Things arising from electrocardiographic imaging: toward a theory of partial inverse problems.
Greensite, Fred
2006-01-01
The task of Electrocardiographic Imaging is an ill-posed inverse problem, requiring regularization. However, it has special features, firstly because it is a "non-stationary" inverse problem, and secondly because the inherent dynamical variety (e.g., epicardial breakthroughs, arrhythmias, ischemic changes) may preclude a fruitful nontrivial process model. Importantly, its structure places it in the category of "partial inverse problems" - a theory that arises from this setting. Surprising features of the resulting regularization methodology include the ability to fashion nontrivial regularization matrices in part (and sometimes entirely) from the data. There is evidence that these theoretical results can have significant practical benefits.
NASA Astrophysics Data System (ADS)
Holman, Benjamin R.
In recent years, revolutionary "hybrid" or "multi-physics" methods of medical imaging have emerged. By combining two or three different types of waves these methods overcome limitations of classical tomography techniques and deliver otherwise unavailable, potentially life-saving diagnostic information. Thermoacoustic (and photoacoustic) tomography is the most developed multi-physics imaging modality. Thermo- and photo- acoustic tomography require reconstructing initial acoustic pressure in a body from time series of pressure measured on a surface surrounding the body. For the classical case of free space wave propagation, various reconstruction techniques are well known. However, some novel measurement schemes place the object of interest between reflecting walls that form a de facto resonant cavity. In this case, known methods cannot be used. In chapter 2 we present a fast iterative reconstruction algorithm for measurements made at the walls of a rectangular reverberant cavity with a constant speed of sound. We prove the convergence of the iterations under a certain sufficient condition, and demonstrate the effectiveness and efficiency of the algorithm in numerical simulations. In chapter 3 we consider the more general problem of an arbitrarily shaped resonant cavity with a non constant speed of sound and present the gradual time reversal method for computing solutions to the inverse source problem. It consists in solving back in time on the interval [0, T] the initial/boundary value problem for the wave equation, with the Dirichlet boundary data multiplied by a smooth cutoff function. If T is sufficiently large one obtains a good approximation to the initial pressure; in the limit of large T such an approximation converges (under certain conditions) to the exact solution.
Inverse heat conduction problems
NASA Astrophysics Data System (ADS)
Orlande, Helcio Rangel Barreto
We present the solution of the following inverse problems: (1) Inverse Problem of Estimating Interface Conductance Between Periodically Contacting Surfaces; (2) Inverse Problem of Estimating Interface Conductance During Solidification via Conjugate Gradient Method; (3) Determination of the Reaction Function in a Reaction-Diffusion Parabolic Problem; and (4) Simultaneous Estimation of Thermal Diffusivity and Relaxation Time with Hyperbolic Heat Conduction Model. Also, we present the solution of a direct problem entitled: Transient Thermal Constriction Resistance in a Finite Heat Flux Tube. The Conjugate Gradient Method with Adjoint Equation was used in chapters 1-3. The more general function estimation approach was treated in these chapters. In chapter 1, we solve the inverse problem of estimating the timewise variation of the interface conductance between periodically contacting solids, under quasi-steady-state conditions. The present method is found to be more accurate than the B-Spline approach for situations involving small periods, which are the most difficult on which to perform the inverse analysis. In chapter 2, we estimate the timewise variation of the interface conductance between casting and mold during the solidification of aluminum. The experimental apparatus used in this study is described. In chapter 3, we present the estimation of the reaction function in a one dimensional parabolic problem. A comparison of the present function estimation approach with the parameter estimation technique, wing B-Splines to approximate the reaction function, revealed that the use of function estimation reduces the computer time requirements. In chapter 4 we present a finite difference solution for the transient constriction resistance in a cylinder of finite length with a circular contact surface. A numerical grid generation scheme was used to concentrate grid points in the regions of high temperature gradients in order to reduce discretization errors. In chapter 6, we
Inverse problems in mathematical physics
NASA Astrophysics Data System (ADS)
Glasko, V. B.
Procedures for the correct formulation and solution of inverse problems, which usually belong to the class of ill-posed problems, are discussed. Attention is given to the concept of the conditionally correct statement of a problem, the concept of quasi-solution, and the fundamentals of regularization theory. The discussion also covers the uniqueness of solutions to inverse problems in mathematical physics, with consideration given to problems involving layered media, impedance problems, gravimetric problems, and inverse problems of heat conduction. The problem of stability and regularizing operators are also discussed.
Aneesur Rahman Prize: The Inverse Ising Problem
NASA Astrophysics Data System (ADS)
Swendsen, Robert
2014-03-01
Many methods are available for carrying out computer simulations of a model Hamiltonian to obtain thermodynamic information by generating a set of configurations. The inverse problem consists of recreating the parameters of the Hamiltonian, given a set of configurations. The problem arises in a variety of contexts, and there has been much interest recently in the inverse Ising problem, in which the configurations consist of Ising spins. I will discuss an efficient method for solving the problem and what it can tell us about the Sherrington-Kirkpatrick model.
Inverse problem in hydrogeology
NASA Astrophysics Data System (ADS)
Carrera, Jesús; Alcolea, Andrés; Medina, Agustín; Hidalgo, Juan; Slooten, Luit J.
2005-03-01
The state of the groundwater inverse problem is synthesized. Emphasis is placed on aquifer characterization, where modelers have to deal with conceptual model uncertainty (notably spatial and temporal variability), scale dependence, many types of unknown parameters (transmissivity, recharge, boundary conditions, etc.), nonlinearity, and often low sensitivity of state variables (typically heads and concentrations) to aquifer properties. Because of these difficulties, calibration cannot be separated from the modeling process, as it is sometimes done in other fields. Instead, it should be viewed as one step in the process of understanding aquifer behavior. In fact, it is shown that actual parameter estimation methods do not differ from each other in the essence, though they may differ in the computational details. It is argued that there is ample room for improvement in groundwater inversion: development of user-friendly codes, accommodation of variability through geostatistics, incorporation of geological information and different types of data (temperature, occurrence and concentration of isotopes, age, etc.), proper accounting of uncertainty, etc. Despite this, even with existing codes, automatic calibration facilitates enormously the task of modeling. Therefore, it is contended that its use should become standard practice. L'état du problème inverse des eaux souterraines est synthétisé. L'accent est placé sur la caractérisation de l'aquifère, où les modélisateurs doivent jouer avec l'incertitude des modèles conceptuels (notamment la variabilité spatiale et temporelle), les facteurs d'échelle, plusieurs inconnues sur différents paramètres (transmissivité, recharge, conditions aux limites, etc.), la non linéarité, et souvent la sensibilité de plusieurs variables d'état (charges hydrauliques, concentrations) des propriétés de l'aquifère. A cause de ces difficultés, le calibrage ne peut êtreséparé du processus de modélisation, comme c'est le
Inversion Algorithms for Geophysical Problems
1987-12-16
ktdud* Sccumy Oass/Kjoon) Inversion Algorithms for Geophysical Problems (U) 12. PERSONAL AUTHOR(S) Lanzano, Paolo 13 «. TYPE OF REPORT Final 13b...spectral density. 20. DISTRIBUTION/AVAILABILITY OF ABSTRACT 13 UNCLASSIFIED/UNLIMITED D SAME AS RPT n OTIC USERS 22a. NAME OF RESPONSIBLE...Research Laboratory ’^^ SSZ ’.Washington. DC 20375-5000 NRLrMemorandum Report-6138 Inversion Algorithms for Geophysical Problems p. LANZANO Space
Mathematical problems arising in interfacial electrohydrodynamics
NASA Astrophysics Data System (ADS)
Tseluiko, Dmitri
In this work we consider the nonlinear stability of thin films in the presence of electric fields. We study a perfectly conducting thin film flow down an inclined plane in the presence of an electric field which is uniform in its undisturbed state, and normal to the plate at infinity. In addition, the effect of normal electric fields on films lying above, or hanging from, horizontal substrates is considered. Systematic asymptotic expansions are used to derive fully nonlinear long wave model equations for the scaled interface motion and corresponding flow fields. For the case of an inclined plane, higher order terms are need to be retained to regularize the problem in the sense that the long wave approximation remains valid for long times. For the case of a horizontal plane the fully nonlinear evolution equation which is derived at the leading order, is asymptotically correct and no regularization procedure is required. In both physical situations, the effect of the electric field is to introduce a non-local term which arises from the potential region above the liquid film, and enters through the electric Maxwell stresses at the interface. This term is always linearly destabilizing and produces growth rates proportional to the cubic power of the wavenumber - surface tension is included and provides a short wavelength cut-off, that is, all sufficiently short waves are linearly stable. For the case of film flow down an inclined plane, the fully nonlinear equation can produce singular solutions (for certain parameter values) after a finite time, even in the absence of an electric field. This difficulty is avoided at smaller amplitudes where the weakly nonlinear evolution is governed by an extension of the Kuramoto-Sivashinsky (KS) equation. Global existence and uniqueness results are proved, and refined estimates of the radius of the absorbing ball in L2 are obtained in terms of the parameters of the equations for a generalized class of modified KS equations. The
Optimization and geophysical inverse problems
Barhen, J.; Berryman, J.G.; Borcea, L.; Dennis, J.; de Groot-Hedlin, C.; Gilbert, F.; Gill, P.; Heinkenschloss, M.; Johnson, L.; McEvilly, T.; More, J.; Newman, G.; Oldenburg, D.; Parker, P.; Porto, B.; Sen, M.; Torczon, V.; Vasco, D.; Woodward, N.B.
2000-10-01
A fundamental part of geophysics is to make inferences about the interior of the earth on the basis of data collected at or near the surface of the earth. In almost all cases these measured data are only indirectly related to the properties of the earth that are of interest, so an inverse problem must be solved in order to obtain estimates of the physical properties within the earth. In February of 1999 the U.S. Department of Energy sponsored a workshop that was intended to examine the methods currently being used to solve geophysical inverse problems and to consider what new approaches should be explored in the future. The interdisciplinary area between inverse problems in geophysics and optimization methods in mathematics was specifically targeted as one where an interchange of ideas was likely to be fruitful. Thus about half of the participants were actively involved in solving geophysical inverse problems and about half were actively involved in research on general optimization methods. This report presents some of the topics that were explored at the workshop and the conclusions that were reached. In general, the objective of a geophysical inverse problem is to find an earth model, described by a set of physical parameters, that is consistent with the observational data. It is usually assumed that the forward problem, that of calculating simulated data for an earth model, is well enough understood so that reasonably accurate synthetic data can be generated for an arbitrary model. The inverse problem is then posed as an optimization problem, where the function to be optimized is variously called the objective function, misfit function, or fitness function. The objective function is typically some measure of the difference between observational data and synthetic data calculated for a trial model. However, because of incomplete and inaccurate data, the objective function often incorporates some additional form of regularization, such as a measure of smoothness
Kapteyn series arising in radiation problems
NASA Astrophysics Data System (ADS)
Lerche, I.; Tautz, R. C.
2008-01-01
In discussing radiation from multiple point charges or magnetic dipoles, moving in circles or ellipses, a variety of Kapteyn series of the second kind arises. Some of the series have been known in closed form for a hundred years or more, others appear not to be available to analytic persuasion. This paper shows how 12 such generic series can be developed to produce either closed analytic expressions or integrals that are not analytically tractable. In addition, the method presented here may be of benefit when one has other Kapteyn series of the second kind to consider, thereby providing an additional reason to consider such series anew.
Statistical inference for inverse problems
NASA Astrophysics Data System (ADS)
Bissantz, Nicolai; Holzmann, Hajo
2008-06-01
In this paper we study statistical inference for certain inverse problems. We go beyond mere estimation purposes and review and develop the construction of confidence intervals and confidence bands in some inverse problems, including deconvolution and the backward heat equation. Further, we discuss the construction of certain hypothesis tests, in particular concerning the number of local maxima of the unknown function. The methods are illustrated in a case study, where we analyze the distribution of heliocentric escape velocities of galaxies in the Centaurus galaxy cluster, and provide statistical evidence for its bimodality.
Computationally efficient Bayesian inference for inverse problems.
Marzouk, Youssef M.; Najm, Habib N.; Rahn, Larry A.
2007-10-01
Bayesian statistics provides a foundation for inference from noisy and incomplete data, a natural mechanism for regularization in the form of prior information, and a quantitative assessment of uncertainty in the inferred results. Inverse problems - representing indirect estimation of model parameters, inputs, or structural components - can be fruitfully cast in this framework. Complex and computationally intensive forward models arising in physical applications, however, can render a Bayesian approach prohibitive. This difficulty is compounded by high-dimensional model spaces, as when the unknown is a spatiotemporal field. We present new algorithmic developments for Bayesian inference in this context, showing strong connections with the forward propagation of uncertainty. In particular, we introduce a stochastic spectral formulation that dramatically accelerates the Bayesian solution of inverse problems via rapid evaluation of a surrogate posterior. We also explore dimensionality reduction for the inference of spatiotemporal fields, using truncated spectral representations of Gaussian process priors. These new approaches are demonstrated on scalar transport problems arising in contaminant source inversion and in the inference of inhomogeneous material or transport properties. We also present a Bayesian framework for parameter estimation in stochastic models, where intrinsic stochasticity may be intermingled with observational noise. Evaluation of a likelihood function may not be analytically tractable in these cases, and thus several alternative Markov chain Monte Carlo (MCMC) schemes, operating on the product space of the observations and the parameters, are introduced.
Estimating uncertainties in complex joint inverse problems
NASA Astrophysics Data System (ADS)
Afonso, Juan Carlos
2016-04-01
Sources of uncertainty affecting geophysical inversions can be classified either as reflective (i.e. the practitioner is aware of her/his ignorance) or non-reflective (i.e. the practitioner does not know that she/he does not know!). Although we should be always conscious of the latter, the former are the ones that, in principle, can be estimated either empirically (by making measurements or collecting data) or subjectively (based on the experience of the researchers). For complex parameter estimation problems in geophysics, subjective estimation of uncertainty is the most common type. In this context, probabilistic (aka Bayesian) methods are commonly claimed to offer a natural and realistic platform from which to estimate model uncertainties. This is because in the Bayesian approach, errors (whatever their nature) can be naturally included as part of the global statistical model, the solution of which represents the actual solution to the inverse problem. However, although we agree that probabilistic inversion methods are the most powerful tool for uncertainty estimation, the common claim that they produce "realistic" or "representative" uncertainties is not always justified. Typically, ALL UNCERTAINTY ESTIMATES ARE MODEL DEPENDENT, and therefore, besides a thorough characterization of experimental uncertainties, particular care must be paid to the uncertainty arising from model errors and input uncertainties. We recall here two quotes by G. Box and M. Gunzburger, respectively, of special significance for inversion practitioners and for this session: "…all models are wrong, but some are useful" and "computational results are believed by no one, except the person who wrote the code". In this presentation I will discuss and present examples of some problems associated with the estimation and quantification of uncertainties in complex multi-observable probabilistic inversions, and how to address them. Although the emphasis will be on sources of uncertainty related
Parabolic Perturbation of a Nonlinear Hyperbolic Problem Arising in Physiology
NASA Astrophysics Data System (ADS)
Colli, P.; Grasselli, M.
We study a transport-diffusion initial value problem where the diffusion codlicient is "small" and the transport coefficient is a time function depending on the solution in a nonlinear and nonlocal way. We show the existence and the uniqueness of a weak solution of this problem. Moreover we discuss its asymptotic behaviour as the diffusion coefficient goes to zero, obtaining a well-posed first-order nonlinear hyperbolic problem. These problems arise from mathematical models of muscle contraction in the framework of the sliding filament theory.
Minimax approach to inverse problems of geophysics
NASA Astrophysics Data System (ADS)
Balk, P. I.; Dolgal, A. S.; Balk, T. V.; Khristenko, L. A.
2016-03-01
A new approach is suggested for solving the inverse problems that arise in the different fields of applied geophysics (gravity, magnetic, and electrical prospecting, geothermy) and require assessing the spatial region occupied by the anomaly-generating masses in the presence of different types of a priori information. The interpretation which provides the maximum guaranteed proximity of the model field sources to the real perturbing object is treated as the best interpretation. In some fields of science (game theory, economics, operations research), the decision-making principle that lies in minimizing the probable losses which cannot be prevented if the situation develops by the worst-case scenario is referred to as minimax. The minimax criterion of choice is interesting as, instead of being confined to the indirect (and sometimes doubtful) signs of the "optimal" solution, it relies on the actual properties of the information in the results of a particular interpretation. In the hierarchy of the approaches to the solution of the inverse problems of geophysics ordered by the volume and quality of the retrieved information about the sources of the field, the minimax approach should take special place.
L∞ fitting for inverse problems with uniform noise
NASA Astrophysics Data System (ADS)
Clason, Christian
2012-10-01
For inverse problems where the data are corrupted by uniform noise such as arising from quantization errors, the L∞ norm is a more robust data-fitting term than the standard L2 norm. Well-posedness and regularization properties for linear inverse problems with L∞ data fitting are shown, and the automatic choice of the regularization parameter is discussed. After introducing an equivalent reformulation of the problem and a Moreau-Yosida approximation, a superlinearly convergent semi-smooth Newton method becomes applicable for the numerical solution of L∞ fitting problems. Numerical examples illustrate the performance of the proposed approach as well as the qualitative behavior of L∞ fitting.
