorem concerning the boundaries of its minors is presented which guarantees the existence of the inverse matrix of a nonsingular flexible matrix.

SU-F-R-45: The Prognostic Value of Radiotherapy Based On the Changes of Texture Features Between Pre-Treatment and Post-Treatment FDG PET Image for NSCLC Patients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ma, C; Yin, Y

Purpose: The purpose of this research is investigating which texture features extracted from FDG-PET images by gray-level co-occurrence matrix(GLCM) have a higher prognostic value than the other texture features. Methods: 21 non-small cell lung cancer(NSCLC) patients were approved in the study. Patients underwent 18F-FDG PET/CT scans with both pre-treatment and post-treatment. Firstly, the tumors were extracted by our house developed software. Secondly, the clinical features including the maximum SUV and tumor volume were extracted by MIM vista software, and texture features including angular second moment, contrast, inverse different moment, entropy and correlation were extracted using MATLAB.The differences can be calculatedmore » by using post-treatment features to subtract pre-treatment features. Finally, the SPSS software was used to get the Pearson correlation coefficients and Spearman rank correlation coefficients between the change ratios of texture features and change ratios of clinical features. Results: The Pearson and Spearman rank correlation coefficient between contrast and SUV maximum is 0.785 and 0.709. The P and S value between inverse difference moment and tumor volume is 0.953 and 0.942. Conclusion: This preliminary study showed that the relationships between different texture features and the same clinical feature are different. Finding the prognostic value of contrast and inverse difference moment were higher than the other three textures extracted by GLCM.« less

Solving inversion problems with neural networks

NASA Technical Reports Server (NTRS)

Kamgar-Parsi, Behzad; Gualtieri, J. A.

1990-01-01

A class of inverse problems in remote sensing can be characterized by Q = F(x), where F is a nonlinear and noninvertible (or hard to invert) operator, and the objective is to infer the unknowns, x, from the observed quantities, Q. Since the number of observations is usually greater than the number of unknowns, these problems are formulated as optimization problems, which can be solved by a variety of techniques. The feasibility of neural networks for solving such problems is presently investigated. As an example, the problem of finding the atmospheric ozone profile from measured ultraviolet radiances is studied.

Approximation of the ruin probability using the scaled Laplace transform inversion

PubMed Central

Mnatsakanov, Robert M.; Sarkisian, Khachatur; Hakobyan, Artak

2015-01-01

The problem of recovering the ruin probability in the classical risk model based on the scaled Laplace transform inversion is studied. It is shown how to overcome the problem of evaluating the ruin probability at large values of an initial surplus process. Comparisons of proposed approximations with the ones based on the Laplace transform inversions using a fixed Talbot algorithm as well as on the ones using the Trefethen–Weideman–Schmelzer and maximum entropy methods are presented via a simulation study. PMID:26752796

Inverse problems and coherence

NASA Astrophysics Data System (ADS)

Baltes, H. P.; Ferwerda, H. A.

1981-03-01

A summary of current inverse problems of statistical optics is presented together with a short guide to the pertinent review-type literature. The retrieval of structural information from the far-zone degree of coherence and the average intensity distribution of radiation scattered by a superposition of random and periodic scatterers is discussed.

Application of quasi-distributions for solving inverse problems of neutron and {gamma}-ray transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pogosbekyan, L.R.; Lysov, D.A.

The considered inverse problems deal with the calculation of the unknown values of nuclear installations by means of the known (goal) functionals of neutron/{gamma}-ray distributions. The example of these problems might be the calculation of the automatic control rods position as function of neutron sensors reading, or the calculation of experimentally-corrected values of cross-sections, isotopes concentration, fuel enrichment via the measured functional. The authors have developed the new method to solve inverse problem. It finds flux density as quasi-solution of the particles conservation linear system adjointed to equalities for functionals. The method is more effective compared to the one basedmore » on the classical perturbation theory. It is suitable for vectorization and it can be used successfully in optimization codes.« less

SIAM conference on inverse problems: Geophysical applications. Final technical report

DOE Office of Scientific and Technical Information (OSTI.GOV)

NONE

1995-12-31

This conference was the second in a series devoted to a particular area of inverse problems. The theme of this series is to discuss problems of major scientific importance in a specific area from a mathematical perspective. The theme of this symposium was geophysical applications. In putting together the program we tried to include a wide range of mathematical scientists and to interpret geophysics in as broad a sense as possible. Our speaker came from industry, government laboratories, and diverse departments in academia. We managed to attract a geographically diverse audience with participation from five continents. There were talks devotedmore » to seismology, hydrology, determination of the earth`s interior on a global scale as well as oceanographic and atmospheric inverse problems.« less

Influence of cost functions and optimization methods on solving the inverse problem in spatially resolved diffuse reflectance spectroscopy

NASA Astrophysics Data System (ADS)

Rakotomanga, Prisca; Soussen, Charles; Blondel, Walter C. P. M.

2017-03-01

Diffuse reflectance spectroscopy (DRS) has been acknowledged as a valuable optical biopsy tool for in vivo characterizing pathological modifications in epithelial tissues such as cancer. In spatially resolved DRS, accurate and robust estimation of the optical parameters (OP) of biological tissues is a major challenge due to the complexity of the physical models. Solving this inverse problem requires to consider 3 components: the forward model, the cost function, and the optimization algorithm. This paper presents a comparative numerical study of the performances in estimating OP depending on the choice made for each of the latter components. Mono- and bi-layer tissue models are considered. Monowavelength (scalar) absorption and scattering coefficients are estimated. As a forward model, diffusion approximation analytical solutions with and without noise are implemented. Several cost functions are evaluated possibly including normalized data terms. Two local optimization methods, Levenberg-Marquardt and TrustRegion-Reflective, are considered. Because they may be sensitive to the initial setting, a global optimization approach is proposed to improve the estimation accuracy. This algorithm is based on repeated calls to the above-mentioned local methods, with initial parameters randomly sampled. Two global optimization methods, Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), are also implemented. Estimation performances are evaluated in terms of relative errors between the ground truth and the estimated values for each set of unknown OP. The combination between the number of variables to be estimated, the nature of the forward model, the cost function to be minimized and the optimization method are discussed.

In vivo repeatability of the pulse wave inverse problem in human carotid arteries.

PubMed

McGarry, Matthew; Nauleau, Pierre; Apostolakis, Iason; Konofagou, Elisa

2017-11-07

Accurate arterial stiffness measurement would improve diagnosis and monitoring for many diseases. Atherosclerotic plaques and aneurysms are expected to involve focal changes in vessel wall properties; therefore, a method to image the stiffness variation would be a valuable clinical tool. The pulse wave inverse problem (PWIP) fits unknown parameters from a computational model of arterial pulse wave propagation to ultrasound-based measurements of vessel wall displacements by minimizing the difference between the model and measured displacements. The PWIP has been validated in phantoms, and this study presents the first in vivo demonstration. The common carotid arteries of five healthy volunteers were imaged five times in a single session with repositioning of the probe and subject between each scan. The 1D finite difference computational model used in the PWIP spanned from the start of the transducer to the carotid bifurcation, where a resistance outlet boundary condition was applied to approximately model the downstream reflection of the pulse wave. Unknown parameters that were estimated by the PWIP included a 10-segment linear piecewise compliance distribution and 16 discrete cosine transformation coefficients for each of the inlet boundary conditions. Input data was selected to include pulse waves resulting from the primary pulse and dicrotic notch. The recovered compliance maps indicate that the compliance increases close to the bifurcation, and the variability of the average pulse wave velocity estimated through the PWIP is on the order of 11%, which is similar to that of the conventional processing technique which tracks the wavefront arrival time (13%). Copyright © 2017 Elsevier Ltd. All rights reserved.

Inverse problems and optimal experiment design in unsteady heat transfer processes identification

NASA Technical Reports Server (NTRS)

Artyukhin, Eugene A.

1991-01-01

Experimental-computational methods for estimating characteristics of unsteady heat transfer processes are analyzed. The methods are based on the principles of distributed parameter system identification. The theoretical basis of such methods is the numerical solution of nonlinear ill-posed inverse heat transfer problems and optimal experiment design problems. Numerical techniques for solving problems are briefly reviewed. The results of the practical application of identification methods are demonstrated when estimating effective thermophysical characteristics of composite materials and thermal contact resistance in two-layer systems.

A Differential Evolution Based Approach to Estimate the Shape and Size of Complex Shaped Anomalies Using EIT Measurements

NASA Astrophysics Data System (ADS)

Rashid, Ahmar; Khambampati, Anil Kumar; Kim, Bong Seok; Liu, Dong; Kim, Sin; Kim, Kyung Youn

EIT image reconstruction is an ill-posed problem, the spatial resolution of the estimated conductivity distribution is usually poor and the external voltage measurements are subject to variable noise. Therefore, EIT conductivity estimation cannot be used in the raw form to correctly estimate the shape and size of complex shaped regional anomalies. An efficient algorithm employing a shape based estimation scheme is needed. The performance of traditional inverse algorithms, such as the Newton Raphson method, used for this purpose is below par and depends upon the initial guess and the gradient of the cost functional. This paper presents the application of differential evolution (DE) algorithm to estimate complex shaped region boundaries, expressed as coefficients of truncated Fourier series, using EIT. DE is a simple yet powerful population-based, heuristic algorithm with the desired features to solve global optimization problems under realistic conditions. The performance of the algorithm has been tested through numerical simulations, comparing its results with that of the traditional modified Newton Raphson (mNR) method.

Modelling mass diffusion for a multi-layer sphere immersed in a semi-infinite medium: application to drug delivery.

PubMed

Carr, Elliot J; Pontrelli, Giuseppe

2018-04-12

We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as those imposing a finite mass resistance at the external surface of the sphere. While the work is applicable to the generic problem of heat or mass transfer in a multi-layer sphere, the analysis and results are presented in the context of drug kinetics for desorbing and absorbing spherical microcapsules. We derive an analytical solution for the concentration in the sphere and in the surrounding medium that avoids any artificial truncation at a finite distance. The closed-form solution in each concentric layer is expressed in terms of a suitably-defined inverse Laplace transform that can be evaluated numerically. Concentration profiles and drug mass curves in the spherical layers and in the external environment are presented and the dependency of the solution on the mass transfer coefficient at the surface of the sphere analyzed. Copyright © 2018 Elsevier Inc. All rights reserved.

The CFL condition for spectral approximations to hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Gottlieb, David; Tadmor, Eitan

1991-01-01

The stability of spectral approximations to scalar hyperbolic initial-boundary value problems with variable coefficients are studied. Time is discretized by explicit multi-level or Runge-Kutta methods of order less than or equal to 3 (forward Euler time differencing is included), and spatial discretizations are studied by spectral and pseudospectral approximations associated with the general family of Jacobi polynomials. It is proved that these fully explicit spectral approximations are stable provided their time-step, delta t, is restricted by the CFL-like condition, delta t less than Const. N(exp-2), where N equals the spatial number of degrees of freedom. We give two independent proofs of this result, depending on two different choices of approximate L(exp 2)-weighted norms. In both approaches, the proofs hinge on a certain inverse inequality interesting for its own sake. The result confirms the commonly held belief that the above CFL stability restriction, which is extensively used in practical implementations, guarantees the stability (and hence the convergence) of fully-explicit spectral approximations in the nonperiodic case.

The CFL condition for spectral approximations to hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Gottlieb, David; Tadmor, Eitan

1990-01-01

The stability of spectral approximations to scalar hyperbolic initial-boundary value problems with variable coefficients are studied. Time is discretized by explicit multi-level or Runge-Kutta methods of order less than or equal to 3 (forward Euler time differencing is included), and spatial discretizations are studied by spectral and pseudospectral approximations associated with the general family of Jacobi polynomials. It is proved that these fully explicit spectral approximations are stable provided their time-step, delta t, is restricted by the CFL-like condition, delta t less than Const. N(exp-2), where N equals the spatial number of degrees of freedom. We give two independent proofs of this result, depending on two different choices of approximate L(exp 2)-weighted norms. In both approaches, the proofs hinge on a certain inverse inequality interesting for its own sake. The result confirms the commonly held belief that the above CFL stability restriction, which is extensively used in practical implementations, guarantees the stability (and hence the convergence) of fully-explicit spectral approximations in the nonperiodic case.

Inverse problem of the vibrational band gap of periodically supported beam

NASA Astrophysics Data System (ADS)

Shi, Xiaona; Shu, Haisheng; Dong, Fuzhen; Zhao, Lei

2017-04-01

The researches of periodic structures have a long history with the main contents confined in the field of forward problem. In this paper, the inverse problem is considered and an overall frame is proposed which includes two main stages, i.e., the band gap criterion and its optimization. As a preliminary investigation, the inverse problem of the flexural vibrational band gap of a periodically supported beam is analyzed. According to existing knowledge of its forward problem, the band gap criterion is given in implicit form. Then, two cases with three independent parameters, namely the double supported case and the triple one, are studied in detail and the explicit expressions of the feasible domain are constructed by numerical fitting. Finally, the parameter optimization of the double supported case with three variables is conducted using genetic algorithm aiming for the best mean attenuation within specified frequency band.

Large-scale inverse model analyses employing fast randomized data reduction

NASA Astrophysics Data System (ADS)

Lin, Youzuo; Le, Ellen B.; O'Malley, Daniel; Vesselinov, Velimir V.; Bui-Thanh, Tan

2017-08-01

When the number of observations is large, it is computationally challenging to apply classical inverse modeling techniques. We have developed a new computationally efficient technique for solving inverse problems with a large number of observations (e.g., on the order of 107 or greater). Our method, which we call the randomized geostatistical approach (RGA), is built upon the principal component geostatistical approach (PCGA). We employ a data reduction technique combined with the PCGA to improve the computational efficiency and reduce the memory usage. Specifically, we employ a randomized numerical linear algebra technique based on a so-called "sketching" matrix to effectively reduce the dimension of the observations without losing the information content needed for the inverse analysis. In this way, the computational and memory costs for RGA scale with the information content rather than the size of the calibration data. Our algorithm is coded in Julia and implemented in the MADS open-source high-performance computational framework (http://mads.lanl.gov). We apply our new inverse modeling method to invert for a synthetic transmissivity field. Compared to a standard geostatistical approach (GA), our method is more efficient when the number of observations is large. Most importantly, our method is capable of solving larger inverse problems than the standard GA and PCGA approaches. Therefore, our new model inversion method is a powerful tool for solving large-scale inverse problems. The method can be applied in any field and is not limited to hydrogeological applications such as the characterization of aquifer heterogeneity.

Geophysical approaches to inverse problems: A methodological comparison. Part 1: A Posteriori approach

NASA Technical Reports Server (NTRS)

Seidman, T. I.; Munteanu, M. J.

1979-01-01

The relationships of a variety of general computational methods (and variances) for treating illposed problems such as geophysical inverse problems are considered. Differences in approach and interpretation based on varying assumptions as to, e.g., the nature of measurement uncertainties are discussed along with the factors to be considered in selecting an approach. The reliability of the results of such computation is addressed.

Layer Stripping Solutions of Inverse Seismic Problems.

DTIC Science & Technology

1985-03-21

problems--more so than has generally been recognized. The subject of this thesis is the theoretical development of the . layer-stripping methodology , and...medium varies sharply at each interface, which would be expected to cause difficulties for the algorithm, since it was designed for a smoothy varying... methodology was applied in a novel way. The inverse problem considered in this chapter was that of reconstructing a layered medium from measurement of its

Hydromagnetic conditions near the core-mantle boundary

NASA Technical Reports Server (NTRS)

Backus, George E.

1995-01-01

The main results of the grant were (1) finishing the manuscript of a proof of completeness of the Poincare modes in an incompressible nonviscous fluid corotating with a rigid ellipsoidal boundary, (2) partial completion of a manuscript describing a definition of helicity that resolved questions in the literature about calculating the helicities of vector fields with complicated topologies, and (3) the beginning of a reexamination of the inverse problem of inferring properties of the geomagnetic field B just outside the core-mantle boundary (CMB) from measurements of elements of B at and above the earth's surface. This last work has led to a simple general formalism for linear and nonlinear inverse problems that appears to include all the inversion schemes so far considered for the uniqueness problem in geomagnetic inversion. The technique suggests some new methods for error estimation that form part of this report.

The Relationship Between Non-Symbolic Multiplication and Division in Childhood

PubMed Central

McCrink, Koleen; Shafto, Patrick; Barth, Hilary

2016-01-01

Children without formal education in addition and subtraction are able to perform multi-step operations over an approximate number of objects. Further, their performance improves when solving approximate (but not exact) addition and subtraction problems that allow for inversion as a shortcut (e.g., a + b − b = a). The current study examines children’s ability to perform multi-step operations, and the potential for an inversion benefit, for the operations of approximate, non-symbolic multiplication and division. Children were trained to compute a multiplication and division scaling factor (*2 or /2, *4 or /4), and then tested on problems that combined two of these factors in a way that either allowed for an inversion shortcut (e.g., 8 * 4 / 4) or did not (e.g., 8 * 4 / 2). Children’s performance was significantly better than chance for all scaling factors during training, and they successfully computed the outcomes of the multi-step testing problems. They did not exhibit a performance benefit for problems with the a * b / b structure, suggesting they did not draw upon inversion reasoning as a logical shortcut to help them solve the multi-step test problems. PMID:26880261

Effects of adaptive refinement on the inverse EEG solution

NASA Astrophysics Data System (ADS)

Weinstein, David M.; Johnson, Christopher R.; Schmidt, John A.

1995-10-01

One of the fundamental problems in electroencephalography can be characterized by an inverse problem. Given a subset of electrostatic potentials measured on the surface of the scalp and the geometry and conductivity properties within the head, calculate the current vectors and potential fields within the cerebrum. Mathematically the generalized EEG problem can be stated as solving Poisson's equation of electrical conduction for the primary current sources. The resulting problem is mathematically ill-posed i.e., the solution does not depend continuously on the data, such that small errors in the measurement of the voltages on the scalp can yield unbounded errors in the solution, and, for the general treatment of a solution of Poisson's equation, the solution is non-unique. However, if accurate solutions the general treatment of a solution of Poisson's equation, the solution is non-unique. However, if accurate solutions to such problems could be obtained, neurologists would gain noninvasive accesss to patient-specific cortical activity. Access to such data would ultimately increase the number of patients who could be effectively treated for pathological cortical conditions such as temporal lobe epilepsy. In this paper, we present the effects of spatial adaptive refinement on the inverse EEG problem and show that the use of adaptive methods allow for significantly better estimates of electric and potential fileds within the brain through an inverse procedure. To test these methods, we have constructed several finite element head models from magneteic resonance images of a patient. The finite element meshes ranged in size from 2724 nodes and 12,812 elements to 5224 nodes and 29,135 tetrahedral elements, depending on the level of discretization. We show that an adaptive meshing algorithm minimizes the error in the forward problem due to spatial discretization and thus increases the accuracy of the inverse solution.

Solving an inverse eigenvalue problem with triple constraints on eigenvalues, singular values, and diagonal elements

NASA Astrophysics Data System (ADS)

Wu, Sheng-Jhih; Chu, Moody T.

2017-08-01

An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing-Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations.

A quasi-spectral method for Cauchy problem of 2/D Laplace equation on an annulus

NASA Astrophysics Data System (ADS)

Saito, Katsuyoshi; Nakada, Manabu; Iijima, Kentaro; Onishi, Kazuei

2005-01-01

Real numbers are usually represented in the computer as a finite number of digits hexa-decimal floating point numbers. Accordingly the numerical analysis is often suffered from rounding errors. The rounding errors particularly deteriorate the precision of numerical solution in inverse and ill-posed problems. We attempt to use a multi-precision arithmetic for reducing the rounding error evil. The use of the multi-precision arithmetic system is by the courtesy of Dr Fujiwara of Kyoto University. In this paper we try to show effectiveness of the multi-precision arithmetic by taking two typical examples; the Cauchy problem of the Laplace equation in two dimensions and the shape identification problem by inverse scattering in three dimensions. It is concluded from a few numerical examples that the multi-precision arithmetic works well on the resolution of those numerical solutions, as it is combined with the high order finite difference method for the Cauchy problem and with the eigenfunction expansion method for the inverse scattering problem.

Problems on Divisibility of Binomial Coefficients

ERIC Educational Resources Information Center

Osler, Thomas J.; Smoak, James

2004-01-01

Twelve unusual problems involving divisibility of the binomial coefficients are represented in this article. The problems are listed in "The Problems" section. All twelve problems have short solutions which are listed in "The Solutions" section. These problems could be assigned to students in any course in which the binomial theorem and Pascal's…

Inverse problems with nonnegative and sparse solutions: algorithms and application to the phase retrieval problem

NASA Astrophysics Data System (ADS)

Quy Muoi, Pham; Nho Hào, Dinh; Sahoo, Sujit Kumar; Tang, Dongliang; Cong, Nguyen Huu; Dang, Cuong

2018-05-01

In this paper, we study a gradient-type method and a semismooth Newton method for minimization problems in regularizing inverse problems with nonnegative and sparse solutions. We propose a special penalty functional forcing the minimizers of regularized minimization problems to be nonnegative and sparse, and then we apply the proposed algorithms in a practical the problem. The strong convergence of the gradient-type method and the local superlinear convergence of the semismooth Newton method are proven. Then, we use these algorithms for the phase retrieval problem and illustrate their efficiency in numerical examples, particularly in the practical problem of optical imaging through scattering media where all the noises from experiment are presented.

Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Luo, Xu-Dan; Musslimani, Ziad H.

2018-01-01

In 2013, a new nonlocal symmetry reduction of the well-known AKNS (an integrable system of partial differential equations, introduced by and named after Mark J. Ablowitz, David J. Kaup, and Alan C. Newell et al. (1974)) scattering problem was found. It was shown to give rise to a new nonlocal PT symmetric and integrable Hamiltonian nonlinear Schrödinger (NLS) equation. Subsequently, the inverse scattering transform was constructed for the case of rapidly decaying initial data and a family of spatially localized, time periodic one-soliton solutions was found. In this paper, the inverse scattering transform for the nonlocal NLS equation with nonzero boundary conditions at infinity is presented in four different cases when the data at infinity have constant amplitudes. The direct and inverse scattering problems are analyzed. Specifically, the direct problem is formulated, the analytic properties of the eigenfunctions and scattering data and their symmetries are obtained. The inverse scattering problem, which arises from a novel nonlocal system, is developed via a left-right Riemann-Hilbert problem in terms of a suitable uniformization variable and the time dependence of the scattering data is obtained. This leads to a method to linearize/solve the Cauchy problem. Pure soliton solutions are discussed, and explicit 1-soliton solution and two 2-soliton solutions are provided for three of the four different cases corresponding to two different signs of nonlinearity and two different values of the phase difference between plus and minus infinity. In another case, there are no solitons.

Fast Component Pursuit for Large-Scale Inverse Covariance Estimation.

PubMed

Han, Lei; Zhang, Yu; Zhang, Tong

2016-08-01

The maximum likelihood estimation (MLE) for the Gaussian graphical model, which is also known as the inverse covariance estimation problem, has gained increasing interest recently. Most existing works assume that inverse covariance estimators contain sparse structure and then construct models with the ℓ 1 regularization. In this paper, different from existing works, we study the inverse covariance estimation problem from another perspective by efficiently modeling the low-rank structure in the inverse covariance, which is assumed to be a combination of a low-rank part and a diagonal matrix. One motivation for this assumption is that the low-rank structure is common in many applications including the climate and financial analysis, and another one is that such assumption can reduce the computational complexity when computing its inverse. Specifically, we propose an efficient COmponent Pursuit (COP) method to obtain the low-rank part, where each component can be sparse. For optimization, the COP method greedily learns a rank-one component in each iteration by maximizing the log-likelihood. Moreover, the COP algorithm enjoys several appealing properties including the existence of an efficient solution in each iteration and the theoretical guarantee on the convergence of this greedy approach. Experiments on large-scale synthetic and real-world datasets including thousands of millions variables show that the COP method is faster than the state-of-the-art techniques for the inverse covariance estimation problem when achieving comparable log-likelihood on test data.

Inverse problems in the modeling of vibrations of flexible beams

NASA Technical Reports Server (NTRS)

Banks, H. T.; Powers, R. K.; Rosen, I. G.

1987-01-01

The formulation and solution of inverse problems for the estimation of parameters which describe damping and other dynamic properties in distributed models for the vibration of flexible structures is considered. Motivated by a slewing beam experiment, the identification of a nonlinear velocity dependent term which models air drag damping in the Euler-Bernoulli equation is investigated. Galerkin techniques are used to generate finite dimensional approximations. Convergence estimates and numerical results are given. The modeling of, and related inverse problems for the dynamics of a high pressure hose line feeding a gas thruster actuator at the tip of a cantilevered beam are then considered. Approximation and convergence are discussed and numerical results involving experimental data are presented.

An inverse finance problem for estimation of the volatility

NASA Astrophysics Data System (ADS)

Neisy, A.; Salmani, K.

2013-01-01

Black-Scholes model, as a base model for pricing in derivatives markets has some deficiencies, such as ignoring market jumps, and considering market volatility as a constant factor. In this article, we introduce a pricing model for European-Options under jump-diffusion underlying asset. Then, using some appropriate numerical methods we try to solve this model with integral term, and terms including derivative. Finally, considering volatility as an unknown parameter, we try to estimate it by using our proposed model. For the purpose of estimating volatility, in this article, we utilize inverse problem, in which inverse problem model is first defined, and then volatility is estimated using minimization function with Tikhonov regularization.

Real Variable Inversion of Laplace Transforms: An Application in Plasma Physics.

ERIC Educational Resources Information Center

Bohn, C. L.; Flynn, R. W.

1978-01-01

Discusses the nature of Laplace transform techniques and explains an alternative to them: the Widder's real inversion. To illustrate the power of this new technique, it is applied to a difficult inversion: the problem of Landau damping. (GA)

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Hongyu; Petra, Noemi; Stadler, Georg

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

DOE PAGES

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; ...

2016-07-13

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

NASA Astrophysics Data System (ADS)

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; Isaac, Tobin; Hughes, Thomas J. R.; Ghattas, Omar

2016-07-01

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection-diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov-Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems - i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian - we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. We show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.

The Modularized Software Package ASKI - Full Waveform Inversion Based on Waveform Sensitivity Kernels Utilizing External Seismic Wave Propagation Codes

NASA Astrophysics Data System (ADS)

Schumacher, F.; Friederich, W.

2015-12-01

We present the modularized software package ASKI which is a flexible and extendable toolbox for seismic full waveform inversion (FWI) as well as sensitivity or resolution analysis operating on the sensitivity matrix. It utilizes established wave propagation codes for solving the forward problem and offers an alternative to the monolithic, unflexible and hard-to-modify codes that have typically been written for solving inverse problems. It is available under the GPL at www.rub.de/aski. The Gauss-Newton FWI method for 3D-heterogeneous elastic earth models is based on waveform sensitivity kernels and can be applied to inverse problems at various spatial scales in both Cartesian and spherical geometries. The kernels are derived in the frequency domain from Born scattering theory as the Fréchet derivatives of linearized full waveform data functionals, quantifying the influence of elastic earth model parameters on the particular waveform data values. As an important innovation, we keep two independent spatial descriptions of the earth model - one for solving the forward problem and one representing the inverted model updates. Thereby we account for the independent needs of spatial model resolution of forward and inverse problem, respectively. Due to pre-integration of the kernels over the (in general much coarser) inversion grid, storage requirements for the sensitivity kernels are dramatically reduced.ASKI can be flexibly extended to other forward codes by providing it with specific interface routines that contain knowledge about forward code-specific file formats and auxiliary information provided by the new forward code. In order to sustain flexibility, the ASKI tools must communicate via file output/input, thus large storage capacities need to be accessible in a convenient way. Storing the complete sensitivity matrix to file, however, permits the scientist full manual control over each step in a customized procedure of sensitivity/resolution analysis and full waveform inversion.

Combined experimental-numerical identification of radiative transfer coefficients in white LED phosphor layers

NASA Astrophysics Data System (ADS)

Akolkar, A.; Petrasch, J.; Finck, S.; Rahmatian, N.

2018-02-01

An inverse analysis of the phosphor layer of a commercially available, conformally coated, white LED is done based on tomographic and spectrometric measurements. The aim is to determine the radiative transfer coefficients of the phosphor layer from the measurements of the finished device, with minimal assumptions regarding the composition of the phosphor layer. These results can be used for subsequent opto-thermal modelling and optimization of the device. For this purpose, multiple integrating sphere and gonioradiometric measurements are done to obtain statistical bounds on spectral radiometric values and angular color distributions for ten LEDs belonging to the same color bin of the product series. Tomographic measurements of the LED package are used to generate a tetrahedral grid of the 3D LED geometry. A radiative transfer model using Monte Carlo Ray Tracing in the tetrahedral grid is developed. Using a two-wavelength model consisting of a blue emission wavelength and a yellow, Stokes-shifted re-emission wavelength, the angular color distribution of the LED is simulated over wide ranges of the absorption and scattering coefficients of the phosphor layer, for the blue and yellow wavelengths. Using a two-step, iterative space search, combinations of the radiative transfer coefficients are obtained for which the simulations are consistent with the integrating sphere and gonioradiometric measurements. The results show an inverse relationship between the scattering and absorption coefficients of the phosphor layer for blue light. Scattering of yellow light acts as a distribution and loss mechanism for yellow light and affects the shape of the angular color distribution significantly, especially at larger viewing angles. The spread of feasible coefficients indicates that measured optical behavior of the LEDs may be reproduced using a range of combinations of radiative coefficients. Given that coefficients predicted by the Mie theory usually must be corrected in order to reproduce experimental results, these results indicate that a more complete model of radiative transfer in phosphor layers is required.

Estimating uncertainty of Full Waveform Inversion with Ensemble-based methods

NASA Astrophysics Data System (ADS)

Thurin, J.; Brossier, R.; Métivier, L.

2017-12-01

Uncertainty estimation is one key feature of tomographic applications for robust interpretation. However, this information is often missing in the frame of large scale linearized inversions, and only the results at convergence are shown, despite the ill-posed nature of the problem. This issue is common in the Full Waveform Inversion community.While few methodologies have already been proposed in the literature, standard FWI workflows do not include any systematic uncertainty quantifications methods yet, but often try to assess the result's quality through cross-comparison with other results from seismic or comparison with other geophysical data. With the development of large seismic networks/surveys, the increase in computational power and the more and more systematic application of FWI, it is crucial to tackle this problem and to propose robust and affordable workflows, in order to address the uncertainty quantification problem faced for near surface targets, crustal exploration, as well as regional and global scales.In this work (Thurin et al., 2017a,b), we propose an approach which takes advantage of the Ensemble Transform Kalman Filter (ETKF) proposed by Bishop et al., (2001), in order to estimate a low-rank approximation of the posterior covariance matrix of the FWI problem, allowing us to evaluate some uncertainty information of the solution. Instead of solving the FWI problem through a Bayesian inversion with the ETKF, we chose to combine a conventional FWI, based on local optimization, and the ETKF strategies. This scheme allows combining the efficiency of local optimization for solving large scale inverse problems and make the sampling of the local solution space possible thanks to its embarrassingly parallel property. References:Bishop, C. H., Etherton, B. J. and Majumdar, S. J., 2001. Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Monthly weather review, 129(3), 420-436.Thurin, J., Brossier, R. and Métivier, L. 2017,a.: Ensemble-Based Uncertainty Estimation in Full Waveform Inversion. 79th EAGE Conference and Exhibition 2017, (12 - 15 June, 2017)Thurin, J., Brossier, R. and Métivier, L. 2017,b.: An Ensemble-Transform Kalman Filter - Full Waveform Inversion scheme for Uncertainty estimation; SEG Technical Program Expanded Abstracts 2012

A Non-linear Geodetic Data Inversion Using ABIC for Slip Distribution on a Fault With an Unknown dip Angle

NASA Astrophysics Data System (ADS)

Fukahata, Y.; Wright, T. J.