2012-08-01
AFRL-RX-WP-TP-2012-0397 INVERSE PROBLEM FOR ELECTROMAGNETIC PROPAGATION IN A DIELECTRIC MEDIUM USING MARKOV CHAIN MONTE CARLO METHOD ...SUBTITLE INVERSE PROBLEM FOR ELECTROMAGNETIC PROPAGATION IN A DIELECTRIC MEDIUM USING MARKOV CHAIN MONTE CARLO METHOD (PREPRINT) 5a. CONTRACT...a stochastic inverse methodology arising in electromagnetic imaging. Nondestructive testing using guided microwaves covers a wide range of
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
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 Born series for the Calderon problem
NASA Astrophysics Data System (ADS)
Arridge, Simon; Moskow, Shari; Schotland, John C.
2012-03-01
We propose a direct reconstruction method for the Calderon problem based on inversion of the Born series. We characterize the convergence, stability and approximation error of the method and illustrate its use in numerical reconstructions.
An Inverse Problem Statistical Methodology Summary
2008-01-12
R. Vogel, Computational Methods for Inverse Problems, SIAM, Philadelphia, 2002. [36] D. D. Wackerly, W. Mendenhall III, and R. L. Scheaffer , Mathematical Statistics with Applications, Duxbury Thompson Learning, USA, 2002. 56
Some inverse problems arising from elastic scattering by rigid obstacles
NASA Astrophysics Data System (ADS)
Hu, Guanghui; Kirsch, Andreas; Sini, Mourad
2013-01-01
In the first part of this paper, it is proved that a C2-regular rigid scatterer in { {R}}^3 can be uniquely identified by the shear part (i.e. S-part) of the far-field pattern corresponding to all incident shear waves at any fixed frequency. The proof is short and it is based on a kind of decoupling of the S-part of scattered wave from its pressure part (i.e. P-part) on the boundary of the scatterer. Moreover, uniqueness using the S-part of the far-field pattern corresponding to only one incident plane shear wave holds for a ball or a convex Lipschitz polyhedron. In the second part, we adapt the factorization method to recover the shape of a rigid body from the scattered S-waves (resp. P-waves) corresponding to all incident plane shear (resp. pressure) waves. Numerical examples illustrate the accuracy of our reconstruction in { {R}}^2. In particular, the factorization method also leads to some uniqueness results for all frequencies excluding possibly a discrete set.
A Stochastic Problem Arising in the Storage of Radioactive Waste
Williams, M.M.R.
2004-07-15
Nuclear waste drums can contain a collection of radioactive components of uncertain activity and randomly dispersed in position. This implies that the dose-rate at the surface of different drums in a large assembly of similar drums can have significant variations according to the physical makeup and configuration of the waste components. The present paper addresses this problem by treating the drum, and its waste, as a stochastic medium. It is assumed that the sources in the drum contribute a dose-rate to some external point. The strengths and positions are chosen by random numbers, the dose-rate is calculated and, from several thousand realizations, a probability distribution for the dose-rate is obtained. It is shown that a very close approximation to the dose-rate probability function is the log-normal distribution. This allows some useful statistical indicators, which are of environmental importance, to be calculated with little effort.As an example of a practical situation met in the storage of radioactive waste containers, we study the problem of 'hotspots'. These arise in drums in which most of the activity is concentrated on one radioactive component and hence can lead to the possibility of large surface dose-rates. It is shown how the dose-rate, the variance, and some other statistical indicators depend on the relative activities on the sources. The results highlight the importance of such hotspots and the need to quantify their effect.
Linear inverse problem of the reactor dynamics
NASA Astrophysics Data System (ADS)
Volkov, N. P.
2017-01-01
The aim of this work is the study transient processes in nuclear reactors. The mathematical model of the reactor dynamics excluding reverse thermal coupling is investigated. This model is described by a system of integral-differential equations, consisting of a non-stationary anisotropic multispeed kinetic transport equation and a delayed neutron balance equation. An inverse problem was formulated to determine the stationary part of the function source along with the solution of the direct problem. The author obtained sufficient conditions for the existence and uniqueness of a generalized solution of this inverse problem.
Molecular seismology: an inverse problem in nanobiology.
Hinow, Peter; Boczko, Erik M
2007-05-07
The density profile of an elastic fiber like DNA will change in space and time as ligands associate with it. This observation affords a new direction in single molecule studies provided that density profiles can be measured in space and time. In fact, this is precisely the objective of seismology, where the mathematics of inverse problems have been employed with success. We argue that inverse problems in elastic media can be directly applied to biophysical problems of fiber-ligand association, and demonstrate that robust algorithms exist to perform density reconstruction in the condensed phase.
Estimating nuisance parameters in inverse problems
NASA Astrophysics Data System (ADS)
Aravkin, Aleksandr Y.; van Leeuwen, Tristan
2012-11-01
Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. The structure of these problems allows efficient optimization strategies—a well-known example is variable projection, where nonlinear least-squares problems which are linear in some parameters can be very efficiently optimized. In this paper, we extend the idea of projecting out a subset over the variables to a broad class of maximum likelihood and maximum a posteriori likelihood problems with nuisance parameters, such as variance or degrees of freedom (d.o.f.). As a result, we are able to incorporate nuisance parameter estimation into large-scale constrained and unconstrained inverse problem formulations. We apply the approach to a variety of problems, including estimation of unknown variance parameters in the Gaussian model, d.o.f. parameter estimation in the context of robust inverse problems, and automatic calibration. Using numerical examples, we demonstrate improvement in recovery of primary parameters for several large-scale inverse problems. The proposed approach is compatible with a wide variety of algorithms and formulations, and its implementation requires only minor modifications to existing algorithms.
Urban surface water pollution problems arising from misconnections.
Revitt, D Michael; Ellis, J Bryan
2016-05-01
The impacts of misconnections on the organic and nutrient loadings to surface waters are assessed using specific household appliance data for two urban sub-catchments located in the London metropolitan region and the city of Swansea. Potential loadings of biochemical oxygen demand (BOD), soluble reactive phosphorus (PO4-P) and ammoniacal nitrogen (NH4-N) due to misconnections are calculated for three different scenarios based on the measured daily flows from specific appliances and either measured daily pollutant concentrations or average pollutant concentrations for relevant greywater and black water sources obtained from an extensive review of the literature. Downstream receiving water concentrations, together with the associated uncertainties, are predicted from derived misconnection discharge concentrations and compared to existing freshwater standards for comparable river types. Consideration of dilution ratios indicates that these would need to be of the order of 50-100:1 to maintain high water quality with respect to BOD and NH4-N following typical misconnection discharges but only poor quality for PO4-P is likely to be achievable. The main pollutant loading contributions to misconnections arise from toilets (NH4-N and BOD), kitchen sinks (BOD and PO4-P) washing machines (PO4-P and BOD) and, to a lesser extent, dishwashers (PO4-P). By completely eliminating toilet misconnections and ensuring misconnections from all other appliances do not exceed 2%, the potential pollution problems due to BOD and NH4-N discharges would be alleviated but this would not be the case for PO4-P. In the event of a treatment option being preferred to solve the misconnection problem, it is shown that for an area the size of metropolitan Greater London, a sewage treatment plant with a Population Equivalent value approaching 900,000 would be required to efficiently remove BOD and NH4-N to safely dischargeable levels but such a plant is unlikely to have the capacity to deal
NASA Astrophysics Data System (ADS)
Kamimura, Yutaka; Usami, Hiroyuki
2016-12-01
This paper studies an inverse problem to determine a nonlinearity of an autonomous equation from blow-up time of solutions to the equation. Firstly we prove a global continuation result showing that a nonlinearity realizing blow-up time for large initial data can be continued in the direction of smaller data as long as the blow-up time is Lipschitz continuous. Secondly we develop a method based upon a Wiener-Hopf structure by which the existence and uniqueness of a nonlinearity realizing blow-up time for large initial data is shown. These enable us to establish a global existence and uniqueness result for the inverse problem.
Inverse problem of electro-seismic conversion
NASA Astrophysics Data System (ADS)
Chen, Jie; Yang, Yang
2013-11-01
When a porous rock is saturated with an electrolyte, electrical fields are coupled with seismic waves via the electro-seismic conversion. Pride (1994 Phys. Rev. B 50 15678-96) derived the governing models, in which Maxwell equations are coupled with Biot's equations through the electro-kinetic mobility parameter. The inverse problem of the linearized electro-seismic conversion consists in two steps, namely the inversion of Biot's equations and the inversion of Maxwell equations. We analyze the reconstruction of conductivity and electro-kinetic mobility parameter in Maxwell equations with internal measurements, while the internal measurements are provided by the results of the inversion of Biot's equations. We show that knowledge of two internal data based on well-chosen boundary conditions uniquely determines these two parameters. Moreover, a Lipschitz-type stability is proved based on the same sets of well-chosen boundary conditions.
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.
PUBLISHER'S ANNOUNCEMENT: New developments for Inverse Problems
NASA Astrophysics Data System (ADS)
2006-12-01
2006 has proved to be a very successful year for Inverse Problems. After an increase for the fourth successive year, we achieved our highest impact factor to date, 1.541 (Source: 2005 ISI® Journal Citation Report), and the Editorial Board is keen to build on this success by continuing to improve the service we offer to our readers and authors. The Board has observed that Inverse Problems receives very few Letters to the Editor submissions, and that moreover those that we do receive rarely conform to the requirements for Letters to the Editor set out in the journal's editorial policy. The Board has therefore decided to merge the current Letters to the Editor section into our regular Papers section, which will now accommodate all research articles that meet the journal's high quality standards. Any submissions that would previously have been Letters to the Editor are still very welcome as Papers, and can be submitted by e-mail to ip@iop.org or online using our online submissions form at authors.iop.org/submit. Inverse Problems' processing times are already among the fastest in the field—on average, authors receive our decision on their paper in less than three months. Thanks to our easy-to-use online refereeing system, publishing a Paper is now just as fast as publishing a Letter to the Editor, and we are striving to ensure that the journal's high standards are applied consistently to all our Papers, maintaining Inverse Problems' position as the leading journal in the field. Our highly acclaimed Topical Review section will also continue and grow; providing timely insights into the development of all topical fields within Inverse Problems. We have many exciting Topical Reviews currently in preparation for 2007 and will continue to commission articles at the cutting edge of research. We look forward to receiving your contributions and to continuing to provide the best publication service available.
An efficient method for inverse problems
NASA Technical Reports Server (NTRS)
Daripa, Prabir
1987-01-01
A new inverse method for aerodynamic design of subcritical airfoils is presented. The pressure distribution in this method can be prescribed in a natural way, i.e. as a function of arclength of the as yet unknown body. This inverse problem is shown to be mathematically equivalent to solving a single nonlinear boundary value problem subject to known Dirichlet data on the boundary. The solution to this problem determines the airfoil, the free stream Mach number M(sub x) and the upstream flow direction theta(sub x). The existence of a solution for any given pressure distribution is discussed. The method is easy to implement and extremely efficient. We present a series of results for which comparisons are made with the known airfoils.
A Reassessment of the Groundwater Inverse Problem
NASA Astrophysics Data System (ADS)
McLaughlin, Dennis; Townley, Lloyd R.
1996-05-01
This paper presents a functional formulation of the groundwater flow inverse problem that is sufficiently general to accommodate most commonly used inverse algorithms. Unknown hydrogeological properties are assumed to be spatial functions that can be represented in terms of a (possibly infinite) basis function expansion with random coefficients. The unknown parameter function is related to the measurements used for estimation by a "forward operator" which describes the measurement process. In the particular case considered here, the parameter of interest is the large-scale log hydraulic conductivity, the measurements are point values of log conductivity and piezometric head, and the forward operator is derived from an upscaled groundwater flow equation. The inverse algorithm seeks the "most probable" or maximum a posteriori estimate of the unknown parameter function. When the measurement errors and parameter function are Gaussian and independent, the maximum a posteriori estimate may be obtained by minimizing a least squares performance index which can be partitioned into goodness-of-fit and prior terms. When the parameter is a stationary random function the prior portion of the performance index is equivalent to a regularization term which imposes a smoothness constraint on the estimate. This constraint tends to make the problem well-posed by limiting the range of admissible solutions. The Gaussian maximum a posteriori problem may be solved with variational methods, using functional generalizations of Gauss-Newton or gradient-based search techniques. Several popular groundwater inverse algorithms are either special cases of, or variants on, the functional maximum a posteriori algorithm. These algorithms differ primarily with respect to the way they describe spatial variability and the type of search technique they use (linear versus nonlinear). The accuracy of estimates produced by both linear and nonlinear inverse algorithms may be measured in terms of a Bayesian
Inverse spectral problem for delta potentials
NASA Astrophysics Data System (ADS)
Shabat, A. B.
2015-11-01
The scattering problem for the linear Schrödinger equation on the entire axis has been considered. Conditions under which the knowledge of the discrete spectrum of the Schrödinger operator is sufficient for the reconstruction of the potential have been determined. The main difference from the soliton sector is the self-similarity of the problem under consideration with respect to the extension of the spectral parameter λ. This makes it possible to reduce the inverse scattering problem to the study of the singularity of the Green's function at λ = 0.
Inverse problems biomechanical imaging (Conference Presentation)
NASA Astrophysics Data System (ADS)
Oberai, Assad A.
2016-03-01
It is now well recognized that a host of imaging modalities (a list that includes Ultrasound, MRI, Optical Coherence Tomography, and optical microscopy) can be used to "watch" tissue as it deforms in response to an internal or external excitation. The result is a detailed map of the deformation field in the interior of the tissue. This deformation field can be used in conjunction with a material mechanical response to determine the spatial distribution of material properties of the tissue by solving an inverse problem. Images of material properties thus obtained can be used to quantify the health of the tissue. Recently, they have been used to detect, diagnose and monitor cancerous lesions, detect vulnerable plaque in arteries, diagnose liver cirrhosis, and possibly detect the onset of Alzheimer's disease. In this talk I will describe the mathematical and computational aspects of solving this class of inverse problems, and their applications in biology and medicine. In particular, I will discuss the well-posedness of these problems and quantify the amount of displacement data necessary to obtain a unique property distribution. I will describe an efficient algorithm for solving the resulting inverse problem. I will also describe some recent developments based on Bayesian inference in estimating the variance in the estimates of material properties. I will conclude with the applications of these techniques in diagnosing breast cancer and in characterizing the mechanical properties of cells with sub-cellular resolution.
The Convex Geometry of Linear Inverse Problems
2010-12-02
The Convex Geometry of Linear Inverse Problems Venkat Chandrasekaranm, Benjamin Rechtw, Pablo A. Parrilom, and Alan S. Willskym ∗ m Laboratory for...83) = 3r(m1 +m2 − r) + 2(m1 − r − r2) (84) where the second inequality follows from the fact that (a+ b)2 ≤ 2a2 + 2b2. References [1] Aja- Fernandez , S
Inverse scattering problem for quantum graph vertices
Cheon, Taksu; Turek, Ondrej; Exner, Pavel
2011-06-15
We demonstrate how the inverse scattering problem of a quantum star graph can be solved by means of diagonalization of the Hermitian unitary matrix when the vertex coupling is of the scale-invariant (or Fueloep-Tsutsui) form. This enables the construction of quantum graphs with desired properties in a tailor-made fashion. The procedure is illustrated on the example of quantum vertices with equal transmission probabilities.
Variational Bayesian Approximation methods for inverse problems
NASA Astrophysics Data System (ADS)
Mohammad-Djafari, Ali
2012-09-01
Variational Bayesian Approximation (VBA) methods are recent tools for effective Bayesian computations. In this paper, these tools are used for inverse problems where the prior models include hidden variables and where where the estimation of the hyper parameters has also to be addressed. In particular two specific prior models (Student-t and mixture of Gaussian models) are considered and details of the algorithms are given.
Riemann–Hilbert problem approach for two-dimensional flow inverse scattering
Agaltsov, A. D.; Novikov, R. G.
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.
Modelling and inversion -progress, problems, and challenges
NASA Astrophysics Data System (ADS)
Raiche, Art
1994-03-01
Researchers in the field of electromagnetic modelling and inversion have taken advantage of the impressive improvements of new computer hardware to explore exciting new initiatives and solid extensions of older ideas. Finite-difference time-stepping methods have been successfully applied to full-domain 3D models. Another new method combines time-stepping with spatial frequency solutions. The 2D model 3D source (2.5D) problem is also receiving fresh attention both for continental and sea floor applications. The 3D inversion problem is being attacked by several researchers using distorted Born approximation methods. Q-domain inversions using transformation to pseudo-wave field and travel time tomography have also been successfully tested for low contrast problems. Subspace methods have been successful in dramatically reducing the computational burden of the under-determined style of inversion. Static magnetic field interpretation methods are proving useful for delineating the position of closely-spaced multiple targets. Novel (“appeals to nature”) methods are also being investigated. Neural net algorithms have been tested for determining the depth and offset of buried pipes from EM ellipticity data. Genetic algorithms and simulated annealing have been tested for extremal model construction. The failure of researchers to take adequate account of the properties of the mathematical transformation from algorithms to the number domain represented by the computing process remains a major stumbling block. Structured programming, functional languages, and other software tools and methods are presented as an essential part of the serial process leading from EM theory to geological interpretation.