2006-12-01

We developed a method of geodetic data inversion for slip distribution on a fault with an unknown dip angle. When fault geometry is unknown, the problem of geodetic data inversion is non-linear. A common strategy for obtaining slip distribution is to first determine the fault geometry by minimizing the square misfit under the assumption of a uniform slip on a rectangular fault, and then apply the usual linear inversion technique to estimate a slip distribution on the determined fault. It is not guaranteed, however, that the fault determined under the assumption of a uniform slip gives the best fault geometry for a spatially variable slip distribution. In addition, in obtaining a uniform slip fault model, we have to simultaneously determine the values of the nine mutually dependent parameters, which is a highly non-linear, complicated process. Although the inverse problem is non-linear for cases with unknown fault geometries, the non-linearity of the problems is actually weak, when we can assume the fault surface to be flat. In particular, when a clear fault trace is observed on the EarthOs surface after an earthquake, we can precisely estimate the strike and the location of the fault. In this case only the dip angle has large ambiguity. In geodetic data inversion we usually need to introduce smoothness constraints in order to compromise reciprocal requirements for model resolution and estimation errors in a natural way. Strictly speaking, the inverse problem with smoothness constraints is also non-linear, even if the fault geometry is known. The non-linearity has been dissolved by introducing AkaikeOs Bayesian Information Criterion (ABIC), with which the optimal value of the relative weight of observed data to smoothness constraints is objectively determined. In this study, using ABIC in determining the optimal dip angle, we dissolved the non-linearity of the inverse problem. We applied the method to the InSAR data of the 1995 Dinar, Turkey earthquake and obtained a much shallower dip angle than before.

Mixed boundary-value problem for an orthotropic rectangular strip with variable coefficients of elasticity

NASA Astrophysics Data System (ADS)

Sargsyan, M. Z.; Poghosyan, H. M.

2018-04-01

A dynamical problem for a rectangular strip with variable coefficients of elasticity is solved by an asymptotic method. It is assumed that the strip is orthotropic, the elasticity coefficients are exponential functions of y, and mixed boundary conditions are posed. The solution of the inner problem is obtained using Bessel functions.

An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology

NASA Astrophysics Data System (ADS)

Beretta, Elena; Cavaterra, Cecilia; Cerutti, M. Cristina; Manzoni, Andrea; Ratti, Luca

2017-10-01

In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the electric potential in the myocardial tissue. The goal is the detection of an inhomogeneity \

Analysis of the Hessian for Inverse Scattering Problems. Part 1: Inverse Shape Scattering of Acoustic Waves

DTIC Science & Technology

2011-06-01

in giving us of a copy of his habilitation thesis, without which this article would not have been possible. We also thank Prof. Karsten Eppler for...John Wiley & Sons, 1983. [19] Andreas Kirsch. Generalized boundary value- and control problems for the Helmholtz equation. Habilitation thesis, 1984

A posteriori error estimates in voice source recovery

NASA Astrophysics Data System (ADS)

Leonov, A. S.; Sorokin, V. N.

2017-12-01

The inverse problem of voice source pulse recovery from a segment of a speech signal is under consideration. A special mathematical model is used for the solution that relates these quantities. A variational method of solving inverse problem of voice source recovery for a new parametric class of sources, that is for piecewise-linear sources (PWL-sources), is proposed. Also, a technique for a posteriori numerical error estimation for obtained solutions is presented. A computer study of the adequacy of adopted speech production model with PWL-sources is performed in solving the inverse problems for various types of voice signals, as well as corresponding study of a posteriori error estimates. Numerical experiments for speech signals show satisfactory properties of proposed a posteriori error estimates, which represent the upper bounds of possible errors in solving the inverse problem. The estimate of the most probable error in determining the source-pulse shapes is about 7-8% for the investigated speech material. It is noted that a posteriori error estimates can be used as a criterion of the quality for obtained voice source pulses in application to speaker recognition.

Solving ill-posed inverse problems using iterative deep neural networks

NASA Astrophysics Data System (ADS)

Adler, Jonas; Öktem, Ozan

2017-12-01

We propose a partially learned approach for the solution of ill-posed inverse problems with not necessarily linear forward operators. The method builds on ideas from classical regularisation theory and recent advances in deep learning to perform learning while making use of prior information about the inverse problem encoded in the forward operator, noise model and a regularising functional. The method results in a gradient-like iterative scheme, where the ‘gradient’ component is learned using a convolutional network that includes the gradients of the data discrepancy and regulariser as input in each iteration. We present results of such a partially learned gradient scheme on a non-linear tomographic inversion problem with simulated data from both the Sheep-Logan phantom as well as a head CT. The outcome is compared against filtered backprojection and total variation reconstruction and the proposed method provides a 5.4 dB PSNR improvement over the total variation reconstruction while being significantly faster, giving reconstructions of 512 × 512 pixel images in about 0.4 s using a single graphics processing unit (GPU).

Full Waveform Inversion for Seismic Velocity And Anelastic Losses in Heterogeneous Structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Askan, A.; /Carnegie Mellon U.; Akcelik, V.

2009-04-30

We present a least-squares optimization method for solving the nonlinear full waveform inverse problem of determining the crustal velocity and intrinsic attenuation properties of sedimentary valleys in earthquake-prone regions. Given a known earthquake source and a set of seismograms generated by the source, the inverse problem is to reconstruct the anelastic properties of a heterogeneous medium with possibly discontinuous wave velocities. The inverse problem is formulated as a constrained optimization problem, where the constraints are the partial and ordinary differential equations governing the anelastic wave propagation from the source to the receivers in the time domain. This leads to amore » variational formulation in terms of the material model plus the state variables and their adjoints. We employ a wave propagation model in which the intrinsic energy-dissipating nature of the soil medium is modeled by a set of standard linear solids. The least-squares optimization approach to inverse wave propagation presents the well-known difficulties of ill posedness and multiple minima. To overcome ill posedness, we include a total variation regularization functional in the objective function, which annihilates highly oscillatory material property components while preserving discontinuities in the medium. To treat multiple minima, we use a multilevel algorithm that solves a sequence of subproblems on increasingly finer grids with increasingly higher frequency source components to remain within the basin of attraction of the global minimum. We illustrate the methodology with high-resolution inversions for two-dimensional sedimentary models of the San Fernando Valley, under SH-wave excitation. We perform inversions for both the seismic velocity and the intrinsic attenuation using synthetic waveforms at the observer locations as pseudoobserved data.« less

Trimming and procrastination as inversion techniques

NASA Astrophysics Data System (ADS)

Backus, George E.

1996-12-01

By examining the processes of truncating and approximating the model space (trimming it), and by committing to neither the objectivist nor the subjectivist interpretation of probability (procrastinating), we construct a formal scheme for solving linear and non-linear geophysical inverse problems. The necessary prior information about the correct model xE can be either a collection of inequalities or a probability measure describing where xE was likely to be in the model space X before the data vector y0 was measured. The results of the inversion are (1) a vector z0 that estimates some numerical properties zE of xE; (2) an estimate of the error δz = z0 - zE. As y0 is finite dimensional, so is z0, and hence in principle inversion cannot describe all of xE. The error δz is studied under successively more specialized assumptions about the inverse problem, culminating in a complete analysis of the linear inverse problem with a prior quadratic bound on xE. Our formalism appears to encompass and provide error estimates for many of the inversion schemes current in geomagnetism, and would be equally applicable in geodesy and seismology if adequate prior information were available there. As an idealized example we study the magnetic field at the core-mantle boundary, using satellite measurements of field elements at sites assumed to be almost uniformly distributed on a single spherical surface. Magnetospheric currents are neglected and the crustal field is idealized as a random process with rotationally invariant statistics. We find that an appropriate data compression diagonalizes the variance matrix of the crustal signal and permits an analytic trimming of the idealized problem.

Characterization of compressed earth blocks using low frequency guided acoustic waves.

PubMed

Ben Mansour, Mohamed; Ogam, Erick; Fellah, Z E A; Soukaina Cherif, Amel; Jelidi, Ahmed; Ben Jabrallah, Sadok

2016-05-01

The objective of this work was to analyze the influence of compaction pressure on the intrinsic acoustic parameters (porosity, tortuosity, air-flow resistivity, viscous, and thermal characteristic lengths) of compressed earth blocks through their identification by solving an inverse acoustic wave transmission problem. A low frequency acoustic pipe (60-6000 Hz of length 22 m, internal diameter 3.4 cm) was used for the experimental characterization of the samples. The parameters were identified by the minimization of the difference between the transmissions coefficients data obtained in the pipe with that from an analytical interaction model in which the compressed earth blocks were considered as having rigid frames. The viscous and thermal effects in the pores were accounted for by employing the Johnson-Champoux-Allard-Lafarge model. The results obtained by inversion for high-density compressed earth blocks showed some discordance between the model and experiment especially for the high frequency limit of the acoustic characteristics studied. This was as a consequence of applying high compaction pressure rendering them very highly resistive therefore degrading the signal-to-noise ratios of the transmitted waves. The results showed that the airflow resistivity was very sensitive to the degree of the applied compaction pressure used to form the blocks.

Inversion of sonobuoy data from shallow-water sites with simulated annealing.

PubMed

Lindwall, Dennis; Brozena, John

2005-02-01

An enhanced simulated annealing algorithm is used to invert sparsely sampled seismic data collected with sonobuoys to obtain seafloor geoacoustic properties at two littoral marine environments as well as for a synthetic data set. Inversion of field data from a 750-m water-depth site using a water-gun sound source found a good solution which included a pronounced subbottom reflector after 6483 iterations over seven variables. Field data from a 250-m water-depth site using an air-gun source required 35,421 iterations for a good inversion solution because 30 variables had to be solved for, including the shot-to-receiver offsets. The sonobuoy derived compressional wave velocity-depth (Vp-Z) models compare favorably with Vp-Z models derived from nearby, high-quality, multichannel seismic data. There are, however, substantial differences between seafloor reflection coefficients calculated from field models and seafloor reflection coefficients based on commonly used Vp regression curves (gradients). Reflection loss is higher at one field site and lower at the other than predicted from commonly used Vp gradients for terrigenous sediments. In addition, there are strong effects on reflection loss due to the subseafloor interfaces that are also not predicted by Vp gradients.