Finite element based inversion for time-harmonic electromagnetic problems
NASA Astrophysics Data System (ADS)
Schwarzbach, Christoph; Haber, Eldad
2013-05-01
In this paper we address the inverse problem and present some recent advances in numerical methods to recover the subsurface electrical conductivity from time-harmonic electromagnetic data. We rigorously formulate and discretize both the forward and the inverse problem in the finite element framework. To solve the forward problem, we derive a finite element discretization of the first-order system of Maxwell's equations in terms of the electric field and the magnetic induction. We show that our approach is equivalent to the standard discretization of the vector Helmholtz equation in terms of the electric field and that the discretization of magnetic induction of the same approximation order is hidden in the standard discretization. We implement the forward solver on unstructured tetrahedral meshes using edge elements. Unstructured meshes are not only capable of representing complex geometry. They can also reduce the overall problem size and, thus, the size of the system of linear equations arising from the forward problem such that direct methods for its solution using a sparse matrix factorization become feasible. The inverse problem is formulated as a regularized output least squares problem. We consider two regularization functions. First, we derive a smoothness regularizer using a primal-dual mixed finite element formulation which generalizes the standard Laplacian operator for a piecewise constant conductivity model on unstructured meshes. Secondly, we derive a total variation regularizer for the same class of models. For the choice of the regularization parameter we revisit the so-called dynamic regularization and compare it to a standard regularization scheme with fixed regularization parameter. The optimization problem is solved by the Gauss-Newton method which can be efficiently implemented using sparse matrix-vector operations and exploiting the sparse matrix factorization of the forward problem system matrix. A synthetic data example from marine
Inverse scattering problem in turbulent magnetic fluctuations
NASA Astrophysics Data System (ADS)
Treumann, Rudolf A.; Baumjohann, Wolfgang; Narita, Yasuhito
2016-08-01
We apply a particular form of the inverse scattering theory to turbulent magnetic fluctuations in a plasma. In the present note we develop the theory, formulate the magnetic fluctuation problem in terms of its electrodynamic turbulent response function, and reduce it to the solution of a special form of the famous Gelfand-Levitan-Marchenko equation of quantum mechanical scattering theory. The last of these applies to transmission and reflection in an active medium. The theory of turbulent magnetic fluctuations does not refer to such quantities. It requires a somewhat different formulation. We reduce the theory to the measurement of the low-frequency electromagnetic fluctuation spectrum, which is not the turbulent spectral energy density. The inverse theory in this form enables obtaining information about the turbulent response function of the medium. The dynamic causes of the electromagnetic fluctuations are implicit to it. Thus, it is of vital interest in low-frequency magnetic turbulence. The theory is developed until presentation of the equations in applicable form to observations of turbulent electromagnetic fluctuations as input from measurements. Solution of the final integral equation should be done by standard numerical methods based on iteration. We point to the possibility of treating power law fluctuation spectra as an example. Formulation of the problem to include observations of spectral power densities in turbulence is not attempted. This leads to severe mathematical problems and requires a reformulation of inverse scattering theory. One particular aspect of the present inverse theory of turbulent fluctuations is that its structure naturally leads to spatial information which is obtained from the temporal information that is inherent to the observation of time series. The Taylor assumption is not needed here. This is a consequence of Maxwell's equations, which couple space and time evolution. The inversion procedure takes advantage of a particular
Network connections that evolve to circumvent the inverse optics problem.
Ng, Cherlyn; Sundararajan, Janani; Hogan, Michael; Purves, Dale
2013-01-01
A fundamental problem in vision science is how useful perceptions and behaviors arise in the absence of information about the physical sources of retinal stimuli (the inverse optics problem). Psychophysical studies show that human observers contend with this problem by using the frequency of occurrence of stimulus patterns in cumulative experience to generate percepts. To begin to understand the neural mechanisms underlying this strategy, we examined the connectivity of simple neural networks evolved to respond according to the cumulative rank of stimulus luminance values. Evolved similarities with the connectivity of early level visual neurons suggests that biological visual circuitry uses the same mechanisms as a means of creating useful perceptions and behaviors without information about the real world.
EDITORIAL: Inverse Problems' 25th year of publication Inverse Problems' 25th year of publication
NASA Astrophysics Data System (ADS)
2008-01-01
2009 is Inverse Problems' 25th year of publication. In this quarter-century, the journal has established itself as the premier publication venue for inverse problems research. It has matured from its beginnings as a niche journal serving the emerging field of inverse and ill-posed problems to a monthly publication in 2009 covering all aspects of a well-established, vibrant and still-expanding subject. Along with its core readership of pure and applied mathematicians and physicists, Inverse Problems has become widely known across a broad range of researchers in areas such as geophysics, optics, radar, acoustics, communication theory, signal processing and medical imaging, amongst others. The journal's appeal to the inverse problems community and those researchers from the varied fields that encounter such problems can be attributed to our commitment to publishing only the very best papers, and to offering unique services to the community. Besides our regular research papers, which average a remarkably short five months from submission to electronic publication, we regularly publish heavily cited topical review papers and topic-specific special sections, which first appeared in 2004. These highly-downloaded invited articles focus on the latest developments and hot topics in all areas of inverse problems. No other journal in the field offers these features. I am very pleased to take Inverse Problems into its 25th year as Editor-in-Chief. The journal has an impressive tradition of scholarship, established at its inception by the founder and first Editor-in-Chief, Professor Pierre Sabatier. Professor Sabatier envisioned the journal in 1985 as providing a medium for publication of exemplary research in our intrinsically interdisciplinary field. I am glad to say that the support of our authors, readers, referees, Editors-in-Chief, Editorial Boards and Advisory Panels over the years, has resulted in Inverse Problems becoming the top publication in this field, publishing
An inverse problem by boundary element method
Tran-Cong, T.; Nguyen-Thien, T.; Graham, A.L.
1996-02-01
Boundary Element Methods (BEM) have been established as useful and powerful tools in a wide range of engineering applications, e.g. Brebbia et al. In this paper, we report a particular three dimensional implementation of a direct boundary integral equation (BIE) formulation and its application to numerical simulations of practical polymer processing operations. In particular, we will focus on the application of the present boundary element technology to simulate an inverse problem in plastics processing.by extrusion. The task is to design profile extrusion dies for plastics. The problem is highly non-linear due to material viscoelastic behaviours as well as unknown free surface conditions. As an example, the technique is shown to be effective in obtaining the die profiles corresponding to a square viscoelastic extrudate under different processing conditions. To further illustrate the capability of the method, examples of other non-trivial extrudate profiles and processing conditions are also given.
Inverse Variational Problem for Nonstandard Lagrangians
NASA Astrophysics Data System (ADS)
Saha, A.; Talukdar, B.
2014-06-01
In the mathematical physics literature the nonstandard Lagrangians (NSLs) were introduced in an ad hoc fashion rather than being derived from the solution of the inverse problem of variational calculus. We begin with the first integral of the equation of motion and solve the associated inverse problem to obtain some of the existing results for NSLs. In addition, we provide a number of alternative Lagrangian representations. The case studies envisaged by us include (i) the usual modified Emden-type equation, (ii) Emden-type equation with dissipative term quadratic in velocity, (iii) Lotka-Volterra model and (vi) a number of the generic equations for dissipative-like dynamical systems. Our method works for nonstandard Lagrangians corresponding to the usual action integral of mechanical systems but requires modification for those associated with the modified actions like S =∫abe L(x ,x˙ , t) dt and S =∫abL 1 - γ(x ,x˙ , t) dt because in the latter case one cannot construct expressions for the Jacobi integrals.
Boundary layer problem on a hyperbolic system arising from chemotaxis
NASA Astrophysics Data System (ADS)
Hou, Qianqian; Wang, Zhi-An; Zhao, Kun
2016-11-01
This paper is concerned with the boundary layer problem for a hyperbolic system transformed via a Cole-Hopf type transformation from a repulsive chemotaxis model with logarithmic sensitivity proposed in [23,34] modeling the biological movement of reinforced random walkers which deposit a non-diffusible (or slowly moving) signal that modifies the local environment for succeeding passages. By prescribing the Dirichlet boundary conditions to the transformed hyperbolic system in an interval (0 , 1), we show that the system has the boundary layer solutions as the chemical diffusion coefficient ε → 0, and further use the formal asymptotic analysis to show that the boundary layer thickness is ε 1 / 2. Our work justifies the boundary layer phenomenon that was numerically found in the recent work [25]. However we find that the original chemotaxis system does not possess boundary layer solutions when the results are reverted to the pre-transformed system.
Inverse spectral problems for differential operators on spatial networks
NASA Astrophysics Data System (ADS)
Yurko, V. A.
2016-06-01
A short survey is given of results on inverse spectral problems for ordinary differential operators on spatial networks (geometrical graphs). The focus is on the most important non-linear inverse problems of recovering coefficients of differential equations from spectral characteristics when the structure of the graph is known a priori. The first half of the survey presents results related to inverse Sturm-Liouville problems on arbitrary compact graphs. Results on inverse problems for differential operators of arbitrary order on compact graphs are then presented. In the conclusion the main results on inverse problems on non-compact graphs are given. Bibliography: 55 titles.
The inverse gravimetric problem in gravity modelling
NASA Technical Reports Server (NTRS)
Sanso, F.; Tscherning, C. C.
1989-01-01
One of the main purposes of geodesy is to determine the gravity field of the Earth in the space outside its physical surface. This purpose can be pursued without any particular knowledge of the internal density even if the exact shape of the physical surface of the Earth is not known, though this seems to entangle the two domains, as it was in the old Stoke's theory before the appearance of Molodensky's approach. Nevertheless, even when large, dense and homogeneous data sets are available, it was always recognized that subtracting from the gravity field the effect of the outer layer of the masses (topographic effect) yields a much smoother field. This is obviously more important when a sparse data set is bad so that any smoothing of the gravity field helps in interpolating between the data without raising the modeling error, this approach is generally followed because it has become very cheap in terms of computing time since the appearance of spectral techniques. The mathematical description of the Inverse Gravimetric Problem (IGP) is dominated mainly by two principles, which in loose terms can be formulated as follows: the knowledge of the external gravity field determines mainly the lateral variations of the density; and the deeper the density anomaly giving rise to a gravity anomaly, the more improperly posed is the problem of recovering the former from the latter. The statistical relation between rho and n (and its inverse) is also investigated in its general form, proving that degree cross-covariances have to be introduced to describe the behavior of rho. The problem of the simultaneous estimate of a spherical anomalous potential and of the external, topographic masses is addressed criticizing the choice of the mixed collection approach.
The inverse problem for Schwinger pair production
NASA Astrophysics Data System (ADS)
Hebenstreit, Florian
2016-02-01
The production of electron-positron pairs in time-dependent electric fields (Schwinger mechanism) depends non-linearly on the applied field profile. Accordingly, the resulting momentum spectrum is extremely sensitive to small variations of the field parameters. Owing to this non-linear dependence it is so far unpredictable how to choose a field configuration such that a predetermined momentum distribution is generated. We show that quantum kinetic theory along with optimal control theory can be used to approximately solve this inverse problem for Schwinger pair production. We exemplify this by studying the superposition of a small number of harmonic components resulting in predetermined signatures in the asymptotic momentum spectrum. In the long run, our results could facilitate the observation of this yet unobserved pair production mechanism in quantum electrodynamics by providing suggestions for tailored field configurations.
Stochastic inverse problems: Models and metrics
Sabbagh, Elias H.; Sabbagh, Harold A.; Murphy, R. Kim; Aldrin, John C.; Annis, Charles; Knopp, Jeremy S.
2015-03-31
In past work, we introduced model-based inverse methods, and applied them to problems in which the anomaly could be reasonably modeled by simple canonical shapes, such as rectangular solids. In these cases the parameters to be inverted would be length, width and height, as well as the occasional probe lift-off or rotation. We are now developing a formulation that allows more flexibility in modeling complex flaws. The idea consists of expanding the flaw in a sequence of basis functions, and then solving for the expansion coefficients of this sequence, which are modeled as independent random variables, uniformly distributed over their range of values. There are a number of applications of such modeling: 1. Connected cracks and multiple half-moons, which we have noted in a POD set. Ideally we would like to distinguish connected cracks from one long shallow crack. 2. Cracks of irregular profile and shape which have appeared in cold work holes during bolt-hole eddy-current inspection. One side of such cracks is much deeper than other. 3. L or C shaped crack profiles at the surface, examples of which have been seen in bolt-hole cracks. By formulating problems in a stochastic sense, we are able to leverage the stochastic global optimization algorithms in NLSE, which is resident in VIC-3D®, to answer questions of global minimization and to compute confidence bounds using the sensitivity coefficient that we get from NLSE. We will also address the issue of surrogate functions which are used during the inversion process, and how they contribute to the quality of the estimation of the bounds.
Inverse Problem in Self-assembly
NASA Astrophysics Data System (ADS)
Tkachenko, Alexei
2012-02-01
By decorating colloids and nanoparticles with DNA, one can introduce highly selective key-lock interactions between them. This leads to a new class of systems and problems in soft condensed matter physics. In particular, this opens a possibility to solve inverse problem in self-assembly: how to build an arbitrary desired structure with the bottom-up approach? I will present a theoretical and computational analysis of the hierarchical strategy in attacking this problem. It involves self-assembly of particular building blocks (``octopus particles''), that in turn would assemble into the target structure. On a conceptual level, our approach combines elements of three different brands of programmable self assembly: DNA nanotechnology, nanoparticle-DNA assemblies and patchy colloids. I will discuss the general design principles, theoretical and practical limitations of this approach, and illustrate them with our simulation results. Our crucial result is that not only it is possible to design a system that has a given nanostructure as a ground state, but one can also program and optimize the kinetic pathway for its self-assembly.
The relativistic inverse stellar structure problem
Lindblom, Lee
2014-01-14
The observable macroscopic properties of relativistic stars (whose equations of state are known) can be predicted by solving the stellar structure equations that follow from Einstein’s equation. For neutron stars, however, our knowledge of the equation of state is poor, so the direct stellar structure problem can not be solved without modeling the highest density part of the equation of state in some way. This talk will describe recent work on developing a model independent approach to determining the high-density neutron-star equation of state by solving an inverse stellar structure problem. This method uses the fact that Einstein’s equation provides a deterministic relationship between the equation of state and the macroscopic observables of the stars which are composed of that material. This talk illustrates how this method will be able to determine the high-density part of the neutron-star equation of state with few percent accuracy when high quality measurements of the masses and radii of just two or three neutron stars become available. This talk will also show that this method can be used with measurements of other macroscopic observables, like the masses and tidal deformabilities, which can (in principle) be measured by gravitational wave observations of binary neutron-star mergers.
The inverse problem of estimating the gravitational time dilation
NASA Astrophysics Data System (ADS)
Gusev, A. V.; Litvinov, D. A.; Rudenko, V. N.
2016-11-01
Precise testing of the gravitational time dilation effect suggests comparing the clocks at points with different gravitational potentials. Such a configuration arises when radio frequency standards are installed at orbital and ground stations. The ground-based standard is accessible directly, while the spaceborne one is accessible only via the electromagnetic signal exchange. Reconstructing the current frequency of the spaceborne standard is an ill-posed inverse problem whose solution depends significantly on the characteristics of the stochastic electromagnetic background. The solution for Gaussian noise is known, but the nature of the standards themselves is associated with nonstationary fluctuations of a wide class of distributions. A solution is proposed for a background of flicker fluctuations with a spectrum (1/ f)γ, where 1 < γ < 3, and stationary increments. The results include formulas for the error in reconstructing the frequency of the spaceborne standard and numerical estimates for the accuracy of measuring the relativistic redshift effect.
Direct and Inverse Problems in Statistical Wavefields
Wolf, Emil
2002-09-01
In this report account is presented of research carried out during the period September 1, 1999-August 31, 2002 under the sponsorship of the Department of Energy, grant DE-FG02-90ER14119. The research covered several areas of modern optical physics, particularly propagation of partially coherent light and its interaction with deterministic and with random media, spectroscopy with partially coherent light, polarization properties of statistical wave fields, effects of moving diffusers on coherence and on the spectra of light transmitted and scattered by them, reciprocity inequalities involving spatial and angular correlations of partially coherent beams, spreading of partially coherent beams in-random media, inverse source problems, computed and diffraction tomography and partially coherent solitons. We have discovered a new phenomenon in an emerging field of physical optics, known as singular optics; specifically we found that the spectrum of light changes drastically in the neighborhood of points where the intensity has zero value and where, consequently, the phase becomes singular, We noted some potential applications of this phenomenon. The results of our investigations were reported in 39 publications. They are listed on pages 3 to 5. Summaries of these publications are given on pages 6-13. Scientists who have participated in this research are listed on page 14.
PREFACE: International Conference on Inverse Problems 2010
NASA Astrophysics Data System (ADS)
Hon, Yiu-Chung; Ling, Leevan
2011-03-01
Following the first International Conference on Inverse Problems - Recent Theoretical Development and Numerical Approaches held at the City University of Hong Kong in 2002, the fifth International Conference was held again at the City University during December 13-17, 2010. This fifth conference was jointly organized by Professor Yiu-Chung Hon (Co-Chair, City University of Hong Kong, HKSAR), Dr Leevan Ling (Co-Chair, Hong Kong Baptist University, HKSAR), Professor Jin Cheng (Fudan University, China), Professor June-Yub Lee (Ewha Womans University, South Korea), Professor Gui-Rong Liu (University of Cincinnati, USA), Professor Jenn-Nan Wang (National Taiwan University, Taiwan), and Professor Masahiro Yamamoto (The University of Tokyo, Japan). It was agreed to alternate holding the conference among the above places (China, Japan, Korea, Taiwan, and Hong Kong) once every two years. The next conference has been scheduled to be held at the Southeast University (Nanjing, China) in 2012. The purpose of this series of conferences is to establish a strong collaborative link among the universities of the Asian-Pacific regions and worldwide leading researchers in inverse problems. The conference addressed both theoretical (mathematics), applied (engineering) and developmental aspects of inverse problems. The conference was intended to nurture Asian-American-European collaborations in the evolving interdisciplinary areas and it was envisioned that the conference would lead to long-term commitments and collaborations among the participating countries and researchers. There was a total of more than 100 participants. A call for the submission of papers was sent out after the conference, and a total of 19 papers were finally accepted for publication in this proceedings. The papers included in the proceedings cover a wide scope, which reflects the current flourishing theoretical and numerical research into inverse problems. Finally, as the co-chairs of the Inverse Problems
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.
Inverse Problem;Litho_Inversion; Geology and Geophysics
NASA Astrophysics Data System (ADS)
Antonio, Guillen; Gabriel, Courrioux; Bernard, Bourgine
2015-04-01
Subsurface modeling is a key tool to describe, understand and quantify geological processes. As the subsurface is inaccessible and its observation is limited by acquisition methods, 3D models of the subsurface are usually built from the interpretation of sparse data with limited resolution. Therefore, uncertainties occur during the model building process, due to possible cognitive human biais, natural variability of geological objects and intrinsic uncertainties of data. In such context, the predictibility of models is limited by uncertainties, which must be assessed in order to reduce economical and human risks linked to the use of models. This work focuses more specifically on uncertainties about geological structures. In this context, a stochastic method is developed for generating structural models with various fault and horizon geometries as well as fault connections. Realistic geological objects are obtained using implicit modeling that represents a surface by an equipotential of a volumetric scalar field. Faults have also been described by a reduced set of uncertain parameters, which opens the way to the inversion of structural objects using geophysical data by baysian methods.
Index Theory-Based Algorithm for the Gradiometer Inverse Problem
2015-03-28
Index Theory-Based Algorithm for the Gradiometer Inverse Problem Robert C. Anderson and Jonathan W. Fitton Abstract: We present an Index Theory...based gravity gradiometer inverse problem algorithm. This algorithm relates changes in the index value computed on a closed curve containing a line...field generated by the positive eigenvector of the gradiometer tensor to the closeness of fit of the proposed inverse solution to the mass and
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…
Solutions of inverse problems for biodegradation of xenobiotic polymers
NASA Astrophysics Data System (ADS)
Watanabe, Masaji; Kawai, Fusako
2016-02-01
Mathematical techniques are applied to a microbial depolymerization process. A mathematical model for the transition of the weight distribution and the microbial population is described. Inverse problems for a molecular factor and a time factor of a degradation rate are derived. Numerical techniques to solve the inverse problems are illustrated, and numerical results are presented.
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.)
Geometric MCMC for infinite-dimensional inverse problems
NASA Astrophysics Data System (ADS)
Beskos, Alexandros; Girolami, Mark; Lan, Shiwei; Farrell, Patrick E.; Stuart, Andrew M.
2017-04-01
Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement, when the finite-dimensional approximations become more accurate. Such methods are typically forced to reduce step-sizes as the discretization gets finer, and thus are expensive as a function of dimension. Recently, a new class of MCMC methods with mesh-independent convergence times has emerged. However, few of them take into account the geometry of the posterior informed by the data. At the same time, recently developed geometric MCMC algorithms have been found to be powerful in exploring complicated distributions that deviate significantly from elliptic Gaussian laws, but are in general computationally intractable for models defined in infinite dimensions. In this work, we combine geometric methods on a finite-dimensional subspace with mesh-independent infinite-dimensional approaches. Our objective is to speed up MCMC mixing times, without significantly increasing the computational cost per step (for instance, in comparison with the vanilla preconditioned Crank-Nicolson (pCN) method). This is achieved by using ideas from geometric MCMC to probe the complex structure of an intrinsic finite-dimensional subspace where most data information concentrates, while retaining robust mixing times as the dimension grows by using pCN-like methods in the complementary subspace. The resulting algorithms are demonstrated in the context of three challenging inverse problems arising in subsurface flow, heat conduction and incompressible flow control. The algorithms exhibit up to two orders of magnitude improvement in sampling efficiency when compared with the pCN method.
Research on the Inverse Problem of Scattering
1981-10-01
Levitan equation for the r)ne- dimensional and radial Schroedinger equations., ( b ) provided a vuiri•jtiona1 prine.l pie, and (c) extended inverse techniques...Variational Principle for the Gelfand- Levitan Equation and the Korteweg-deVries Equation (with M . Kanal), J. Math. Phys., 18, 2445 (1977). 3. A...Operators are Identical (with P. B . Abraham and B . DeFaclo), Studies in App. Math. (in press). 9. The Ceifand- Levitan Equation can Give Simple Examples of
An Inverse Problem for a Class of Conditional Probability Measure-Dependent Evolution Equations.
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.
An inverse problem for a class of conditional probability measure-dependent evolution equations
NASA Astrophysics Data System (ADS)
Mirzaev, Inom; Byrne, Erin C.; Bortz, David M.
2016-09-01
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 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.
Numerical solution of an inverse conductive boundary value problem
NASA Astrophysics Data System (ADS)
Yaman, F.
2008-12-01
In this paper, we derive a numerical solution of an inverse obstacle scattering problem with conductive boundary condition. The aim of the direct problem is the computation of the scattered field for a given arbitrarily shaped cylinder with conductive boundary condition on its surface.The inverse problem considered here is the reconstruction of the conductivity function of the scatterer from meausurements of the far field. A potential approach is used to obtain boundary layer integral equations both for the solution of the direct and the inverse problem. The numerical solutions of the integral equations which contain logarithmically singular kernels are evaluated by a Nyström method and Tikhonov regularization is used to solve the first kind of integral equations occuring in the solution of the inverse problem. Finally, numerical simulations are carried out to test the applicability and the effectiveness of the method.
On Linear Infeasibility Arising in Intensity-Modulated Radiation Therapy Inverse Planning.
Censor, Yair; Ben-Israel, Adi; Xiao, Ying; Galvin, James M
2008-03-01
Intensity-modulated radiation therapy (IMRT) gives rise to systems of linear inequalities, representing the effects of radiation on the irradiated body. These systems are often infeasible, in which case one settles for an approximate solution, such as an {α, β}-relaxation, meaning that no more than α percent of the inequalities are violated by no more than β percent. For real-world IMRT problems, there is a feasible {α, β}-relaxation for sufficiently large α, β > 0, however large values of these parameters may be unacceptable medically.The {α, β}-relaxation problem is combinatorial, and for given values of the parameters can be solved exactly by Mixed Integer Programming (MIP), but this may be impractical because of problem size, and the need for repeated solutions as the treatment progresses.As a practical alternative to the MIP approach we present a heuristic non-combinatorial method for finding an approximate relaxation. The method solves a Linear Program (LP) for each pair of values of the parameters {α, β} and progresses through successively increasing values until an acceptable solution is found, or is determined non-existent. The method is fast and reliable, since it consists of solving a sequence of LP's.
Some Numerical Results of Multipoints Bomndary Value Problems Arise in Environmental Protection
NASA Astrophysics Data System (ADS)
Pop, Daniel N.
2016-12-01
In this paper, we investigate two problems arise in pollutant transport in rivers, and we give some numerical results to approximate this solutions. We determined the approximate solutions using two numerical methods: 1. B-splines combined with Runge-Kutta methods, 2. BVP4C solver of MATLAB and then we compare the run-times.
Inverse Scattering Problems for Acoustic Waves in AN Inhomogeneous Medium.
NASA Astrophysics Data System (ADS)
Kedzierawski, Andrzej Wladyslaw
1990-01-01
This dissertation considers the inverse scattering problem of determining either the absorption of sound in an inhomogeneous medium or the surface impedance of an obstacle from a knowledge of the far-field patterns of the scattered fields corresponding to many incident time -harmonic plane waves. First, we consider the inverse problem in the case when the scattering object is an inhomogeneous medium with complex refraction index having compact support. Our approach to this problem is the orthogonal projection method of Colton-Monk (cf. The inverse scattering problem for time acoustic waves in an inhomogeneous medium, Quart. J. Mech. Appl. Math. 41 (1988), 97-125). After that, we prove the analogue of Karp's Theorem for the scattering of acoustic waves through an inhomogeneous medium with compact support. We then generalize some of these results to the case when the inhomogeneous medium is no longer of compact support. If the acoustic wave penetrates the inhomogeneous medium by only a small amount then the inverse medium problem leads to the inverse obstacle problem with an impedance boundary condition. We solve the inverse impedance problem of determining the surface impedance of an obstacle of known shape by using both the methods of Kirsch-Kress and Colton-Monk (cf. R. Kress, Linear Integral Equations, Springer-Verlag, New York, 1989).
Inverse scattering problems for acoustic waves in an inhomogeneous medium
NASA Astrophysics Data System (ADS)
Kedzierawski, Andrzej Wladyslaw
The inverse scattering problem is considered of determining either the absorption of sound in an inhomogeneous medium or the surface impedance of an obstacle from a knowledge of the far field patterns of the scattered field corresponding to many incident time-harmonic plane waves. First, the inverse problem is studied in the case when the scattering object is an inhomogeneous medium with complex refractive index having compact support. The approach to this problem is the orthogonal projection method of Colton-Monk (1988). After that, the analogue is proven of Karp's Theorem for the scattering of acoustic waves through an inhomogeneous medium with compact support. Some of these results are then generalized to the case when the inhomogeneous medium is no longer of compact support. If the acoustic wave penetrates the inhomogeneous medium by only a small amount then the inverse medium problem leads to the inverse obstacle problem with an impedance boundary condition. The inverse impedance problem is solved of determining the surface impedance of an obstacle of known shape by using both the methods of Kirsch-Kress and Colton-Monk (1989).
Inverse problem in nondestructive testing using arrayed eddy current sensors.
Zaoui, Abdelhalim; Menana, Hocine; Feliachi, Mouloud; Berthiau, Gérard
2010-01-01
A fast crack profile reconstitution model in nondestructive testing is developed using an arrayed eddy current sensor. The inverse problem is based on an iterative solving of the direct problem using genetic algorithms. In the direct problem, assuming a current excitation, the incident field produced by all the coils of the arrayed sensor is obtained by the translation and superposition of the 2D axisymmetric finite element results obtained for one coil; the impedance variation of each coil, due to the crack, is obtained by the reciprocity principle involving the dyadic Green's function. For the inverse problem, the surface of the crack is subdivided into rectangular cells, and the objective function is expressed only in terms of the depth of each cell. The evaluation of the dyadic Green's function matrix is made independently of the iterative procedure, making the inversion very fast.
Correct averaging in transmission radiography: Analysis of the inverse problem
NASA Astrophysics Data System (ADS)
Wagner, Michael; Hampel, Uwe; Bieberle, Martina
2016-05-01
Transmission radiometry is frequently used in industrial measurement processes as a means to assess the thickness or composition of a material. A common problem encountered in such applications is the so-called dynamic bias error, which results from averaging beam intensities over time while the material distribution changes. We recently reported on a method to overcome the associated measurement error by solving an inverse problem, which in principle restores the exact average attenuation by considering the Poisson statistics of the underlying particle or photon emission process. In this paper we present a detailed analysis of the inverse problem and its optimal regularized numerical solution. As a result we derive an optimal parameter configuration for the inverse problem.
Accounting for correlated errors in inverse radiation transport problems.
Mattingly, John K.; Stork, Christopher Lyle; Thomas, Edward Victor
2010-11-01
Inverse radiation transport focuses on identifying the configuration of an unknown radiation source given its observed radiation signatures. The inverse problem is solved by finding the set of transport model variables that minimizes a weighted sum of the squared differences by channel between the observed signature and the signature predicted by the hypothesized model parameters. The weights per channel are inversely proportional to the sum of the variances of the measurement and model errors at a given channel. In the current treatment, the implicit assumption is that the errors (differences between the modeled and observed radiation signatures) are independent across channels. In this paper, an alternative method that accounts for correlated errors between channels is described and illustrated for inverse problems based on gamma spectroscopy.
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.
On a recursive inverse eigenvalue problem
NASA Astrophysics Data System (ADS)
Ikramov, Kh. D.
2009-05-01
Let s 1, ..., s n be arbitrary complex scalars. It is required to construct an n × n normal matrix A such that s i is an eigenvalue of the leading principal submatrix A i , i = 1, 2, ..., n. It is shown that, along with the obvious diagonal solution diag( s 1, ..., s n ), this problem always admits a much more interesting nondiagonal solution A. As a rule, this solution is a dense matrix; with the diagonal solution, it shares the property that each submatrix A i is itself a normal matrix, which implies interesting connections between the spectra of the neighboring submatrices A i and A i + 1.
Numerical study of a parametric parabolic equation and a related inverse boundary value problem
NASA Astrophysics Data System (ADS)
Mustonen, Lauri
2016-10-01
We consider a time-dependent linear diffusion equation together with a related inverse boundary value problem. The aim of the inverse problem is to determine, based on observations on the boundary, the nonhomogeneous diffusion coefficient in the interior of an object. The method in this paper relies on solving the forward problem for a whole family of diffusivities by using a spectral Galerkin method in the high-dimensional parameter domain. The evaluation of the parametric solution and its derivatives is then completely independent of spatial and temporal discretizations. In the case of a quadratic approximation for the parameter dependence and a direct solver for linear least squares problems, we show that the evaluation of the parametric solution does not increase the complexity of any linearized subproblem arising from a Gauss-Newtonian method that is used to minimize a Tikhonov functional. The feasibility of the proposed algorithm is demonstrated by diffusivity reconstructions in two and three spatial dimensions.
From inverse problems in mathematical physiology to quantitative differential diagnoses.
Zenker, Sven; Rubin, Jonathan; Clermont, Gilles
2007-11-01
The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data interpretation and decision making. In particular, the application of mathematical models of experimentally elucidated physiological mechanisms could augment the interpretation of quantitative, patient-specific information and help to better target therapy. Yet, such models are typically complex and nonlinear, a reality that often precludes the identification of unique parameters and states of the model that best represent available data. Hypothesizing that this non-uniqueness can convey useful information, we implemented a simplified simulation of a common differential diagnostic process (hypotension in an acute care setting), using a combination of a mathematical model of the cardiovascular system, a stochastic measurement model, and Bayesian inference techniques to quantify parameter and state uncertainty. The output of this procedure is a probability density function on the space of model parameters and initial conditions for a particular patient, based on prior population information together with patient-specific clinical observations. We show that multimodal posterior probability density functions arise naturally, even when unimodal and uninformative priors are used. The peaks of these densities correspond to clinically relevant differential diagnoses and can, in the simplified simulation setting, be constrained to a single diagnosis by assimilating additional observations from dynamical interventions (e.g., fluid challenge). We conclude that the ill-posedness of the inverse problem in quantitative physiology is not merely a technical obstacle, but rather reflects clinical reality and, when addressed adequately in the solution process, provides a novel link between mathematically described physiological knowledge and the clinical concept of differential diagnoses
1980-10-01
SOLRED 53. C NFGSW =1 DAM PROBLEM 54. C =2 PROBLEM (5.3),(5.4). 55. C 56. C 57. C NINTSW =1 INJECTION. SUBROUTINE INTADD -77- ==.... APPX-C-PFMG 58. C =2...ARRAY Q SIZE SHOULD BE AT LEAST =1, 110) 256. STOP 257. 92 CONTINUE 258. C 259. C 260. CALL SOLRED 261. C 262. C INITIALIZE 263. WU=0 264. CALL...CONTINUE 996. PRINT *,(QTEM(LL),LL=1,L) 997. 20 CONTINUE 998. CALL URTIMS(TIME) 999. RETURN 1000. END 1001. C 1002. C 1003. C 1004. SUBROUTINE SOLRED
Inverse problems of ultrasound tomography in models with attenuation.
Goncharsky, Alexander V; Romanov, Sergey Y
2014-04-21
We develop efficient methods for solving inverse problems of ultrasound tomography in models with attenuation. We treat the inverse problem as a coefficient inverse problem for unknown coordinate-dependent functions that characterize both the speed cross section and the coefficients of the wave equation describing attenuation in the diagnosed region. We derive exact formulas for the gradient of the residual functional in models with attenuation, and develop efficient algorithms for minimizing the gradient of the residual by solving the conjugate problem. These algorithms are easy to parallelize when implemented on supercomputers, allowing the computation time to be reduced by a factor of several hundred compared to a PC. The numerical analysis of model problems shows that it is possible to reconstruct not only the speed cross section, but also the properties of the attenuating medium. We investigate the choice of the initial approximation for iterative algorithms used to solve inverse problems. The algorithms considered are primarily meant for the development of ultrasound tomographs for differential diagnosis of breast cancer.
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
NASA Astrophysics Data System (ADS)
Plestenjak, Bor; Gheorghiu, Călin I.; Hochstenbach, Michiel E.
2015-10-01
In numerous science and engineering applications a partial differential equation has to be solved on some fairly regular domain that allows the use of the method of separation of variables. In several orthogonal coordinate systems separation of variables applied to the Helmholtz, Laplace, or Schrödinger equation leads to a multiparameter eigenvalue problem (MEP); important cases include Mathieu's system, Lamé's system, and a system of spheroidal wave functions. Although multiparameter approaches are exploited occasionally to solve such equations numerically, MEPs remain less well known, and the variety of available numerical methods is not wide. The classical approach of discretizing the equations using standard finite differences leads to algebraic MEPs with large matrices, which are difficult to solve efficiently. The aim of this paper is to change this perspective. We show that by combining spectral collocation methods and new efficient numerical methods for algebraic MEPs it is possible to solve such problems both very efficiently and accurately. We improve on several previous results available in the literature, and also present a MATLAB toolbox for solving a wide range of problems.
Improved TV-CS Approaches for Inverse Scattering Problem
Bevacqua, M. T.; Di Donato, L.