Research on fusion algorithm of polarization image in tetrolet domain

NASA Astrophysics Data System (ADS)

Zhang, Dexiang; Yuan, BaoHong; Zhang, Jingjing

2015-12-01

Tetrolets are Haar-type wavelets whose supports are tetrominoes which are shapes made by connecting four equal-sized squares. A fusion method for polarization images based on tetrolet transform is proposed. Firstly, the magnitude of polarization image and angle of polarization image can be decomposed into low-frequency coefficients and high-frequency coefficients with multi-scales and multi-directions using tetrolet transform. For the low-frequency coefficients, the average fusion method is used. According to edge distribution differences in high frequency sub-band images, for the directional high-frequency coefficients are used to select the better coefficients by region spectrum entropy algorithm for fusion. At last the fused image can be obtained by utilizing inverse transform for fused tetrolet coefficients. Experimental results show that the proposed method can detect image features more effectively and the fused image has better subjective visual effect

CRI Summer Conference (2005) on Inverse Scattering Held in Charlotte. North Carolina on May 30 - June 3, 2005

DTIC Science & Technology

2005-08-30

of the computed Rayleigh coefficients from the measured data, and the third is a regularization term to cope with the ill-posedness of the inverse...objects and properties of non-scattering scatterers. This was a residential workshop organized along the lines of a Gordon Conference, with talks... with all of those inevitable logistical and planning details that go into making a workshop such as this a success. This meeting would not have

Fourier analysis and signal processing by use of the Moebius inversion formula

NASA Technical Reports Server (NTRS)

Reed, Irving S.; Yu, Xiaoli; Shih, Ming-Tang; Tufts, Donald W.; Truong, T. K.

1990-01-01

A novel Fourier technique for digital signal processing is developed. This approach to Fourier analysis is based on the number-theoretic method of the Moebius inversion of series. The Fourier transform method developed is shown also to yield the convolution of two signals. A computer simulation shows that this method for finding Fourier coefficients is quite suitable for digital signal processing. It competes with the classical FFT (fast Fourier transform) approach in terms of accuracy, complexity, and speed.

A general approach to regularizing inverse problems with regional data using Slepian wavelets

NASA Astrophysics Data System (ADS)

Michel, Volker; Simons, Frederik J.

2017-12-01

Slepian functions are orthogonal function systems that live on subdomains (for example, geographical regions on the Earth’s surface, or bandlimited portions of the entire spectrum). They have been firmly established as a useful tool for the synthesis and analysis of localized (concentrated or confined) signals, and for the modeling and inversion of noise-contaminated data that are only regionally available or only of regional interest. In this paper, we consider a general abstract setup for inverse problems represented by a linear and compact operator between Hilbert spaces with a known singular-value decomposition (svd). In practice, such an svd is often only given for the case of a global expansion of the data (e.g. on the whole sphere) but not for regional data distributions. We show that, in either case, Slepian functions (associated to an arbitrarily prescribed region and the given compact operator) can be determined and applied to construct a regularization for the ill-posed regional inverse problem. Moreover, we describe an algorithm for constructing the Slepian basis via an algebraic eigenvalue problem. The obtained Slepian functions can be used to derive an svd for the combination of the regionalizing projection and the compact operator. As a result, standard regularization techniques relying on a known svd become applicable also to those inverse problems where the data are regionally given only. In particular, wavelet-based multiscale techniques can be used. An example for the latter case is elaborated theoretically and tested on two synthetic numerical examples.

Bayesian parameter estimation in spectral quantitative photoacoustic tomography

NASA Astrophysics Data System (ADS)

Pulkkinen, Aki; Cox, Ben T.; Arridge, Simon R.; Kaipio, Jari P.; Tarvainen, Tanja

2016-03-01

Photoacoustic tomography (PAT) is an imaging technique combining strong contrast of optical imaging to high spatial resolution of ultrasound imaging. These strengths are achieved via photoacoustic effect, where a spatial absorption of light pulse is converted into a measurable propagating ultrasound wave. The method is seen as a potential tool for small animal imaging, pre-clinical investigations, study of blood vessels and vasculature, as well as for cancer imaging. The goal in PAT is to form an image of the absorbed optical energy density field via acoustic inverse problem approaches from the measured ultrasound data. Quantitative PAT (QPAT) proceeds from these images and forms quantitative estimates of the optical properties of the target. This optical inverse problem of QPAT is illposed. To alleviate the issue, spectral QPAT (SQPAT) utilizes PAT data formed at multiple optical wavelengths simultaneously with optical parameter models of tissue to form quantitative estimates of the parameters of interest. In this work, the inverse problem of SQPAT is investigated. Light propagation is modelled using the diffusion equation. Optical absorption is described with chromophore concentration weighted sum of known chromophore absorption spectra. Scattering is described by Mie scattering theory with an exponential power law. In the inverse problem, the spatially varying unknown parameters of interest are the chromophore concentrations, the Mie scattering parameters (power law factor and the exponent), and Gruneisen parameter. The inverse problem is approached with a Bayesian method. It is numerically demonstrated, that estimation of all parameters of interest is possible with the approach.

A geostatistical approach to the change-of-support problem and variable-support data fusion in spatial analysis

NASA Astrophysics Data System (ADS)

Wang, Jun; Wang, Yang; Zeng, Hui

2016-01-01

A key issue to address in synthesizing spatial data with variable-support in spatial analysis and modeling is the change-of-support problem. We present an approach for solving the change-of-support and variable-support data fusion problems. This approach is based on geostatistical inverse modeling that explicitly accounts for differences in spatial support. The inverse model is applied here to produce both the best predictions of a target support and prediction uncertainties, based on one or more measurements, while honoring measurements. Spatial data covering large geographic areas often exhibit spatial nonstationarity and can lead to computational challenge due to the large data size. We developed a local-window geostatistical inverse modeling approach to accommodate these issues of spatial nonstationarity and alleviate computational burden. We conducted experiments using synthetic and real-world raster data. Synthetic data were generated and aggregated to multiple supports and downscaled back to the original support to analyze the accuracy of spatial predictions and the correctness of prediction uncertainties. Similar experiments were conducted for real-world raster data. Real-world data with variable-support were statistically fused to produce single-support predictions and associated uncertainties. The modeling results demonstrate that geostatistical inverse modeling can produce accurate predictions and associated prediction uncertainties. It is shown that the local-window geostatistical inverse modeling approach suggested offers a practical way to solve the well-known change-of-support problem and variable-support data fusion problem in spatial analysis and modeling.

Restart Operator Meta-heuristics for a Problem-Oriented Evolutionary Strategies Algorithm in Inverse Mathematical MISO Modelling Problem Solving

NASA Astrophysics Data System (ADS)

Ryzhikov, I. S.; Semenkin, E. S.

2017-02-01

This study is focused on solving an inverse mathematical modelling problem for dynamical systems based on observation data and control inputs. The mathematical model is being searched in the form of a linear differential equation, which determines the system with multiple inputs and a single output, and a vector of the initial point coordinates. The described problem is complex and multimodal and for this reason the proposed evolutionary-based optimization technique, which is oriented on a dynamical system identification problem, was applied. To improve its performance an algorithm restart operator was implemented.

An Inverse Problem for a Class of Conditional Probability Measure-Dependent Evolution Equations

PubMed Central

Mirzaev, Inom; Byrne, Erin C.; Bortz, David M.

2016-01-01

We investigate the inverse problem of identifying a conditional probability measure in measure-dependent evolution equations arising in size-structured population modeling. We formulate the inverse problem as a least squares problem for the probability measure estimation. Using the Prohorov metric framework, we prove existence and consistency of the least squares estimates and outline a discretization scheme for approximating a conditional probability measure. For this scheme, we prove general method stability. The work is motivated by Partial Differential Equation (PDE) models of flocculation for which the shape of the post-fragmentation conditional probability measure greatly impacts the solution dynamics. To illustrate our methodology, we apply the theory to a particular PDE model that arises in the study of population dynamics for flocculating bacterial aggregates in suspension, and provide numerical evidence for the utility of the approach. PMID:28316360

Bayesian inference in geomagnetism

NASA Technical Reports Server (NTRS)

Backus, George E.

1988-01-01

The inverse problem in empirical geomagnetic modeling is investigated, with critical examination of recently published studies. Particular attention is given to the use of Bayesian inference (BI) to select the damping parameter lambda in the uniqueness portion of the inverse problem. The mathematical bases of BI and stochastic inversion are explored, with consideration of bound-softening problems and resolution in linear Gaussian BI. The problem of estimating the radial magnetic field B(r) at the earth core-mantle boundary from surface and satellite measurements is then analyzed in detail, with specific attention to the selection of lambda in the studies of Gubbins (1983) and Gubbins and Bloxham (1985). It is argued that the selection method is inappropriate and leads to lambda values much larger than those that would result if a reasonable bound on the heat flow at the CMB were assumed.

Solving Inverse Kinematics of Robot Manipulators by Means of Meta-Heuristic Optimisation

NASA Astrophysics Data System (ADS)

Wichapong, Kritsada; Bureerat, Sujin; Pholdee, Nantiwat

2018-05-01

This paper presents the use of meta-heuristic algorithms (MHs) for solving inverse kinematics of robot manipulators based on using forward kinematic. Design variables are joint angular displacements used to move a robot end-effector to the target in the Cartesian space while the design problem is posed to minimize error between target points and the positions of the robot end-effector. The problem is said to be a dynamic problem as the target points always changed by a robot user. Several well established MHs are used to solve the problem and the results obtained from using different meta-heuristics are compared based on the end-effector error and searching speed of the algorithms. From the study, the best performer will be obtained for setting as the baseline for future development of MH-based inverse kinematic solving.

Total variation regularization of the 3-D gravity inverse problem using a randomized generalized singular value decomposition

NASA Astrophysics Data System (ADS)

Vatankhah, Saeed; Renaut, Rosemary A.; Ardestani, Vahid E.

2018-04-01

We present a fast algorithm for the total variation regularization of the 3-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved better than when using a conventional minimum-structure inversion. The associated problem formulation for the regularization is nonlinear but can be solved using an iteratively reweighted least-squares algorithm. For small-scale problems the regularized least-squares problem at each iteration can be solved using the generalized singular value decomposition. This is not feasible for large-scale, or even moderate-scale, problems. Instead we introduce the use of a randomized generalized singular value decomposition in order to reduce the dimensions of the problem and provide an effective and efficient solution technique. For further efficiency an alternating direction algorithm is used to implement the total variation weighting operator within the iteratively reweighted least-squares algorithm. Presented results for synthetic examples demonstrate that the novel randomized decomposition provides good accuracy for reduced computational and memory demands as compared to use of classical approaches.

ANNIT - An Efficient Inversion Algorithm based on Prediction Principles

NASA Astrophysics Data System (ADS)

Růžek, B.; Kolář, P.