2015-01-01
Total Variation and Compressive Sensing (TV-CS) techniques represent a very attractive approach to inverse scattering problems. In fact, if the unknown is piecewise constant and so has a sparse gradient, TV-CS approaches allow us to achieve optimal reconstructions, reducing considerably the number of measurements and enforcing the sparsity on the gradient of the sought unknowns. In this paper, we introduce two different techniques based on TV-CS that exploit in a different manner the concept of gradient in order to improve the solution of the inverse scattering problems obtained by TV-CS approach. Numerical examples are addressed to show the effectiveness of the method. PMID:26495420
Solving probabilistic inverse problems rapidly with prior samples
NASA Astrophysics Data System (ADS)
Käufl, Paul; Valentine, Andrew P.; de Wit, Ralph W.; Trampert, Jeannot
2016-06-01
Owing to the increasing availability of computational resources, in recent years the probabilistic solution of non-linear, geophysical inverse problems by means of sampling methods has become increasingly feasible. Nevertheless, we still face situations in which a Monte Carlo approach is not practical. This is particularly true in cases where the evaluation of the forward problem is computationally intensive or where inversions have to be carried out repeatedly or in a timely manner, as in natural hazards monitoring tasks such as earthquake early warning. Here, we present an alternative to Monte Carlo sampling, in which inferences are entirely based on a set of prior samples-that is, samples that have been obtained independent of a particular observed datum. This has the advantage that the computationally expensive sampling stage becomes separated from the inversion stage, and the set of prior samples-once obtained-can be reused for repeated evaluations of the inverse mapping without additional computational effort. This property is useful if the problem is such that repeated inversions of independent data have to be carried out. We formulate the inverse problem in a Bayesian framework and present a practical way to make posterior inferences based on a set of prior samples. We compare the prior sampling based approach to a Markov Chain Monte Carlo approach that samples from the posterior probability distribution. We show results for both a toy example, and a realistic seismological source parameter estimation problem. We find that the posterior uncertainty estimates obtained based on prior sampling can be considered conservative estimates of the uncertainties obtained by directly sampling from the posterior distribution.
A tutorial on inverse problems for anomalous diffusion processes
NASA Astrophysics Data System (ADS)
Jin, Bangti; Rundell, William
2015-03-01
Over the last two decades, anomalous diffusion processes in which the mean squares variance grows slower or faster than that in a Gaussian process have found many applications. At a macroscopic level, these processes are adequately described by fractional differential equations, which involves fractional derivatives in time or/and space. The fractional derivatives describe either history mechanism or long range interactions of particle motions at a microscopic level. The new physics can change dramatically the behavior of the forward problems. For example, the solution operator of the time fractional diffusion diffusion equation has only limited smoothing property, whereas the solution for the space fractional diffusion equation may contain weak singularity. Naturally one expects that the new physics will impact related inverse problems in terms of uniqueness, stability, and degree of ill-posedness. The last aspect is especially important from a practical point of view, i.e., stably reconstructing the quantities of interest. In this paper, we employ a formal analytic and numerical way, especially the two-parameter Mittag-Leffler function and singular value decomposition, to examine the degree of ill-posedness of several ‘classical’ inverse problems for fractional differential equations involving a Djrbashian-Caputo fractional derivative in either time or space, which represent the fractional analogues of that for classical integral order differential equations. We discuss four inverse problems, i.e., backward fractional diffusion, sideways problem, inverse source problem and inverse potential problem for time fractional diffusion, and inverse Sturm-Liouville problem, Cauchy problem, backward fractional diffusion and sideways problem for space fractional diffusion. It is found that contrary to the wide belief, the influence of anomalous diffusion on the degree of ill-posedness is not definitive: it can either significantly improve or worsen the conditioning of
A non-local free boundary problem arising in a theory of financial bubbles
Berestycki, Henri; Monneau, Regis; Scheinkman, José A.
2014-01-01
We consider an evolution non-local free boundary problem that arises in the modelling of speculative bubbles. The solution of the model is the speculative component in the price of an asset. In the framework of viscosity solutions, we show the existence and uniqueness of the solution. We also show that the solution is convex in space, and establish several monotonicity properties of the solution and of the free boundary with respect to parameters of the problem. To study the free boundary, we use, in particular, the fact that the odd part of the solution solves a more standard obstacle problem. We show that the free boundary is and describe the asymptotics of the free boundary as c, the cost of transacting the asset, goes to zero. PMID:25288815
Inverse scattering problems for perturbed bi-harmonic operator
NASA Astrophysics Data System (ADS)
Serov, Valery; Tyni, Teemu
2016-10-01
Some inverse scattering problems for operator of order 4 which is the perturbation (in smaller terms) of the biharmonic operator in one and three dimensions are considered. The coefficients of this perturbation are assumed to be from some Sobolev spaces (they might be singular). The classical (as for the Schrödinger operator) scattering theory is developed for this operator of order 4. The classical inverse scattering problems are considered and their uniqueness is proved. The method of inverse scattering Born approximation and an analogue of Saito's formula are justified for this operator of order 4. Using this approximate method the reconstruction of the singularities of the unknown coefficients is proved in the scale of Sobolev spaces. The results have natural generalization for any dimensions.
A reduced computational and geometrical framework for inverse problems in hemodynamics.
Lassila, Toni; Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi
2013-07-01
The solution of inverse problems in cardiovascular mathematics is computationally expensive. In this paper, we apply a domain parametrization technique to reduce both the geometrical and computational complexities of the forward problem and replace the finite element solution of the incompressible Navier-Stokes equations by a computationally less-expensive reduced-basis approximation. This greatly reduces the cost of simulating the forward problem. We then consider the solution of inverse problems both in the deterministic sense, by solving a least-squares problem, and in the statistical sense, by using a Bayesian framework for quantifying uncertainty. Two inverse problems arising in hemodynamics modeling are considered: (i) a simplified fluid-structure interaction model problem in a portion of a stenosed artery for quantifying the risk of atherosclerosis by identifying the material parameters of the arterial wall on the basis of pressure measurements; (ii) a simplified femoral bypass graft model for robust shape design under uncertain residual flow in the main arterial branch identified from pressure measurements.
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…
Inversion problem for singular integral operators: C*-approach
Dynin, Alexander
1978-01-01
The inversion problem is solved for a wide class of singular integral operators, in particular for Wiener-Hopf operators in several variables, Mihlin-Calderon-Zygmund operators on bounded domains, and Folland-Stein operators on compact nondegenerate Cauchy-Riemann manifolds. PMID:16592574
Toward precise solution of one-dimensional velocity inverse problems
Gray, S.; Hagin, F.
1980-01-01
A family of one-dimensional inverse problems are considered with the goal of reconstructing velocity profiles to reasonably high accuracy. The travel-time variable change is used together with an iteration scheme to produce an effective algorithm for computation. Under modest assumptions the scheme is shown to be convergent.
Kılıç, Emre Eibert, Thomas F.
2015-05-01
An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.
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
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.
Improved regularized solution of the inverse problem in turbidimetric measurements.
Mroczka, Janusz; Szczuczyński, Damian
2010-08-20
We present results of simulation research on the constrained regularized least-squares (RLS) solution of the ill-conditioned inverse problem in turbidimetric measurements. The problem is formulated in terms of the discretized Fredholm integral equation of the first kind. The inverse problem in turbidimetric measurements consists in determining particle size distribution (PSD) function of particulate system on the basis of turbidimetric measurements. The desired PSD should satisfy two constraints: nonnegativity of PSD values and normalization of PSD to unity when integrated over the whole range of particle size. Incorporating the constraints into the RLS method leads to the constrained regularized least-squares (CRLS) method, which is realized by means of an active set algorithm of quadratic programming. Results of simulation research prove that the CRLS method performs considerably better with reconstruction of PSD than the RLS method in terms of better fidelity and smaller uncertainty.
A reduced basis Landweber method for nonlinear inverse problems
NASA Astrophysics Data System (ADS)
Garmatter, Dominik; Haasdonk, Bernard; Harrach, Bastian
2016-03-01
We consider parameter identification problems in parametrized partial differential equations (PDEs). These lead to nonlinear ill-posed inverse problems. One way of solving them is using iterative regularization methods, which typically require numerous amounts of forward solutions during the solution process. In this article we consider the nonlinear Landweber method and couple it with the reduced basis method as a model order reduction technique in order to reduce the overall computational time. In particular, we consider PDEs with a high-dimensional parameter space, which are known to pose difficulties in the context of reduced basis methods. We present a new method that is able to handle such high-dimensional parameter spaces by combining the nonlinear Landweber method with adaptive online reduced basis updates. It is then applied to the inverse problem of reconstructing the conductivity in the stationary heat equation.
Stochastic inverse problem in the radiation of noise
NASA Technical Reports Server (NTRS)
Chow, P. L.; Maestrello, L.
1978-01-01
The reported investigation is concerned with a stochastic inverse radiation problem in a uniform medium. The problem is illustrated with the aid of a simple model consisting of an array of point sources. The entropy functional is chosen to be the structural functional in determining the source distribution. A general theory for the stochastic inverse problem is introduced. It is shown that the general procedure yields the methods of the Lagrangian multiplier, when the structural and residual functionals are specialized. Tihonov's regularization and a method related to generalized or pseudoinverses are also obtained. Examples considered for purposes of illustration are related to a continuous source with the least noise intensity, a continuous source with a potential, and an axisymmetric line source.
SIAM conference on inverse problems: Geophysical applications. Final technical report
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 devoted to seismology, hydrology, determination of the earth`s interior on a global scale as well as oceanographic and atmospheric inverse problems.
An inverse problem approach for elasticity imaging through vibroacoustics.
Aguiló, Miguel A; Aquino, Wilkins; Brigham, John C; Fatemi, Mostafa
2010-04-01
A methodology for estimating the spatial distribution of elastic moduli using the steady-state dynamic response of solids immersed in fluids is presented. The technique relies on the ensuing acoustic field from a remotely excited solid to inversely estimate the spatial distribution of Young's modulus of biological structures (e.g., breast tissue). This work proposes the use of Gaussian radial basis functions (GRBF) to represent the spatial variation of elastic moduli. GRBF are shown to possess the advantage of representing smooth functions with quasi-compact support and can efficiently represent elastic moduli distributions such as those that occur in soft biological tissue in the presence of unhealthy tissue (e.g., tumors and calcifications). The direct problem consists of a coupled acoustic-structure interaction boundary-value problem solved in the frequency domain using the finite element method. The inverse problem is cast as an optimization problem in which the error functional is defined as a measure of discrepancy between an experimentally measured response and a finite element representation of the system. Nongradient based optimization algorithms are used to solve the resulting optimization problem. The feasibility of the proposed approach is demonstrated through a series of simulations and an experiment. For comparison purposes, the surface velocity response was also used for the inverse characterization as the measured response in place of the acoustic pressure.
General bounds for electrode mislocation on the EEG inverse problem.
Beltrachini, L; von Ellenrieder, N; Muravchik, C H
2011-07-01
We analyze the effect of electrode mislocation on the electroencephalography (EEG) inverse problem using the Cramér-Rao bound (CRB) for single dipolar source parameters. We adopt a realistic head shape model, and solve the forward problem using the Boundary Element Method; the use of the CRB allows us to obtain general results which do not depend on the algorithm used for solving the inverse problem. We consider two possible causes for the electrode mislocation, errors in the measurement of the electrode positions and an imperfect registration between the electrodes and the scalp surfaces. For 120 electrodes placed in the scalp according to the 10-20 standard, and errors on the electrode location with a standard deviation of 5mm, the lower bound on the standard deviation in the source depth estimation is approximately 1mm in the worst case. Therefore, we conclude that errors in the electrode location may be tolerated since their effect on the EEG inverse problem are negligible from a practical point of view.
A penalty method for PDE-constrained optimization in inverse problems
NASA Astrophysics Data System (ADS)
van Leeuwen, T.; Herrmann, F. J.
2016-01-01
Many inverse and parameter estimation problems can be written as PDE-constrained optimization problems. The goal is to infer the parameters, typically coefficients of the PDE, from partial measurements of the solutions of the PDE for several right-hand sides. Such PDE-constrained problems can be solved by finding a stationary point of the Lagrangian, which entails simultaneously updating the parameters and the (adjoint) state variables. For large-scale problems, such an all-at-once approach is not feasible as it requires storing all the state variables. In this case one usually resorts to a reduced approach where the constraints are explicitly eliminated (at each iteration) by solving the PDEs. These two approaches, and variations thereof, are the main workhorses for solving PDE-constrained optimization problems arising from inverse problems. In this paper, we present an alternative method that aims to combine the advantages of both approaches. Our method is based on a quadratic penalty formulation of the constrained optimization problem. By eliminating the state variable, we develop an efficient algorithm that has roughly the same computational complexity as the conventional reduced approach while exploiting a larger search space. Numerical results show that this method indeed reduces some of the nonlinearity of the problem and is less sensitive to the initial iterate.
Inverse problem of HIV cell dynamics using Genetic Algorithms
NASA Astrophysics Data System (ADS)
González, J. A.; Guzmán, F. S.
2017-01-01
In order to describe the cell dynamics of T-cells in a patient infected with HIV, we use a flavour of Perelson's model. This is a non-linear system of Ordinary Differential Equations that describes the evolution of healthy, latently infected, infected T-cell concentrations and the free viral cells. Different parameters in the equations give different dynamics. Considering the concentration of these types of cells is known for a particular patient, the inverse problem consists in estimating the parameters in the model. We solve this inverse problem using a Genetic Algorithm (GA) that minimizes the error between the solutions of the model and the data from the patient. These errors depend on the parameters of the GA, like mutation rate and population, although a detailed analysis of this dependence will be described elsewhere.
Solving the inverse problem of noise-driven dynamic networks
NASA Astrophysics Data System (ADS)
Zhang, Zhaoyang; Zheng, Zhigang; Niu, Haijing; Mi, Yuanyuan; Wu, Si; Hu, Gang
2015-01-01
Nowadays, massive amounts of data are available for analysis in natural and social systems and the tasks to depict system structures from the data, i.e., the inverse problems, become one of the central issues in wide interdisciplinary fields. In this paper, we study the inverse problem of dynamic complex networks driven by white noise. A simple and universal inference formula of double correlation matrices and noise-decorrelation (DCMND) method is derived analytically, and numerical simulations confirm that the DCMND method can accurately depict both network structures and noise correlations by using available output data only. This inference performance has never been regarded possible by theoretical derivation, numerical computation, and experimental design.
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.
Diffuse interface methods for inverse problems: case study for an elliptic Cauchy problem
NASA Astrophysics Data System (ADS)
Burger, Martin; Løseth Elvetun, Ole; Schlottbom, Matthias
2015-12-01
Many inverse problems have to deal with complex, evolving and often not exactly known geometries, e.g. as domains of forward problems modeled by partial differential equations. This makes it desirable to use methods which are robust with respect to perturbed or not well resolved domains, and which allow for efficient discretizations not resolving any fine detail of those geometries. For forward problems in partial differential equations methods based on diffuse interface representations have gained strong attention in the last years, but so far they have not been considered systematically for inverse problems. In this work we introduce a diffuse domain method as a tool for the solution of variational inverse problems. As a particular example we study ECG inversion in further detail. ECG inversion is a linear inverse source problem with boundary measurements governed by an anisotropic diffusion equation, which naturally cries for solutions under changing geometries, namely the beating heart. We formulate a regularization strategy using Tikhonov regularization and, using standard source conditions, we prove convergence rates. A special property of our approach is that not only operator perturbations are introduced by the diffuse domain method, but more important we have to deal with topologies which depend on a parameter \\varepsilon in the diffuse domain method, i.e. we have to deal with \\varepsilon -dependent forward operators and \\varepsilon -dependent norms. In particular the appropriate function spaces for the unknown and the data depend on \\varepsilon . This prevents the application of some standard convergence techniques for inverse problems, in particular interpreting the perturbations as data errors in the original problem does not yield suitable results. We consequently develop a novel approach based on saddle-point problems. The numerical solution of the problem is discussed as well and results for several computational experiments are reported. In
Inverse source problem in an anisotropic medium by boundary measurements
NASA Astrophysics Data System (ADS)
El Badia, Abdellatif
2005-10-01
In this paper, we consider an inverse source problem for an anisotropic elliptic equation, from boundary measurements. A uniqueness result is established and a local Lipshitz stability, for a linear combination of monopolar and dipolar sources, is discussed. Assuming the number of dipoles bounded by a given integer M, we propose an algebraic algorithm which allows us to estimate the number, the locations and the moments of dipoles. Using special functions, we propose a global Lipschitz stability estimate for dipolar sources.
Combined approach to the inverse protein folding problem. Final report
Ruben A. Abagyan
2000-06-01
The main scientific contribution of the project ''Combined approach to the inverse protein folding problem'' submitted in 1996 and funded by the Department of Energy in 1997 is the formulation and development of the idea of the multilink recognition method for identification of functional and structural homologues of newly discovered genes. This idea became very popular after they first announced it and used it in prediction of the threading targets for the CASP2 competition (Critical Assessment of Structure Prediction).
Eddy-current NDE inverse problem with sparse grid algorithm
NASA Astrophysics Data System (ADS)
Zhou, Liming; Sabbagh, Harold A.; Sabbagh, Elias H.; Murphy, R. Kim; Bernacchi, William; Aldrin, John C.; Forsyth, David; Lindgren, Eric
2016-02-01
In model-based inverse problems, the unknown parameters (such as length, width, depth) need to be estimated. When the unknown parameters are few, the conventional mathematical methods are suitable. But the increasing number of unknown parameters will make the computation become heavy. To reduce the burden of computation, the sparse grid algorithm was used in our work. As a result, we obtain a powerful interpolation method that requires significantly fewer support nodes than conventional interpolation on a full grid.
Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians
NASA Astrophysics Data System (ADS)
Guseinov, Gusein Sh.
2009-02-01
In this paper, the concept of generalized spectral function is introduced for finite-order tridiagonal symmetric matrices (Jacobi matrices) with complex entries. The structure of the generalized spectral function is described in terms of spectral data consisting of the eigenvalues and normalizing numbers of the matrix. The inverse problems from generalized spectral function as well as from spectral data are investigated. In this way, a procedure for construction of complex tridiagonal matrices having real eigenvalues is obtained.
NASA Astrophysics Data System (ADS)
Ivanyshyn Yaman, Olha; Le Louër, Frédérique
2016-09-01
This paper deals with the material derivative analysis of the boundary integral operators arising from the scattering theory of time-harmonic electromagnetic waves and its application to inverse problems. We present new results using the Piola transform of the boundary parametrisation to transport the integral operators on a fixed reference boundary. The transported integral operators are infinitely differentiable with respect to the parametrisations and simplified expressions of the material derivatives are obtained. Using these results, we extend a nonlinear integral equations approach developed for solving acoustic inverse obstacle scattering problems to electromagnetism. The inverse problem is formulated as a pair of nonlinear and ill-posed integral equations for the unknown boundary representing the boundary condition and the measurements, for which the iteratively regularized Gauss-Newton method can be applied. The algorithm has the interesting feature that it avoids the numerous numerical solution of boundary value problems at each iteration step. Numerical experiments are presented in the special case of star-shaped obstacles.
Introduction to the 30th volume of Inverse Problems
NASA Astrophysics Data System (ADS)
Louis, Alfred K.
2014-01-01
The field of inverse problems is a fast-developing domain of research originating from the practical demands of finding the cause when a result is observed. The woodpecker, searching for insects, is probing a tree using sound waves: the information searched for is whether there is an insect or not, hence a 0-1 decision. When the result has to contain more information, ad hoc solutions are not at hand and more sophisticated methods have to be developed. Right from its first appearance, the field of inverse problems has been characterized by an interdisciplinary nature: the interpretation of measured data, reinforced by mathematical models serving the analyzing questions of observability, stability and resolution, developing efficient, stable and accurate algorithms to gain as much information as possible from the input and to feedback to the questions of optimal measurement configuration. As is typical for a new area of research, facets of it are separated and studied independently. Hence, fields such as the theory of inverse scattering, tomography in general and regularization methods have developed. However, all aspects have to be reassembled to arrive at the best possible solution to the problem at hand. This development is reflected by the first and still leading journal in the field, Inverse Problems. Founded by pioneers Roy Pike from London and Pierre Sabatier from Montpellier, who enjoyably describes the journal's nascence in his book Rêves et Combats d'un Enseignant-Chercheur, Retour Inverse [1], the journal has developed successfully over the last few decades. Neither the Editors-in-Chief, formerly called Honorary Editors, nor the board or authors could have set the path to success alone. Their fruitful interplay, complemented by the efficient and highly competent publishing team at IOP Publishing, has been fundamental. As such it is my honor and pleasure to follow my renowned colleagues Pierre Sabatier, Mario Bertero, Frank Natterer, Alberto Grünbaum and
Inverse problems with Poisson data: statistical regularization theory, applications and algorithms
NASA Astrophysics Data System (ADS)
Hohage, Thorsten; Werner, Frank
2016-09-01
Inverse problems with Poisson data arise in many photonic imaging modalities in medicine, engineering and astronomy. The design of regularization methods and estimators for such problems has been studied intensively over the last two decades. In this review we give an overview of statistical regularization theory for such problems, the most important applications, and the most widely used algorithms. The focus is on variational regularization methods in the form of penalized maximum likelihood estimators, which can be analyzed in a general setup. Complementing a number of recent convergence rate results we will establish consistency results. Moreover, we discuss estimators based on a wavelet-vaguelette decomposition of the (necessarily linear) forward operator. As most prominent applications we briefly introduce Positron emission tomography, inverse problems in fluorescence microscopy, and phase retrieval problems. The computation of a penalized maximum likelihood estimator involves the solution of a (typically convex) minimization problem. We also review several efficient algorithms which have been proposed for such problems over the last five years.
The inverse problems of wing panel manufacture processes
NASA Astrophysics Data System (ADS)
Oleinikov, A. I.; Bormotin, K. S.
2013-12-01
It is shown that inverse problems of steady-state creep bending of plates in both the geometrically linear and nonlinear formulations can be represented in a variational formulation. Steady-state values of the obtained functionals corresponding to the solutions of the problems of inelastic deformation and springback are determined by applying a finite element procedure to the functionals. Optimal laws of creep deformation are formulated using the criterion of minimizing damage in the functionals of the inverse problems. The formulated problems are reduced to the problems solved by the finite element method using MSC.Marc software. Currently, forming of light metals poses tremendous challenges due to their low ductility at room temperature and their unusual deformation characteristics at hot-cold work: strong asymmetry between tensile and compressive behavior, and a very pronounced anisotropy. We used the constitutive models of steady-state creep of initially transverse isotropy structural materials the kind of the stress state has influence. The paper gives basics of the developed computer-aided system of design, modeling, and electronic simulation targeting the processes of manufacture of wing integral panels. The modeling results can be used to calculate the die tooling, determine the panel processibility, and control panel rejection in the course of forming.
Stochastic reduced order models for inverse problems under uncertainty
Warner, James E.; Aquino, Wilkins; Grigoriu, Mircea D.
2014-01-01
This work presents a novel methodology for solving inverse problems under uncertainty using stochastic reduced order models (SROMs). Given statistical information about an observed state variable in a system, unknown parameters are estimated probabilistically through the solution of a model-constrained, stochastic optimization problem. The point of departure and crux of the proposed framework is the representation of a random quantity using a SROM - a low dimensional, discrete approximation to a continuous random element that permits e cient and non-intrusive stochastic computations. Characterizing the uncertainties with SROMs transforms the stochastic optimization problem into a deterministic one. The non-intrusive nature of SROMs facilitates e cient gradient computations for random vector unknowns and relies entirely on calls to existing deterministic solvers. Furthermore, the method is naturally extended to handle multiple sources of uncertainty in cases where state variable data, system parameters, and boundary conditions are all considered random. The new and widely-applicable SROM framework is formulated for a general stochastic optimization problem in terms of an abstract objective function and constraining model. For demonstration purposes, however, we study its performance in the specific case of inverse identification of random material parameters in elastodynamics. We demonstrate the ability to efficiently recover random shear moduli given material displacement statistics as input data. We also show that the approach remains effective for the case where the loading in the problem is random as well. PMID:25558115
The inverse problems of wing panel manufacture processes
Oleinikov, A. I.; Bormotin, K. S.
2013-12-16
It is shown that inverse problems of steady-state creep bending of plates in both the geometrically linear and nonlinear formulations can be represented in a variational formulation. Steady-state values of the obtained functionals corresponding to the solutions of the problems of inelastic deformation and springback are determined by applying a finite element procedure to the functionals. Optimal laws of creep deformation are formulated using the criterion of minimizing damage in the functionals of the inverse problems. The formulated problems are reduced to the problems solved by the finite element method using MSC.Marc software. Currently, forming of light metals poses tremendous challenges due to their low ductility at room temperature and their unusual deformation characteristics at hot-cold work: strong asymmetry between tensile and compressive behavior, and a very pronounced anisotropy. We used the constitutive models of steady-state creep of initially transverse isotropy structural materials the kind of the stress state has influence. The paper gives basics of the developed computer-aided system of design, modeling, and electronic simulation targeting the processes of manufacture of wing integral panels. The modeling results can be used to calculate the die tooling, determine the panel processibility, and control panel rejection in the course of forming.
Stochastic reduced order models for inverse problems under uncertainty.
Warner, James E; Aquino, Wilkins; Grigoriu, Mircea D
2015-03-01
This work presents a novel methodology for solving inverse problems under uncertainty using stochastic reduced order models (SROMs). Given statistical information about an observed state variable in a system, unknown parameters are estimated probabilistically through the solution of a model-constrained, stochastic optimization problem. The point of departure and crux of the proposed framework is the representation of a random quantity using a SROM - a low dimensional, discrete approximation to a continuous random element that permits e cient and non-intrusive stochastic computations. Characterizing the uncertainties with SROMs transforms the stochastic optimization problem into a deterministic one. The non-intrusive nature of SROMs facilitates e cient gradient computations for random vector unknowns and relies entirely on calls to existing deterministic solvers. Furthermore, the method is naturally extended to handle multiple sources of uncertainty in cases where state variable data, system parameters, and boundary conditions are all considered random. The new and widely-applicable SROM framework is formulated for a general stochastic optimization problem in terms of an abstract objective function and constraining model. For demonstration purposes, however, we study its performance in the specific case of inverse identification of random material parameters in elastodynamics. We demonstrate the ability to efficiently recover random shear moduli given material displacement statistics as input data. We also show that the approach remains effective for the case where the loading in the problem is random as well.
Source localization in electromyography using the inverse potential problem
NASA Astrophysics Data System (ADS)
van den Doel, Kees; Ascher, Uri M.; Pai, Dinesh K.
2011-02-01
We describe an efficient method for reconstructing the activity in human muscles from an array of voltage sensors on the skin surface. MRI is used to obtain morphometric data which are segmented into muscle tissue, fat, bone and skin, from which a finite element model for volume conduction is constructed. The inverse problem of finding the current sources in the muscles is solved using a careful regularization technique which adds a priori information, yielding physically reasonable solutions from among those that satisfy the basic potential problem. Several regularization functionals are considered and numerical experiments on a 2D test model are performed to determine which performs best. The resulting scheme leads to numerical difficulties when applied to large-scale 3D problems. We clarify the nature of these difficulties and provide a method to overcome them, which is shown to perform well in the large-scale problem setting.
Inference in infinite-dimensional inverse problems - Discretization and duality
NASA Technical Reports Server (NTRS)
Stark, Philip B.
1992-01-01
Many techniques for solving inverse problems involve approximating the unknown model, a function, by a finite-dimensional 'discretization' or parametric representation. The uncertainty in the computed solution is sometimes taken to be the uncertainty within the parametrization; this can result in unwarranted confidence. The theory of conjugate duality can overcome the limitations of discretization within the 'strict bounds' formalism, a technique for constructing confidence intervals for functionals of the unknown model incorporating certain types of prior information. The usual computational approach to strict bounds approximates the 'primal' problem in a way that the resulting confidence intervals are at most long enough to have the nominal coverage probability. There is another approach based on 'dual' optimization problems that gives confidence intervals with at least the nominal coverage probability. The pair of intervals derived by the two approaches bracket a correct confidence interval. The theory is illustrated with gravimetric, seismic, geomagnetic, and helioseismic problems and a numerical example in seismology.
Inverse problem for in vivo NMR spatial localization
Hasenfeld, A.C.
1985-11-01
The basic physical problem of NMR spatial localization is considered. To study diseased sites, one must solve the problem of adequately localizing the NMR signal. We formulate this as an inverse problem. As the NMR Bloch equations determine the motion of nuclear spins in applied magnetic fields, a theoretical study is undertaken to answer the question of how to design magnetic field configurations to achieve these localized excited spin populations. Because of physical constraints in the production of the relevant radiofrequency fields, the problem factors into a temporal one and a spatial one. We formulate the temporal problem as a nonlinear transformation, called the Bloch Transform, from the rf input to the magnetization response. In trying to invert this transformation, both linear (for the Fourier Transform) and nonlinear (for the Bloch Transform) modes of radiofrequency excitation are constructed. The spatial problem is essentially a statics problem for the Maxwell equations of electromagnetism, as the wavelengths of the radiation considered are on the order of ten meters, and so propagation effects are negligible. In the general case, analytic solutions are unavailable, and so the methods of computer simulation are used to map the rf field spatial profiles. Numerical experiments are also performed to verify the theoretical analysis, and experimental confirmation of the theory is carried out on the 0.5 Tesla IBM/Oxford Imaging Spectrometer at the LBL NMR Medical Imaging Facility. While no explicit inverse is constructed to ''solve'' this problem, the combined theoretical/numerical analysis is validated experimentally, justifying the approximations made. 56 refs., 31 figs.
Inverse problem of pulsed eddy current field of ferromagnetic plates
NASA Astrophysics Data System (ADS)
Chen, Xing-Le; Lei, Yin-Zhao
2015-03-01
To determine the wall thickness, conductivity and permeability of a ferromagnetic plate, an inverse problem is established with measured values and calculated values of time-domain induced voltage in pulsed eddy current testing on the plate. From time-domain analytical expressions of the partial derivatives of induced voltage with respect to parameters, it is deduced that the partial derivatives are approximately linearly dependent. Then the constraints of these parameters are obtained by solving a partial linear differential equation. It is indicated that only the product of conductivity and wall thickness, and the product of relative permeability and wall thickness can be determined accurately through the inverse problem with time-domain induced voltage. In the practical testing, supposing the conductivity of the ferromagnetic plate under test is a fixed value, and then the relative variation of wall thickness between two testing points can be calculated via the ratio of the corresponding inversion results of the product of conductivity and wall thickness. Finally, this method for wall thickness measurement is verified by the experiment results of a carbon steel plate. Project supported by the National Defense Basic Technology Research Program of China (Grant No. Z132013T001).
The physical and mathematical aspects of inverse problems in radiation detection and applications.
Hussein, Esam M A
2012-07-01
The inverse problem is the problem of converting detectable measurements into useful quantifiable indications. It is the problem of spectrum unfolding, image reconstruction, identifying a threat material, or devising a radiotherapy plan. The solution of an inverse problem requires a forward model that relates the quantities of interest to measurements. This paper explores the physical issues associated with formulating a radiation-transport forward model best suited for inversion, and the mathematical challenges associated with the solution of the corresponding inverse problem.
Inverse problems in heterogeneous and fractured media using peridynamics
Turner, Daniel Z.; van Bloemen Waanders, Bart G.; Parks, Michael L.
2015-12-10
The following work presents an adjoint-based methodology for solving inverse problems in heterogeneous and fractured media using state-based peridynamics. We show that the inner product involving the peridynamic operators is self-adjoint. The proposed method is illustrated for several numerical examples with constant and spatially varying material parameters as well as in the context of fractures. We also present a framework for obtaining material parameters by integrating digital image correlation (DIC) with inverse analysis. This framework is demonstrated by evaluating the bulk and shear moduli for a sample of nuclear graphite using digital photographs taken during the experiment. The resulting measured values correspond well with other results reported in the literature. Lastly, we show that this framework can be used to determine the load state given observed measurements of a crack opening. Furthermore, this type of analysis has many applications in characterizing subsurface stress-state conditions given fracture patterns in cores of geologic material.
Comparison of Optimal Design Methods in Inverse Problems.
Banks, H T; Holm, Kathleen; Kappel, Franz
2011-07-01
Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher Information Matrix (FIM). A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criteria with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model [13], the standard harmonic oscillator model [13] and a popular glucose regulation model [16, 19, 29].
NASA Technical Reports Server (NTRS)
Fymat, A. L.
1976-01-01
The paper studies the inversion of the radiative transfer equation describing the interaction of electromagnetic radiation with atmospheric aerosols. The interaction can be considered as the propagation in the aerosol medium of two light beams: the direct beam in the line-of-sight attenuated by absorption and scattering, and the diffuse beam arising from scattering into the viewing direction, which propagates more or less in random fashion. The latter beam has single scattering and multiple scattering contributions. In the former case and for single scattering, the problem is reducible to first-kind Fredholm equations, while for multiple scattering it is necessary to invert partial integrodifferential equations. A nonlinear minimization search method, applicable to the solution of both types of problems has been developed, and is applied here to the problem of monitoring aerosol pollution, namely the complex refractive index and size distribution of aerosol particles.
TOPICAL REVIEW: Inverse problems in astronomical adaptive optics
NASA Astrophysics Data System (ADS)
Ellerbroek, B. L.; Vogel, C. R.
2009-06-01
Adaptive optics (AO) is a technology used in ground-based astronomy to correct for the wavefront aberrations and loss of image quality caused by atmospheric turbulence. Provided some difficult technical problems can be overcome, AO will enable future astronomers to achieve nearly diffraction-limited performance with the extremely large telescopes that are currently under development, thereby greatly improving spatial resolution, spectral resolution and observing efficiency which will be achieved. The goal of this topical review is to present to the inverse problems community a representative sample of these problems. In this review, we first present a tutorial overview of the mathematical models and techniques used in current AO systems. We then examine in detail the following topics: laser guidestar adaptive optics, multi-conjugate and multi-object adaptive optics, high-contrast imaging and deformable mirror modeling and parameter identification.
Inverse scattering for an AKNS problem with rational reflection coefficients
NASA Astrophysics Data System (ADS)
Steudel, H.; Kaup, D. J.
2008-04-01
We study the AKNS (Ablowitz-Kaup-Newell-Segur) inverse scattering problem for rational reflection coefficients on a semi-infinite interval. We demonstrate that the Marchenko integral equations for the AKNS version on such an interval can be solved in a direct and straightforward way by algebraic methods for any set of rational reflection coefficients, vanishing at infinity. The general AKNS scattering problem for this case, as well as the usual symmetry reductions, are discussed. The connection to an alternative procedure by Rourke and Morris (1992 Phys. Rev. A 46 3631) is pointed out. Our procedure is built around a constant matrix, M, which can be constructed from the poles and residues of the rational reflection coefficients. Under certain conditions, which we define as minimal symmetry and which then suitably constrains the distribution of eigenvalues, we show that it is always possible to represent the resulting potentials as truncated N-soliton potentials. This procedure is of interest for solving initial-boundary value problems of integrable hyperbolic systems by the inverse scattering transform (IST) applied to a semi-infinite or finite interval.