2009-04-01

Solution of inverse problems represents meaningful job in geophysics. The amount of data is continuously increasing, methods of modeling are being improved and the computer facilities are also advancing great technical progress. Therefore the development of new and efficient algorithms and computer codes for both forward and inverse modeling is still up to date. ANNIT is contributing to this stream since it is a tool for efficient solution of a set of non-linear equations. Typical geophysical problems are based on parametric approach. The system is characterized by a vector of parameters p, the response of the system is characterized by a vector of data d. The forward problem is usually represented by unique mapping F(p)=d. The inverse problem is much more complex and the inverse mapping p=G(d) is available in an analytical or closed form only exceptionally and generally it may not exist at all. Technically, both forward and inverse mapping F and G are sets of non-linear equations. ANNIT solves such situation as follows: (i) joint subspaces {pD, pM} of original data and model spaces D, M, resp. are searched for, within which the forward mapping F is sufficiently smooth that the inverse mapping G does exist, (ii) numerical approximation of G in subspaces {pD, pM} is found, (iii) candidate solution is predicted by using this numerical approximation. ANNIT is working in an iterative way in cycles. The subspaces {pD, pM} are searched for by generating suitable populations of individuals (models) covering data and model spaces. The approximation of the inverse mapping is made by using three methods: (a) linear regression, (b) Radial Basis Function Network technique, (c) linear prediction (also known as "Kriging"). The ANNIT algorithm has built in also an archive of already evaluated models. Archive models are re-used in a suitable way and thus the number of forward evaluations is minimized. ANNIT is now implemented both in MATLAB and SCILAB. Numerical tests show good performance of the algorithm. Both versions and documentation are available on Internet and anybody can download them. The goal of this presentation is to offer the algorithm and computer codes for anybody interested in the solution to inverse problems.

A new version of variational integrated technology for environmental modeling with assimilation of available data

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Tsvetova, Elena; Penenko, Aleksey

2014-05-01

A modeling technology based on coupled models of atmospheric dynamics and chemistry are presented [1-3]. It is the result of application of variational methods in combination with the methods of decomposition and splitting. The idea of Euler's integrating factors combined with technique of adjoint problems is also used. In online technologies, a significant part of algorithmic and computational work consist in solving the problems like convection-diffusion-reaction and in organizing data assimilation techniques based on them. For equations of convection-diffusion, the methodology gives us the unconditionally stable and monotone discrete-analytical schemes in the frames of methods of decomposition and splitting. These schemes are exact for locally one-dimensional problems respect to the spatial variables. For stiff systems of equations describing transformation of gas and aerosol substances, the monotone and stable schemes are also obtained. They are implemented by non- iterative algorithms. By construction, all schemes for different components of state functions are structurally uniform. They are coordinated among themselves in the sense of forward and inverse modeling. Variational principles are constructed taking into account the fact that the behavior of the different dynamic and chemical components of the state function is characterized by high variability and uncertainty. Information on the parameters of models, sources and emission impacts is also not determined precisely. Therefore, to obtain the consistent solutions, we construct methods of the sensitivity theory taking into account the influence of uncertainty. For this purpose, new methods of data assimilation of hydrodynamic fields and gas-aerosol substances measured by different observing systems are proposed. Optimization criteria for data assimilation problems are defined so that they include a set of functionals evaluating the total measure of uncertainties. The latter are explicitly introduced into the equations of the model of processes as desired deterministic control functions. This method of data assimilation with control functions is implemented by direct algorithms. The modeling technology presented here focuses on various scientific and applied problems of environmental prediction and design, including risk assessment in relation to existing and potential sources of natural and anthropogenic influences. The work is partially supported by the Programs No 4 of Presidium RAS and No 3 of Mathematical Department of RAS; by RFBR projects NN 11-01-00187 and 14-01-31482; by Integrating projects of SD RAS No 8 and 35. Our studies are in the line with the goals of COST Action ES1004. References 1. V. Penenko, A.Baklanov, E. Tsvetova and A. Mahura. Direct and Inverse Problems in a Variational Concept of Environmental Modeling, Pure and Applied Geoph. 2012.V.169:447-465. 2. A.V. Penenko, Discrete-analytic schemes for solving an inverse coefficient heat conduction problem in a layered medium with gradient methods, Numerical Analysis and Applications, 2012. V. 5:326-341. 3. V. Penenko, E. Tsvetova. Variational methods for constructing the monotone approximations for atmospheric chemistry models, Numerical analysis and applications, 2013. V. 6: 210-220.

Social problem-solving, perceived stress, depression and life-satisfaction in patients suffering from tension type and migraine headaches.

PubMed

Eskin, Mehmet; Akyol, Ali; Çelik, Emine Yilmaz; Gültekin, Bülent Kadri

2013-08-01

This study aimed at investigating social problem solving, perceived stress, depression, and life-satisfaction in patients with tension type and migraine headaches. Forty-nine migraine and 42 tension type headache patients (n = 91) consenting to participate were compared to a total of 49 matched healthy control group. Participants filled in a questionnaire consisting self-report measures of problem solving, perceived stress, depression and life satisfaction. They were also asked about headache duration, frequency, pain severity, psychiatric treatment and sense of control in one's life. T-tests, chi-square, analysis of variance, logistic regression analysis and Pearson product moment correlation coefficient procedures were used to analyze the data. Tension type headache patients reported having had more frequent headaches than the migraine patients but migraine patients reported having had more intense pain than the tension type headache patients. Instances of psychiatric treatment were more common among tension type headache patients than the migraine and the control group. Compared to the healthy controls, headache patients displayed a deficiency in problem solving, higher levels of perceived stress and depression. Levels of problem solving skills in headache patients were related inversely to depression, perceived stress and the number of negative life events but problem solving skills of headache patients was related positively to life-satisfaction. The findings from this study suggested that cognitive behavioral problem solving therapy or training might be a viable option for reducing levels of stress and depression, and to increase life-satisfaction in patients suffering from primary headache. © 2013 The Scandinavian Psychological Associations.

Inverse kinematics of a dual linear actuator pitch/roll heliostat

NASA Astrophysics Data System (ADS)

Freeman, Joshua; Shankar, Balakrishnan; Sundaram, Ganesh

2017-06-01

This work presents a simple, computationally efficient inverse kinematics solution for a pitch/roll heliostat using two linear actuators. The heliostat design and kinematics have been developed, modeled and tested using computer simulation software. A physical heliostat prototype was fabricated to validate the theoretical computations and data. Pitch/roll heliostats have numerous advantages including reduced cost potential and reduced space requirements, with a primary disadvantage being the significantly more complicated kinematics, which are solved here. Novel methods are applied to simplify the inverse kinematics problem which could be applied to other similar problems.

The occurrence of double strand DNA breaks is not the sole condition for meiotic crossing over in Drosophila melanogaster.

PubMed

Portin, P; Rantanen, M

2000-01-01

Analysis of the interchromosomal effects of In(2L + 2R)Cy, In(3L + 3R)LVM and their joint effect on the frequencies of single and double crossovers in the cv-v-f region of the X chromosome as well as interference showed that both inversions, occurring separately, increased the frequency of single as well as double crossovers and the coefficient of coincidence. However, when the inversions occurred together the frequencies of single crossovers no longer increased, but the frequency of double crossovers, as well as the coefficient of coincidence did increase. These results indicate firstly that the interchromosomal effects influence some precondition of exchange, but that this precondition is not an occurrence of double strand DNA breaks. Thus, the occurrence of double strand DNA breaks is not the sole condition for crossing over in Drosophila melanogaster.

Microwave inversion of leaf area and inclination angle distributions from backscattered data

NASA Technical Reports Server (NTRS)

Lang, R. H.; Saleh, H. A.

1985-01-01

The backscattering coefficient from a slab of thin randomly oriented dielectric disks over a flat lossy ground is used to reconstruct the inclination angle and area distributions of the disks. The disks are employed to model a leafy agricultural crop, such as soybeans, in the L-band microwave region of the spectrum. The distorted Born approximation, along with a thin disk approximation, is used to obtain a relationship between the horizontal-like polarized backscattering coefficient and the joint probability density of disk inclination angle and disk radius. Assuming large skin depth reduces the relationship to a linear Fredholm integral equation of the first kind. Due to the ill-posed nature of this equation, a Phillips-Twomey regularization method with a second difference smoothing condition is used to find the inversion. Results are obtained in the presence of 1 and 10 percent noise for both leaf inclination angle and leaf radius densities.

An Exact Formula for Calculating Inverse Radial Lens Distortions

PubMed Central

Drap, Pierre; Lefèvre, Julien

2016-01-01

This article presents a new approach to calculating the inverse of radial distortions. The method presented here provides a model of reverse radial distortion, currently modeled by a polynomial expression, that proposes another polynomial expression where the new coefficients are a function of the original ones. After describing the state of the art, the proposed method is developed. It is based on a formal calculus involving a power series used to deduce a recursive formula for the new coefficients. We present several implementations of this method and describe the experiments conducted to assess the validity of the new approach. Such an approach, non-iterative, using another polynomial expression, able to be deduced from the first one, can actually be interesting in terms of performance, reuse of existing software, or bridging between different existing software tools that do not consider distortion from the same point of view. PMID:27258288

Methods for characterizing subsurface volatile contaminants using in-situ sensors

DOEpatents

Ho, Clifford K [Albuquerque, NM

2006-02-21

An inverse analysis method for characterizing diffusion of vapor from an underground source of volatile contaminant using data taken by an in-situ sensor. The method uses one-dimensional solutions to the diffusion equation in Cartesian, cylindrical, or spherical coordinates for isotropic and homogenous media. If the effective vapor diffusion coefficient is known, then the distance from the source to the in-situ sensor can be estimated by comparing the shape of the predicted time-dependent vapor concentration response curve to the measured response curve. Alternatively, if the source distance is known, then the effective vapor diffusion coefficient can be estimated using the same inverse analysis method. A triangulation technique can be used with multiple sensors to locate the source in two or three dimensions. The in-situ sensor can contain one or more chemiresistor elements housed in a waterproof enclosure with a gas permeable membrane.

Association of sex hormones with physical, laboratory, and imaging markers of anthropometry in men and women from the general population.