Reconstructing Images in Astrophysics, an Inverse Problem Point of View
NASA Astrophysics Data System (ADS)
Theys, Céline; Aime, Claude
2016-04-01
After a short introduction, a first section provides a brief tutorial to the physics of image formation and its detection in the presence of noises. The rest of the chapter focuses on the resolution of the inverse problem
Inverse Retrospective Problem of Thermal Evolution of the Earth Interior
NASA Astrophysics Data System (ADS)
Ismail-Zadeh, A.
2009-04-01
I consider an inverse (time-reverse) problem of thermal evolution of a viscous inhomogeneous incompressible heat-conducting fluid describing dynamics of the Earth's mantle. Present observations of geophysical fields (temperature, velocity) are incorporated in a three-dimensional dynamic model to determine the initial conditions of the fields. I present and compare numerical techniques for assimilation of geophysical and geodetical data into the geological past: backward advection, variational (adjoint), and quasi-reversibility methods. The methods are applied to restore the evolution of the mantle structures such as rising plumes and descending lithospheric plates.
Negative Compressibility and Inverse Problem for Spinning Gas
Vasily Geyko and Nathaniel J. Fisch
2013-01-11
A spinning ideal gas in a cylinder with a smooth surface is shown to have unusual properties. First, under compression parallel to the axis of rotation, the spinning gas exhibits negative compressibility because energy can be stored in the rotation. Second, the spinning breaks the symmetry under which partial pressures of a mixture of gases simply add proportional to the constituent number densities. Thus, remarkably, in a mixture of spinning gases, an inverse problem can be formulated such that the gas constituents can be determined through external measurements only.
SUSY at the ILC and Solving the LHC Inverse Problem
Gainer, James S.; /SLAC
2008-05-28
Recently a large scale study of points in the MSSM parameter space which are problematic at the Large Hadron Collider (LHC) has been performed. This work was carried out in part to determine whether the proposed International Linear Collider (ILC) could be used to solve the LHC inverse problem. The results suggest that while the ILC will be a valuable tool, an energy upgrade may be crucial to its success, and that, in general, precision studies of the MSSM are more difficult at the ILC than has generally been believed.
Solving the inverse problem of magnetisation-stress resolution
NASA Astrophysics Data System (ADS)
Staples, S. G. H.; Vo, C.; Cowell, D. M. J.; Freear, S.; Ives, C.; Varcoe, B. T. H.
2013-04-01
Magnetostriction in various metals has been known since 1842, recently the focus has shifted away from ferrous metals, towards materials with a straightforward or exaggerated stress magnetostriction relationship. However, there is an increasing interest in understanding ferrous metal relationships, especially steels, because of its widespread use in building structures, transportation infrastructure, and pipelines. The aim of this paper is to solve the inverse problem of determining stress from an observed magnetic field which implies a given magnetic structure and to demonstrate that theoretical calculations using a multi-physics modeling technique agree with this experimental observation.
On the Inverse Scattering Problem in the Acoustic Environment
2008-03-03
16 21 ( 1 − cos(3t)) + 5 28 ( 1 − cos(4t)) ) . (264) The scatterer is a c50 -function in R with support in the interval [− 1 , 1 ]. The performance of the...On the inverse scattering problem in the acoustic environment Ran Duan and Vladimir Rokhlin Technical Report YALEU/DCS/TR-1395 March 3, 2008 1 Report...Documentation Page Form ApprovedOMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per
Stability of charge inversion, Thomson problem, and application to electrophoresis
NASA Astrophysics Data System (ADS)
Patra, Michael; Patriarca, Marco; Karttunen, Mikko
2003-03-01
We analyze charge inversion in colloidal systems at zero temperature using stability concepts, and connect this to the classical Thomson problem of arranging electrons on sphere. We show that for a finite microion charge, the globally stable, lowest-energy state of the complex formed by the colloid and the oppositely charged microions is always overcharged. This effect disappears in the continuous limit. Additionally, a layer of at least twice as many microions as required for charge neutrality is always locally stable. In an applied external electric field the stability of the microion cloud is reduced. Finally, this approach is applied to a system of two colloids at low but finite temperature.
Evaluation of simplified evaporation duct refractivity models for inversion problems
NASA Astrophysics Data System (ADS)
Saeger, J. T.; Grimes, N. G.; Rickard, H. E.; Hackett, E. E.
2015-10-01
To assess a radar system's instantaneous performance on any given day, detailed knowledge of the meteorological conditions is required due to the dependency of atmospheric refractivity on thermodynamic properties such as temperature, water vapor, and pressure. Because of the significant challenges involved in obtaining these data, recent efforts have focused on development of methods to obtain the refractivity structure inversely using radar measurements and radar wave propagation models. Such inversion techniques generally use simplified refractivity models in order to reduce the parameter space of the solution. Here the accuracy of three simple refractivity models is examined for the case of an evaporation duct. The models utilize the basic log linear shape classically associated with evaporation ducts, but each model depends on various parameters that affect different aspects of the profile, such as its shape and duct height. The model parameters are optimized using radiosonde data, and their performance is compared to these atmospheric measurements. The optimized models and data are also used to predict propagation using a parabolic equation code with the refractivity prescribed by the models and measured data, and the resulting propagation patterns are compared. The results of this study suggest that the best log linear model formulation for an inversion problem would be a two-layer model that contains at least three parameters: duct height, duct curvature, and mixed layer slope. This functional form permits a reasonably accurate fit to atmospheric measurements as well as embodies key features of the profile required for correct propagation prediction with as few parameters as possible.
Topological inversion for solution of geodesy-constrained geophysical problems
NASA Astrophysics Data System (ADS)
Saltogianni, Vasso; Stiros, Stathis
2015-04-01
Geodetic data, mostly GPS observations, permit to measure displacements of selected points around activated faults and volcanoes, and on the basis of geophysical models, to model the underlying physical processes. This requires inversion of redundant systems of highly non-linear equations with >3 unknowns; a situation analogous to the adjustment of geodetic networks. However, in geophysical problems inversion cannot be based on conventional least-squares techniques, and is based on numerical inversion techniques (a priori fixing of some variables, optimization in steps with values of two variables each time to be regarded fixed, random search in the vicinity of approximate solutions). Still these techniques lead to solutions trapped in local minima, to correlated estimates and to solutions with poor error control (usually sampling-based approaches). To overcome these problems, a numerical-topological, grid-search based technique in the RN space is proposed (N the number of unknown variables). This technique is in fact a generalization and refinement of techniques used in lighthouse positioning and in some cases of low-accuracy 2-D positioning using Wi-Fi etc. The basic concept is to assume discrete possible ranges of each variable, and from these ranges to define a grid G in the RN space, with some of the gridpoints to approximate the true solutions of the system. Each point of hyper-grid G is then tested whether it satisfies the observations, given their uncertainty level, and successful grid points define a sub-space of G containing the true solutions. The optimal (minimal) space containing one or more solutions is obtained using a trial-and-error approach, and a single optimization factor. From this essentially deterministic identification of the set of gridpoints satisfying the system of equations, at a following step, a stochastic optimal solution is computed corresponding to the center of gravity of this set of gridpoints. This solution corresponds to a
3D Magnetic inversion and remanence: solving the problem
NASA Astrophysics Data System (ADS)
Thomson, V.; Morris, W.
2003-04-01
3D inversion of surface magnetic data is a common processing technique when used in mineral exploration. The major drawback of most 3D inversion algorithms is that they assume that the surface magnetic anomaly is produced by induced magnetization and that there are no remanent magnetization or demagnetization effects present. This has a significant impact when modeling magnetic data that has remanent magnetization. The magnetic anomaly produced by a dipping subsurface body will be identical for a consistent relationship between the dip of the body and the dip of the magnetic vector, regardless of the actual dip of the magnetic body. For example, in the case where a subsurface body is dipping, such as a dipping dike, the dip estimated by the inversion routine will be correct only if induced magnetization is present. This has serious implications for mineral exploration. A solution to the remanence problem is to model the surface magnetic anomaly using a constrained 2D approach rather than 3D. Using a priori information on dip and strike length of a source body, it is possible to approximate the remanence direction and intensity. The 2D solutions can then be rendered into a 3D imaging package to create a model in 3D. A case study was performed on a mafic-ultramafic layered igneous intrusion located in Big Trout Lake, northwestern Ontario, Canada. Large layered igneous intrusions are known to have significant remanence. Like many other layered igneous intrusions such as the Bushveld Complex in South Africa, the Big Trout Lake Complex is highly prospective for Platinum Group Elements (PGEs). Intruded during Archean time, the Big Trout Lake Complex has been subsequently folded and faulted to near vertical. As a consequence of limited surface exposures, knowledge of layering within the pluton and the extent of deformation of the pluton is very limited. Newly acquired high-resolution aeromagnetic data shows a strongly mineralized horizon within the intrusion that
Review on solving the inverse problem in EEG source analysis
Grech, Roberta; Cassar, Tracey; Muscat, Joseph; Camilleri, Kenneth P; Fabri, Simon G; Zervakis, Michalis; Xanthopoulos, Petros; Sakkalis, Vangelis; Vanrumste, Bart
2008-01-01
In this primer, we give a review of the inverse problem for EEG source localization. This is intended for the researchers new in the field to get insight in the state-of-the-art techniques used to find approximate solutions of the brain sources giving rise to a scalp potential recording. Furthermore, a review of the performance results of the different techniques is provided to compare these different inverse solutions. The authors also include the results of a Monte-Carlo analysis which they performed to compare four non parametric algorithms and hence contribute to what is presently recorded in the literature. An extensive list of references to the work of other researchers is also provided. This paper starts off with a mathematical description of the inverse problem and proceeds to discuss the two main categories of methods which were developed to solve the EEG inverse problem, mainly the non parametric and parametric methods. The main difference between the two is to whether a fixed number of dipoles is assumed a priori or not. Various techniques falling within these categories are described including minimum norm estimates and their generalizations, LORETA, sLORETA, VARETA, S-MAP, ST-MAP, Backus-Gilbert, LAURA, Shrinking LORETA FOCUSS (SLF), SSLOFO and ALF for non parametric methods and beamforming techniques, BESA, subspace techniques such as MUSIC and methods derived from it, FINES, simulated annealing and computational intelligence algorithms for parametric methods. From a review of the performance of these techniques as documented in the literature, one could conclude that in most cases the LORETA solution gives satisfactory results. In situations involving clusters of dipoles, higher resolution algorithms such as MUSIC or FINES are however preferred. Imposing reliable biophysical and psychological constraints, as done by LAURA has given superior results. The Monte-Carlo analysis performed, comparing WMN, LORETA, sLORETA and SLF, for different noise levels
Inverse Problems in Complex Models and Applications to Earth Sciences
NASA Astrophysics Data System (ADS)
Bosch, M. E.
2015-12-01
The inference of the subsurface earth structure and properties requires the integration of different types of data, information and knowledge, by combined processes of analysis and synthesis. To support the process of integrating information, the regular concept of data inversion is evolving to expand its application to models with multiple inner components (properties, scales, structural parameters) that explain multiple data (geophysical survey data, well-logs, core data). The probabilistic inference methods provide the natural framework for the formulation of these problems, considering a posterior probability density function (PDF) that combines the information from a prior information PDF and the new sets of observations. To formulate the posterior PDF in the context of multiple datasets, the data likelihood functions are factorized assuming independence of uncertainties for data originating across different surveys. A realistic description of the earth medium requires modeling several properties and structural parameters, which relate to each other according to dependency and independency notions. Thus, conditional probabilities across model components also factorize. A common setting proceeds by structuring the model parameter space in hierarchical layers. A primary layer (e.g. lithology) conditions a secondary layer (e.g. physical medium properties), which conditions a third layer (e.g. geophysical data). In general, less structured relations within model components and data emerge from the analysis of other inverse problems. They can be described with flexibility via direct acyclic graphs, which are graphs that map dependency relations between the model components. Examples of inverse problems in complex models can be shown at various scales. At local scale, for example, the distribution of gas saturation is inferred from pre-stack seismic data and a calibrated rock-physics model. At regional scale, joint inversion of gravity and magnetic data is applied
Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1988-01-01
An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.
Inverse Spin Glass and Related Maximum Entropy Problems
NASA Astrophysics Data System (ADS)
Castellana, Michele; Bialek, William
2014-09-01
If we have a system of binary variables and we measure the pairwise correlations among these variables, then the least structured or maximum entropy model for their joint distribution is an Ising model with pairwise interactions among the spins. Here we consider inhomogeneous systems in which we constrain, for example, not the full matrix of correlations, but only the distribution from which these correlations are drawn. In this sense, what we have constructed is an inverse spin glass: rather than choosing coupling constants at random from a distribution and calculating correlations, we choose the correlations from a distribution and infer the coupling constants. We argue that such models generate a block structure in the space of couplings, which provides an explicit solution of the inverse problem. This allows us to generate a phase diagram in the space of (measurable) moments of the distribution of correlations. We expect that these ideas will be most useful in building models for systems that are nonequilibrium statistical mechanics problems, such as networks of real neurons.
Comparison of optimal design methods in inverse problems
NASA Astrophysics Data System (ADS)
Banks, H. T.; Holm, K.; Kappel, F.
2011-07-01
Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667-77 De Gaetano A and Arino O 2000 J. Math. Biol. 40 136-68 Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979-90).
Model selection in cognitive science as an inverse problem
NASA Astrophysics Data System (ADS)
Myung, Jay I.; Pitt, Mark A.; Navarro, Daniel J.
2005-03-01
How should we decide among competing explanations (models) of a cognitive phenomenon? This problem of model selection is at the heart of the scientific enterprise. Ideally, we would like to identify the model that actually generated the data at hand. However, this is an un-achievable goal as it is fundamentally ill-posed. Information in a finite data sample is seldom sufficient to point to a single model. Multiple models may provide equally good descriptions of the data, a problem that is exacerbated by the presence of random error in the data. In fact, model selection bears a striking similarity to perception, in that both require solving an inverse problem. Just as perceptual ambiguity can be addressed only by introducing external constraints on the interpretation of visual images, the ill-posedness of the model selection problem requires us to introduce external constraints on the choice of the most appropriate model. Model selection methods differ in how these external constraints are conceptualized and formalized. In this review we discuss the development of the various approaches, the differences between them, and why the methods perform as they do. An application example of selection methods in cognitive modeling is also discussed.
Inverse zombies, anesthesia awareness, and the hard problem of unconsciousness.
Mashour, George A; LaRock, Eric
2008-12-01
Philosophical (p-) zombies are constructs that possess all of the behavioral features and responses of a sentient human being, yet are not conscious. P-zombies are intimately linked to the hard problem of consciousness and have been invoked as arguments against physicalist approaches. But what if we were to invert the characteristics of p-zombies? Such an inverse (i-) zombie would possess all of the behavioral features and responses of an insensate being, yet would nonetheless be conscious. While p-zombies are logically possible but naturally improbable, an approximation of i-zombies actually exists: individuals experiencing what is referred to as "anesthesia awareness." Patients under general anesthesia may be intubated (preventing speech), paralyzed (preventing movement), and narcotized (minimizing response to nociceptive stimuli). Thus, they appear--and typically are--unconscious. In 1-2 cases/1000, however, patients may be aware of intraoperative events, sometimes without any objective indices. Furthermore, a much higher percentage of patients (22% in a recent study) may have the subjective experience of dreaming during general anesthesia. P-zombies confront us with the hard problem of consciousness--how do we explain the presence of qualia? I-zombies present a more practical problem--how do we detect the presence of qualia? The current investigation compares p-zombies to i-zombies and explores the "hard problem" of unconsciousness with a focus on anesthesia awareness.
Basis set expansion for inverse problems in plasma diagnostic analysis
Jones, B.; Ruiz, C. L.
2013-07-15
A basis set expansion method [V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, Rev. Sci. Instrum. 73, 2634 (2002)] is applied to recover physical information about plasma radiation sources from instrument data, which has been forward transformed due to the nature of the measurement technique. This method provides a general approach for inverse problems, and we discuss two specific examples relevant to diagnosing fast z pinches on the 20–25 MA Z machine [M. E. Savage, L. F. Bennett, D. E. Bliss, W. T. Clark, R. S. Coats, J. M. Elizondo, K. R. LeChien, H. C. Harjes, J. M. Lehr, J. E. Maenchen, D. H. McDaniel, M. F. Pasik, T. D. Pointon, A. C. Owen, D. B. Seidel, D. L. Smith, B. S. Stoltzfus, K. W. Struve, W. A. Stygar, L. K. Warne, J. R. Woodworth, C. W. Mendel, K. R. Prestwich, R. W. Shoup, D. L. Johnson, J. P. Corley, K. C. Hodge, T. C. Wagoner, and P. E. Wakeland, in Proceedings of the Pulsed Power Plasma Sciences Conference (IEEE, 2007), p. 979]. First, Abel inversion of time-gated, self-emission x-ray images from a wire array implosion is studied. Second, we present an approach for unfolding neutron time-of-flight measurements from a deuterium gas puff z pinch to recover information about emission time history and energy distribution. Through these examples, we discuss how noise in the measured data limits the practical resolution of the inversion, and how the method handles discontinuities in the source function and artifacts in the projected image. We add to the method a propagation of errors calculation for estimating uncertainties in the inverted solution.
Basis set expansion for inverse problems in plasma diagnostic analysis
NASA Astrophysics Data System (ADS)
Jones, B.; Ruiz, C. L.