PubMed

Seyfart, Tom; Friedrich, Nele; Kische, Hanna; Bülow, Robin; Wallaschofski, Henri; Völzke, Henry; Nauck, Matthias; Keevil, Brian G; Haring, Robin

2018-01-01

The aim of this study was to evaluate the association of sex hormones with anthropometry in a large population-based cohort, with liquid chromatography-mass spectrometry (LCMS)-based sex hormone measurements and imaging markers. Cross-sectional data from 957 men and women from the population-based Study of Health in Pomerania (SHIP) were used. Associations of a comprehensive panel of LCMS-measured sex hormones with anthropometric parameters, laboratory, and imaging markers were analyzed in multivariable regression models for the full sample and stratified by sex. Sex hormone measures included total testosterone (TT), free testosterone (fT), estrone and estradiol, androstenedione (ASD), dehydroepiandrosterone sulfate (DHEAS), and sex hormone-binding globulin (SHBG). Domains of anthropometry included physical measures (body-mass-index (BMI), waist circumference, waist-to-height-ratio, waist-to-hip-ratio, and hip circumference), laboratory measures of adipokines (leptin and vaspin), and magnet resonance imaging-based measures (visceral and subcutaneous adipose tissue). In men, inverse associations between all considered anthropometric parameters with TT were found: BMI (β-coefficient, standard error (SE): -0.159, 0.037), waist-circumference (β-coefficient, SE: -0.892, 0.292), subcutaneous adipose tissue (β-coefficient, SE: -0.156, 0.023), and leptin (β-coefficient, SE: -0.046, 0.009). In women TT (β-coefficient, SE: 1.356, 0.615) and estrone (β-coefficient, SE: 0.014, 0.005) were positively associated with BMI. In analyses of variance, BMI and leptin were inversely associated with TT, ASD, and DHEAS in men, but positively associated with estrone. In women, BMI and leptin were positively associated with all sex hormones. The present population-based study confirmed and extended previously reported sex-specific associations between sex hormones and various anthropometric markers of overweight and obesity.

Evaluation of the in vivo and ex vivo optical properties in a mouse ear model

NASA Astrophysics Data System (ADS)

Salomatina, E.; Yaroslavsky, A. N.

2008-06-01

Determination of in vivo optical properties is a challenging problem. Absorption and scattering measured ex vivo are often used for in vivo applications. To investigate the validity of this approach, we have obtained and compared the optical properties of mouse ears in vivo and ex vivo in the spectral range from 370 to 1650 nm. Integrating sphere spectrophotometry in combination with the inverse Monte Carlo technique was employed to determine absorption coefficients, μa, scattering coefficients, μs, and anisotropy factors, g. Two groups of mice were used for the study. The first group was measured in vivo and ex vivo within 5-10 min post mortem. The second group was measured in vivo and ex vivo every 24 h for up to 72 h after sacrifice. Between the measurements the tissues were kept at 4 °C wrapped in a gauze moistened with saline solution. Then the specimens were frozen at -25 °C for 40 min, thawed and measured again. The results indicate that the absorption coefficients determined in vivo and ex vivo within 5-10 min post mortem differed considerably only in the spectral range dominated by hemoglobin. These changes can be attributed to rapid deoxygenation of tissue and blood post mortem. Absorption coefficients determined ex vivo up to 72 h post mortem decreased gradually with time in the spectral regions dominated by hemoglobin and water, which can be explained by the continuing loss of blood. Absorption properties of the frozen-thawed ex vivo tissues showed increase in oxygenation, which is likely caused by the release of hemoglobin from hemolyzed erythrocytes. Scattering of the ex vivo tissues decreased gradually with time in the entire spectral range due to the continuing loss of blood and partial cell damage. Anisotropy factors did not change considerably.

Evaluation of the in vivo and ex vivo optical properties in a mouse ear model.

PubMed

Salomatina, E; Yaroslavsky, A N

2008-06-07

Determination of in vivo optical properties is a challenging problem. Absorption and scattering measured ex vivo are often used for in vivo applications. To investigate the validity of this approach, we have obtained and compared the optical properties of mouse ears in vivo and ex vivo in the spectral range from 370 to 1650 nm. Integrating sphere spectrophotometry in combination with the inverse Monte Carlo technique was employed to determine absorption coefficients, mu(a), scattering coefficients, mu(s), and anisotropy factors, g. Two groups of mice were used for the study. The first group was measured in vivo and ex vivo within 5-10 min post mortem. The second group was measured in vivo and ex vivo every 24 h for up to 72 h after sacrifice. Between the measurements the tissues were kept at 4 degrees C wrapped in a gauze moistened with saline solution. Then the specimens were frozen at -25 degrees C for 40 min, thawed and measured again. The results indicate that the absorption coefficients determined in vivo and ex vivo within 5-10 min post mortem differed considerably only in the spectral range dominated by hemoglobin. These changes can be attributed to rapid deoxygenation of tissue and blood post mortem. Absorption coefficients determined ex vivo up to 72 h post mortem decreased gradually with time in the spectral regions dominated by hemoglobin and water, which can be explained by the continuing loss of blood. Absorption properties of the frozen-thawed ex vivo tissues showed increase in oxygenation, which is likely caused by the release of hemoglobin from hemolyzed erythrocytes. Scattering of the ex vivo tissues decreased gradually with time in the entire spectral range due to the continuing loss of blood and partial cell damage. Anisotropy factors did not change considerably.

Appraisal of geodynamic inversion results: a data mining approach

NASA Astrophysics Data System (ADS)

Baumann, T. S.

2016-11-01

Bayesian sampling based inversions require many thousands or even millions of forward models, depending on how nonlinear or non-unique the inverse problem is, and how many unknowns are involved. The result of such a probabilistic inversion is not a single `best-fit' model, but rather a probability distribution that is represented by the entire model ensemble. Often, a geophysical inverse problem is non-unique, and the corresponding posterior distribution is multimodal, meaning that the distribution consists of clusters with similar models that represent the observations equally well. In these cases, we would like to visualize the characteristic model properties within each of these clusters of models. However, even for a moderate number of inversion parameters, a manual appraisal for a large number of models is not feasible. This poses the question whether it is possible to extract end-member models that represent each of the best-fit regions including their uncertainties. Here, I show how a machine learning tool can be used to characterize end-member models, including their uncertainties, from a complete model ensemble that represents a posterior probability distribution. The model ensemble used here results from a nonlinear geodynamic inverse problem, where rheological properties of the lithosphere are constrained from multiple geophysical observations. It is demonstrated that by taking vertical cross-sections through the effective viscosity structure of each of the models, the entire model ensemble can be classified into four end-member model categories that have a similar effective viscosity structure. These classification results are helpful to explore the non-uniqueness of the inverse problem and can be used to compute representative data fits for each of the end-member models. Conversely, these insights also reveal how new observational constraints could reduce the non-uniqueness. The method is not limited to geodynamic applications and a generalized MATLAB code is provided to perform the appraisal analysis.

Solving Large-Scale Inverse Magnetostatic Problems using the Adjoint Method

PubMed Central

Bruckner, Florian; Abert, Claas; Wautischer, Gregor; Huber, Christian; Vogler, Christoph; Hinze, Michael; Suess, Dieter

2017-01-01

An efficient algorithm for the reconstruction of the magnetization state within magnetic components is presented. The occurring inverse magnetostatic problem is solved by means of an adjoint approach, based on the Fredkin-Koehler method for the solution of the forward problem. Due to the use of hybrid FEM-BEM coupling combined with matrix compression techniques the resulting algorithm is well suited for large-scale problems. Furthermore the reconstruction of the magnetization state within a permanent magnet as well as an optimal design application are demonstrated. PMID:28098851

Group-theoretic models of the inversion process in bacterial genomes.

PubMed

Egri-Nagy, Attila; Gebhardt, Volker; Tanaka, Mark M; Francis, Andrew R

2014-07-01

The variation in genome arrangements among bacterial taxa is largely due to the process of inversion. Recent studies indicate that not all inversions are equally probable, suggesting, for instance, that shorter inversions are more frequent than longer, and those that move the terminus of replication are less probable than those that do not. Current methods for establishing the inversion distance between two bacterial genomes are unable to incorporate such information. In this paper we suggest a group-theoretic framework that in principle can take these constraints into account. In particular, we show that by lifting the problem from circular permutations to the affine symmetric group, the inversion distance can be found in polynomial time for a model in which inversions are restricted to acting on two regions. This requires the proof of new results in group theory, and suggests a vein of new combinatorial problems concerning permutation groups on which group theorists will be needed to collaborate with biologists. We apply the new method to inferring distances and phylogenies for published Yersinia pestis data.

Query-based learning for aerospace applications.

PubMed

Saad, E W; Choi, J J; Vian, J L; Wunsch, D C Ii

2003-01-01

Models of real-world applications often include a large number of parameters with a wide dynamic range, which contributes to the difficulties of neural network training. Creating the training data set for such applications becomes costly, if not impossible. In order to overcome the challenge, one can employ an active learning technique known as query-based learning (QBL) to add performance-critical data to the training set during the learning phase, thereby efficiently improving the overall learning/generalization. The performance-critical data can be obtained using an inverse mapping called network inversion (discrete network inversion and continuous network inversion) followed by oracle query. This paper investigates the use of both inversion techniques for QBL learning, and introduces an original heuristic to select the inversion target values for continuous network inversion method. Efficiency and generalization was further enhanced by employing node decoupled extended Kalman filter (NDEKF) training and a causality index (CI) as a means to reduce the input search dimensionality. The benefits of the overall QBL approach are experimentally demonstrated in two aerospace applications: a classification problem with large input space and a control distribution problem.

A practical method to assess model sensitivity and parameter uncertainty in C cycle models

NASA Astrophysics Data System (ADS)

Delahaies, Sylvain; Roulstone, Ian; Nichols, Nancy

2015-04-01

The carbon cycle combines multiple spatial and temporal scales, from minutes to hours for the chemical processes occurring in plant cells to several hundred of years for the exchange between the atmosphere and the deep ocean and finally to millennia for the formation of fossil fuels. Together with our knowledge of the transformation processes involved in the carbon cycle, many Earth Observation systems are now available to help improving models and predictions using inverse modelling techniques. A generic inverse problem consists in finding a n-dimensional state vector x such that h(x) = y, for a given N-dimensional observation vector y, including random noise, and a given model h. The problem is well posed if the three following conditions hold: 1) there exists a solution, 2) the solution is unique and 3) the solution depends continuously on the input data. If at least one of these conditions is violated the problem is said ill-posed. The inverse problem is often ill-posed, a regularization method is required to replace the original problem with a well posed problem and then a solution strategy amounts to 1) constructing a solution x, 2) assessing the validity of the solution, 3) characterizing its uncertainty. The data assimilation linked ecosystem carbon (DALEC) model is a simple box model simulating the carbon budget allocation for terrestrial ecosystems. Intercomparison experiments have demonstrated the relative merit of various inverse modelling strategies (MCMC, ENKF) to estimate model parameters and initial carbon stocks for DALEC using eddy covariance measurements of net ecosystem exchange of CO2 and leaf area index observations. Most results agreed on the fact that parameters and initial stocks directly related to fast processes were best estimated with narrow confidence intervals, whereas those related to slow processes were poorly estimated with very large uncertainties. While other studies have tried to overcome this difficulty by adding complementary data streams or by considering longer observation windows no systematic analysis has been carried out so far to explain the large differences among results. We consider adjoint based methods to investigate inverse problems using DALEC and various data streams. Using resolution matrices we study the nature of the inverse problems (solution existence, uniqueness and stability) and show how standard regularization techniques affect resolution and stability properties. Instead of using standard prior information as a penalty term in the cost function to regularize the problems we constraint the parameter space using ecological balance conditions and inequality constraints. The efficiency and rapidity of this approach allows us to compute ensembles of solutions to the inverse problems from which we can establish the robustness of the variational method and obtain non Gaussian posterior distributions for the model parameters and initial carbon stocks.

A spline-based parameter estimation technique for static models of elastic structures

NASA Technical Reports Server (NTRS)

Dutt, P.; Taasan, S.

1986-01-01

The problem of identifying the spatially varying coefficient of elasticity using an observed solution to the forward problem is considered. Under appropriate conditions this problem can be treated as a first order hyperbolic equation in the unknown coefficient. Some continuous dependence results are developed for this problem and a spline-based technique is proposed for approximating the unknown coefficient, based on these results. The convergence of the numerical scheme is established and error estimates obtained.

Model Order Reduction for the fast solution of 3D Stokes problems and its application in geophysical inversion

NASA Astrophysics Data System (ADS)

Ortega Gelabert, Olga; Zlotnik, Sergio; Afonso, Juan Carlos; Díez, Pedro

2017-04-01

The determination of the present-day physical state of the thermal and compositional structure of the Earth's lithosphere and sub-lithospheric mantle is one of the main goals in modern lithospheric research. All this data is essential to build Earth's evolution models and to reproduce many geophysical observables (e.g. elevation, gravity anomalies, travel time data, heat flow, etc) together with understanding the relationship between them. Determining the lithospheric state involves the solution of high-resolution inverse problems and, consequently, the solution of many direct models is required. The main objective of this work is to contribute to the existing inversion techniques in terms of improving the estimation of the elevation (topography) by including a dynamic component arising from sub-lithospheric mantle flow. In order to do so, we implement an efficient Reduced Order Method (ROM) built upon classic Finite Elements. ROM allows to reduce significantly the computational cost of solving a family of problems, for example all the direct models that are required in the solution of the inverse problem. The strategy of the method consists in creating a (reduced) basis of solutions, so that when a new problem has to be solved, its solution is sought within the basis instead of attempting to solve the problem itself. In order to check the Reduced Basis approach, we implemented the method in a 3D domain reproducing a portion of Earth that covers up to 400 km depth. Within the domain the Stokes equation is solved with realistic viscosities and densities. The different realizations (the family of problems) is created by varying viscosities and densities in a similar way as it would happen in an inversion problem. The Reduced Basis method is shown to be an extremely efficiently solver for the Stokes equation in this context.

The artificial-free technique along the objective direction for the simplex algorithm

NASA Astrophysics Data System (ADS)

Boonperm, Aua-aree; Sinapiromsaran, Krung

2014-03-01

The simplex algorithm is a popular algorithm for solving linear programming problems. If the origin point satisfies all constraints then the simplex can be started. Otherwise, artificial variables will be introduced to start the simplex algorithm. If we can start the simplex algorithm without using artificial variables then the simplex iterate will require less time. In this paper, we present the artificial-free technique for the simplex algorithm by mapping the problem into the objective plane and splitting constraints into three groups. In the objective plane, one of variables which has a nonzero coefficient of the objective function is fixed in terms of another variable. Then it can split constraints into three groups: the positive coefficient group, the negative coefficient group and the zero coefficient group. Along the objective direction, some constraints from the positive coefficient group will form the optimal solution. If the positive coefficient group is nonempty, the algorithm starts with relaxing constraints from the negative coefficient group and the zero coefficient group. We guarantee the feasible region obtained from the positive coefficient group to be nonempty. The transformed problem is solved using the simplex algorithm. Additional constraints from the negative coefficient group and the zero coefficient group will be added to the solved problem and use the dual simplex method to determine the new optimal solution. An example shows the effectiveness of our algorithm.

Inverse modeling for seawater intrusion in coastal aquifers: Insights about parameter sensitivities, variances, correlations and estimation procedures derived from the Henry problem

USGS Publications Warehouse

Sanz, E.; Voss, C.I.

2006-01-01

Inverse modeling studies employing data collected from the classic Henry seawater intrusion problem give insight into several important aspects of inverse modeling of seawater intrusion problems and effective measurement strategies for estimation of parameters for seawater intrusion. Despite the simplicity of the Henry problem, it embodies the behavior of a typical seawater intrusion situation in a single aquifer. Data collected from the numerical problem solution are employed without added noise in order to focus on the aspects of inverse modeling strategies dictated by the physics of variable-density flow and solute transport during seawater intrusion. Covariances of model parameters that can be estimated are strongly dependent on the physics. The insights gained from this type of analysis may be directly applied to field problems in the presence of data errors, using standard inverse modeling approaches to deal with uncertainty in data. Covariance analysis of the Henry problem indicates that in order to generally reduce variance of parameter estimates, the ideal places to measure pressure are as far away from the coast as possible, at any depth, and the ideal places to measure concentration are near the bottom of the aquifer between the center of the transition zone and its inland fringe. These observations are located in and near high-sensitivity regions of system parameters, which may be identified in a sensitivity analysis with respect to several parameters. However, both the form of error distribution in the observations and the observation weights impact the spatial sensitivity distributions, and different choices for error distributions or weights can result in significantly different regions of high sensitivity. Thus, in order to design effective sampling networks, the error form and weights must be carefully considered. For the Henry problem, permeability and freshwater inflow can be estimated with low estimation variance from only pressure or only concentration observations. Permeability, freshwater inflow, solute molecular diffusivity, and porosity can be estimated with roughly equivalent confidence using observations of only the logarithm of concentration. Furthermore, covariance analysis allows a logical reduction of the number of estimated parameters for ill-posed inverse seawater intrusion problems. Ill-posed problems may exhibit poor estimation convergence, have a non-unique solution, have multiple minima, or require excessive computational effort, and the condition often occurs when estimating too many or co-dependent parameters. For the Henry problem, such analysis allows selection of the two parameters that control system physics from among all possible system parameters. ?? 2005 Elsevier Ltd. All rights reserved.

Influence of diffuse reflectance measurement accuracy on the scattering coefficient in determination of optical properties with integrating sphere optics (a secondary publication).

PubMed

Horibe, Takuro; Ishii, Katsunori; Fukutomi, Daichi; Awazu, Kunio

2015-12-30

An estimation error of the scattering coefficient of hemoglobin in the high absorption wavelength range has been observed in optical property calculations of blood-rich tissues. In this study, the relationship between the accuracy of diffuse reflectance measurement in the integrating sphere and calculated scattering coefficient was evaluated with a system to calculate optical properties combined with an integrating sphere setup and the inverse Monte Carlo simulation. Diffuse reflectance was measured with the integrating sphere using a small incident port diameter and optical properties were calculated. As a result, the estimation error of the scattering coefficient was improved by accurate measurement of diffuse reflectance. In the high absorption wavelength range, the accuracy of diffuse reflectance measurement has an effect on the calculated scattering coefficient.

A staggered-grid finite-difference scheme optimized in the time–space domain for modeling scalar-wave propagation in geophysical problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tan, Sirui, E-mail: siruitan@hotmail.com; Huang, Lianjie, E-mail: ljh@lanl.gov

For modeling scalar-wave propagation in geophysical problems using finite-difference schemes, optimizing the coefficients of the finite-difference operators can reduce numerical dispersion. Most optimized finite-difference schemes for modeling seismic-wave propagation suppress only spatial but not temporal dispersion errors. We develop a novel optimized finite-difference scheme for numerical scalar-wave modeling to control dispersion errors not only in space but also in time. Our optimized scheme is based on a new stencil that contains a few more grid points than the standard stencil. We design an objective function for minimizing relative errors of phase velocities of waves propagating in all directions within amore » given range of wavenumbers. Dispersion analysis and numerical examples demonstrate that our optimized finite-difference scheme is computationally up to 2.5 times faster than the optimized schemes using the standard stencil to achieve the similar modeling accuracy for a given 2D or 3D problem. Compared with the high-order finite-difference scheme using the same new stencil, our optimized scheme reduces 50 percent of the computational cost to achieve the similar modeling accuracy. This new optimized finite-difference scheme is particularly useful for large-scale 3D scalar-wave modeling and inversion.« less

Solving the Inverse-Square Problem with Complex Variables

ERIC Educational Resources Information Center

Gauthier, N.

2005-01-01

The equation of motion for a mass that moves under the influence of a central, inverse-square force is formulated and solved as a problem in complex variables. To find the solution, the constancy of angular momentum is first established using complex variables. Next, the complex position coordinate and complex velocity of the particle are assumed…

Backus-Gilbert inversion of travel time data

NASA Technical Reports Server (NTRS)

Johnson, L. E.

1972-01-01

Application of the Backus-Gilbert theory for geophysical inverse problems to the seismic body wave travel-time problem is described. In particular, it is shown how to generate earth models that fit travel-time data to within one standard error and having generated such models how to describe their degree of uniqueness. An example is given to illustrate the process.

Performance evaluation of the inverse dynamics method for optimal spacecraft reorientation

NASA Astrophysics Data System (ADS)

Ventura, Jacopo; Romano, Marcello; Walter, Ulrich

2015-05-01

This paper investigates the application of the inverse dynamics in the virtual domain method to Euler angles, quaternions, and modified Rodrigues parameters for rapid optimal attitude trajectory generation for spacecraft reorientation maneuvers. The impact of the virtual domain and attitude representation is numerically investigated for both minimum time and minimum energy problems. Owing to the nature of the inverse dynamics method, it yields sub-optimal solutions for minimum time problems. Furthermore, the virtual domain improves the optimality of the solution, but at the cost of more computational time. The attitude representation also affects solution quality and computational speed. For minimum energy problems, the optimal solution can be obtained without the virtual domain with any considered attitude representation.

Nonsteady Problem for an Elastic Half-Plane with Mixed Boundary Conditions

NASA Astrophysics Data System (ADS)

Kubenko, V. D.

2016-03-01

An approach to studying nonstationary wave processes in an elastic half-plane with mixed boundary conditions of the fourth boundary-value problem of elasticity is proposed. The Laplace and Fourier transforms are used. The sequential inversion of these transforms or the inversion of the joint transform by the Cagniard method allows obtaining the required solution (stresses, displacements) in a closed analytic form. With this approach, the problem can be solved for various types of loads

Music algorithm for imaging of a sound-hard arc in limited-view inverse scattering problem

NASA Astrophysics Data System (ADS)

Park, Won-Kwang

2017-07-01

MUltiple SIgnal Classification (MUSIC) algorithm for a non-iterative imaging of sound-hard arc in limited-view inverse scattering problem is considered. In order to discover mathematical structure of MUSIC, we derive a relationship between MUSIC and an infinite series of Bessel functions of integer order. This structure enables us to examine some properties of MUSIC in limited-view problem. Numerical simulations are performed to support the identified structure of MUSIC.