2013-07-01
A basis set expansion method [V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, Rev. Sci. Instrum. 73, 2634 (2002)], 10.1063/1.1482156 is applied to recover physical information about plasma radiation sources from instrument data, which has been forward transformed due to the nature of the measurement technique. This method provides a general approach for inverse problems, and we discuss two specific examples relevant to diagnosing fast z pinches on the 20-25 MA Z machine [M. E. Savage, L. F. Bennett, D. E. Bliss, W. T. Clark, R. S. Coats, J. M. Elizondo, K. R. LeChien, H. C. Harjes, J. M. Lehr, J. E. Maenchen, D. H. McDaniel, M. F. Pasik, T. D. Pointon, A. C. Owen, D. B. Seidel, D. L. Smith, B. S. Stoltzfus, K. W. Struve, W. A. Stygar, L. K. Warne, J. R. Woodworth, C. W. Mendel, K. R. Prestwich, R. W. Shoup, D. L. Johnson, J. P. Corley, K. C. Hodge, T. C. Wagoner, and P. E. Wakeland, in Proceedings of the Pulsed Power Plasma Sciences Conference (IEEE, 2007), p. 979]. First, Abel inversion of time-gated, self-emission x-ray images from a wire array implosion is studied. Second, we present an approach for unfolding neutron time-of-flight measurements from a deuterium gas puff z pinch to recover information about emission time history and energy distribution. Through these examples, we discuss how noise in the measured data limits the practical resolution of the inversion, and how the method handles discontinuities in the source function and artifacts in the projected image. We add to the method a propagation of errors calculation for estimating uncertainties in the inverted solution.
NASA Technical Reports Server (NTRS)
Backus, George
1987-01-01
Let R be the real numbers, R(n) the linear space of all real n-tuples, and R(infinity) the linear space of all infinite real sequences x = (x sub 1, x sub 2,...). Let P sub n :R(infinity) approaches R(n) be the projection operator with P sub n (x) = (x sub 1,...,x sub n). Let p(infinity) be a probability measure on the smallest sigma-ring of subsets of R(infinity) which includes all of the cylinder sets P sub n(-1) (B sub n), where B sub n is an arbitrary Borel subset of R(n). Let p sub n be the marginal distribution of p(infinity) on R(n), so p sub n(B sub n) = p(infinity)(P sub n to the -1(B sub n)) for each B sub n. A measure on R(n) is isotropic if it is invariant under all orthogonal transformations of R(n). All members of the set of all isotropic probability distributions on R(n) are described. The result calls into question both stochastic inversion and Bayesian inference, as currently used in many geophysical inverse problems.
An Inverse Problems Approach to MR-EPT Image Reconstruction.
Borsic, A; Perreard, I; Mahara, A; Halter, R J
2016-01-01
Magnetic Resonance-Electrical Properties Tomography (MR-EPT) is an imaging modality that maps the spatial distribution of the electrical conductivity and permittivity using standard MRI systems. The presence of a body within the scanner alters the RF field, and by mapping these alterations it is possible to recover the electrical properties. The field is time-harmonic, and can be described by the Helmholtz equation. Approximations to this equation have been previously used to estimate conductivity and permittivity in terms of first or second derivatives of RF field data. Using these same approximations, an inverse approach to solving the MR-EPT problem is presented here that leverages a forward model for describing the magnitude and phase of the field within the imaging domain, and a fitting approach for estimating the electrical properties distribution. The advantages of this approach are that 1) differentiation of the measured data is not required, thus reducing noise sensitivity, and 2) different regularization schemes can be adopted, depending on prior knowledge of the distribution of conductivity or permittivity, leading to improved image quality. To demonstrate the developed approach, both Quadratic (QR) and Total Variation (TV) regularization methods were implemented and evaluated through numerical simulation and experimentally acquired data. The proposed inverse approach to MR-EPT reconstruction correctly identifies contrasts and accurately reconstructs the geometry in both simulations and experiments. The TV regularized scheme reconstructs sharp spatial transitions, which are difficult to reconstruct with other, more traditional approaches.
Inverse problems in heterogeneous and fractured media using peridynamics
Turner, Daniel Z.; van Bloemen Waanders, Bart G.; Parks, Michael L.
2015-12-10
The following work presents an adjoint-based methodology for solving inverse problems in heterogeneous and fractured media using state-based peridynamics. We show that the inner product involving the peridynamic operators is self-adjoint. The proposed method is illustrated for several numerical examples with constant and spatially varying material parameters as well as in the context of fractures. We also present a framework for obtaining material parameters by integrating digital image correlation (DIC) with inverse analysis. This framework is demonstrated by evaluating the bulk and shear moduli for a sample of nuclear graphite using digital photographs taken during the experiment. The resulting measuredmore » values correspond well with other results reported in the literature. Lastly, we show that this framework can be used to determine the load state given observed measurements of a crack opening. Furthermore, this type of analysis has many applications in characterizing subsurface stress-state conditions given fracture patterns in cores of geologic material.« less
The geometry of discombinations and its applications to semi-inverse problems in anelasticity
Yavari, Arash; Goriely, Alain
2014-01-01
The geometrical formulation of continuum mechanics provides us with a powerful approach to understand and solve problems in anelasticity where an elastic deformation is combined with a non-elastic component arising from defects, thermal stresses, growth effects or other effects leading to residual stresses. The central idea is to assume that the material manifold, prescribing the reference configuration for a body, has an intrinsic, non-Euclidean, geometrical structure. Residual stresses then naturally arise when this configuration is mapped into Euclidean space. Here, we consider the problem of discombinations (a new term that we introduce in this paper), that is, a combined distribution of fields of dislocations, disclinations and point defects. Given a discombination, we compute the geometrical characteristics of the material manifold (curvature, torsion, non-metricity), its Cartan's moving frames and structural equations. This identification provides a powerful algorithm to solve semi-inverse problems with non-elastic components. As an example, we calculate the residual stress field of a cylindrically symmetric distribution of discombinations in an infinite circular cylindrical bar made of an incompressible hyperelastic isotropic elastic solid. PMID:25197257
Multiresolution subspace-based optimization method for inverse scattering problems.
Oliveri, Giacomo; Zhong, Yu; Chen, Xudong; Massa, Andrea
2011-10-01
This paper investigates an approach to inverse scattering problems based on the integration of the subspace-based optimization method (SOM) within a multifocusing scheme in the framework of the contrast source formulation. The scattering equations are solved by a nested three-step procedure composed of (a) an outer multiresolution loop dealing with the identification of the regions of interest within the investigation domain through an iterative information-acquisition process, (b) a spectrum analysis step devoted to the reconstruction of the deterministic components of the contrast sources, and (c) an inner optimization loop aimed at retrieving the ambiguous components of the contrast sources through a conjugate gradient minimization of a suitable objective function. A set of representative reconstruction results is discussed to provide numerical evidence of the effectiveness of the proposed algorithmic approach as well as to assess the features and potentialities of the multifocusing integration in comparison with the state-of-the-art SOM implementation.
The inverse problem for the Gross-Pitaevskii equation.
Malomed, Boris A; Stepanyants, Yury A
2010-03-01
Two different methods are proposed for the generation of wide classes of exact solutions to the stationary Gross-Pitaevskii equation (GPE). The first method, suggested by the work of Kondrat'ev and Miller [Izv. Vyssh. Uchebn. Zaved., Radiofiz IX, 910 (1966)], applies to one-dimensional (1D) GPE. It is based on the similarity between the GPE and the integrable Gardner equation, all solutions of the latter equation (both stationary and nonstationary ones) generating exact solutions to the GPE. The second method is based on the "inverse problem" for the GPE, i.e., construction of a potential function which provides a desirable solution to the equation. Systematic results are presented for one- and two-dimensional cases. Both methods are illustrated by a variety of localized solutions, including solitary vortices, for both attractive and repulsive nonlinearity in the GPE. The stability of the 1D solutions is tested by direct simulations of the time-dependent GPE.
Solving the inverse problem of metamaterials with permittivity measurement
NASA Astrophysics Data System (ADS)
Lee, Hon Ping; Hui, Ka Shing; Yu, Kin Wah
2013-03-01
We have developed a new strategy for the reconstruction of volume fraction distribution of metallic inclusion in a graded composite from the measured electric permittivity data. Some of the techniques by Milton[1] and McPhedran[2] on homogenous two phase composites, together with Bergman-Milton representation, electromagnetic representation of effective permittivity and optimization method are used, and the strategy consist of the following two parts: reconstructing the effective permittivity in spectral space with Bergman representation by minimizing the cost function, and obtaining the volume fraction distribution by a contact of Bergman representation and electromagnetic representation of effective permittivity. Demonstration of the strategy is carried out by typical monotonically decreasing graded profile. The study could be extended to arbitrary profiles. The results obtained are useful for solving various inverse problems for the reconstruction of the structures of composites.
The LHC Inverse Problem, Supersymmetry and the ILC
Berger, C.F.; Gainer, J.S.; Hewett, J.L.; Lillie, B.; Rizzo, T.G.
2007-11-12
We address the question whether the ILC can resolve the LHC Inverse Problem within the framework of the MSSM. We examine 242 points in the MSSM parameter space which were generated at random and were found to give indistinguishable signatures at the LHC. After a realistic simulation including full Standard Model backgrounds and a fast detector simulation, we find that roughly only one third of these scenarios lead to visible signatures of some kind with a significance {ge} 5 at the ILC with {radical}s = 500 GeV. Furthermore, we examine these points in parameter space pairwise and find that only one third of the pairs are distinguishable at the ILC at 5{sigma}.
An inverse problem for a mathematical model of aquaponic agriculture
NASA Astrophysics Data System (ADS)
Bobak, Carly; Kunze, Herb
2017-01-01
Aquaponic agriculture is a sustainable ecosystem that relies on a symbiotic relationship between fish and macrophytes. While the practice has been growing in popularity, relatively little mathematical models exist which aim to study the system processes. In this paper, we present a system of ODEs which aims to mathematically model the population and concetrations dynamics present in an aquaponic environment. Values of the parameters in the system are estimated from the literature so that simulated results can be presented to illustrate the nature of the solutions to the system. As well, a brief sensitivity analysis is performed in order to identify redundant parameters and highlight those which may need more reliable estimates. Specifically, an inverse problem with manufactured data for fish and plants is presented to demonstrate the ability of the collage theorem to recover parameter estimates.
Geomagnetic inverse problem and data assimilation: a progress report
NASA Astrophysics Data System (ADS)
Aubert, Julien; Fournier, Alexandre
2013-04-01
In this presentation I will present two studies recently undertaken by our group in an effort to bring the benefits of data assimilation to the study of Earth's magnetic field and the dynamics of its liquid iron core, where the geodynamo operates. In a first part I will focus on the geomagnetic inverse problem, which attempts to recover the fluid flow in the core from the temporal variation of the magnetic field (known as the secular variation). Geomagnetic data can be downward continued from the surface of the Earth down to the core-mantle boundary, but not further below, since the core is an electrical conductor. Historically, solutions to the geomagnetic inverse problem in such a sparsely observed system were thus found only for flow immediately below the core mantle boundary. We have recently shown that combining a numerical model of the geodynamo together with magnetic observations, through the use of Kalman filtering, now allows to present solutions for flow throughout the core. In a second part, I will present synthetic tests of sequential geomagnetic data assimilation aiming at evaluating the range at which the future of the geodynamo can be predicted, and our corresponding prospects to refine the current geomagnetic predictions. Fournier, Aubert, Thébault: Inference on core surface flow from observations and 3-D dynamo modelling, Geophys. J. Int. 186, 118-136, 2011, doi: 10.1111/j.1365-246X.2011.05037.x Aubert, Fournier: Inferring internal properties of Earth's core dynamics and their evolution from surface observations and a numerical geodynamo model, Nonlinear Proc. Geoph. 18, 657-674, 2011, doi:10.5194/npg-18-657-2011 Aubert: Flow throughout the Earth's core inverted from geomagnetic observations and numerical dynamo models, Geophys. J. Int., 2012, doi: 10.1093/gji/ggs051
The ultrasound elastography inverse problem and the effective criteria.
Aghajani, Atefeh; Haghpanahi, Mohammad; Nikazad, Touraj
2013-11-01
The elastography (elasticity imaging) is one of the recent state-of-the-art methods for diagnosis of abnormalities in soft tissue. The idea is based on the computation of the tissue elasticity distribution. This leads to the inverse elasticity problem; in that, displacement field and boundary conditions are known, and elasticity distribution of the tissue is aimed for computation. We treat this problem by the Gauss-Newton method. This iterative method results in an ill-posed problem, and therefore, regularization schemes are required to deal with this issue. The impacts of the initial guess for tissue elasticity distribution, contrast ratio between elastic modulus of tumor and normal tissue, and noise level of the input data on the estimated solutions are investigated via two different regularization methods. The numerical results show that the accuracy and speed of convergence vary when different regularization methods are applied. Also, the semi-convergence behavior has been observed and discussed. At the end, we signify the necessity of a clever initial guess and intelligent stopping criteria for the iterations. The main purpose here is to highlight some technical factors that have an influence on elasticity image quality and diagnostic accuracy, and we have tried our best to make this article accessible for a broad audience.
Nonlocal regularization of inverse problems: a unified variational framework.
Yang, Zhili; Jacob, Mathews
2013-08-01
We introduce a unifying energy minimization framework for nonlocal regularization of inverse problems. In contrast to the weighted sum of square differences between image pixels used by current schemes, the proposed functional is an unweighted sum of inter-patch distances. We use robust distance metrics that promote the averaging of similar patches, while discouraging the averaging of dissimilar patches. We show that the first iteration of a majorize-minimize algorithm to minimize the proposed cost function is similar to current nonlocal methods. The reformulation thus provides a theoretical justification for the heuristic approach of iterating nonlocal schemes, which re-estimate the weights from the current image estimate. Thanks to the reformulation, we now understand that the widely reported alias amplification associated with iterative nonlocal methods are caused by the convergence to local minimum of the nonconvex penalty. We introduce an efficient continuation strategy to overcome this problem. The similarity of the proposed criterion to widely used nonquadratic penalties (e.g., total variation and lp semi-norms) opens the door to the adaptation of fast algorithms developed in the context of compressive sensing; we introduce several novel algorithms to solve the proposed nonlocal optimization problem. Thanks to the unifying framework, these fast algorithms are readily applicable for a large class of distance metrics.
A regularizing iterative ensemble Kalman method for PDE-constrained inverse problems
NASA Astrophysics Data System (ADS)
Iglesias, Marco A.
2016-02-01
. The numerical investigation is carried out with synthetic experiments on two model inverse problems: (i) identification of conductivity on a Darcy flow model and (ii) electrical impedance tomography with the complete electrode model. We further demonstrate the potential application of the method in solving shape identification problems that arises from the aforementioned forward models by means of a level-set approach for the parameterization of unknown geometries.
An inverse problem approach to modelling coastal effluent plumes
NASA Astrophysics Data System (ADS)
Lam, D. C. L.; Murthy, C. R.; Miners, K. C.
Formulated as an inverse problem, the diffusion parameters associated with length-scale dependent eddy diffusivities can be viewed as the unknowns in the mass conservation equation for coastal zone transport problems. The values of the diffusion parameters can be optimized according to an error function incorporated with observed concentration data. Examples are given for the Fickian, shear diffusion and inertial subrange diffusion models. Based on a new set of dyeplume data collected in the coastal zone off Bronte, Lake Ontario, it is shown that the predictions of turbulence closure models can be evaluated for different flow conditions. The choice of computational schemes for this diagnostic approach is based on tests with analytic solutions and observed data. It is found that the optimized shear diffusion model produced a better agreement with observations for both high and low advective flows than, e.g., the unoptimized semi-empirical model, Ky=0.075 σy1.2, described by Murthy and Kenney.
Church, E.L.; Takacs, P.Z.
1986-04-01
The accurate characterization of mirror surfaces requires the estimation of two-dimensional distribution functions and power spectra from trend-contaminated profile measurements. The rationale behind this, and our measurement and processing procedures, are described. The distinction between profile and area spectra is indicated, and since measurements often suggest inverse-power-law forms, a discussion of classical and fractal models of processes leading to these forms is included. 9 refs.
NASA Astrophysics Data System (ADS)
Zhan, Qin; Yuan, Yuan; Fan, Xiangtao; Huang, Jianyong; Xiong, Chunyang; Yuan, Fan
2016-06-01
Digital image correlation (DIC) is essentially implicated in a class of inverse problem. Here, a regularization scheme is developed for the subset-based DIC technique to effectively inhibit potential ill-posedness that likely arises in actual deformation calculations and hence enhance numerical stability, accuracy and precision of correlation measurement. With the aid of a parameterized two-dimensional Butterworth window, a regularized subpixel registration strategy is established, in which the amount of speckle information introduced to correlation calculations may be weighted through equivalent subset size constraint. The optimal regularization parameter associated with each individual sampling point is determined in a self-adaptive way by numerically investigating the curve of 2-norm condition number of coefficient matrix versus the corresponding equivalent subset size, based on which the regularized solution can eventually be obtained. Numerical results deriving from both synthetic speckle images and actual experimental images demonstrate the feasibility and effectiveness of the set of newly-proposed regularized DIC algorithms.
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 inequal- ity 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.
NASA Astrophysics Data System (ADS)
Siddheshwar, P. G.; Mahabaleswar, U. S.; Andersson, H. I.
2013-08-01
The paper discusses a new analytical procedure for solving the non-linear boundary layer equation arising in a linear stretching sheet problem involving a Newtonian/non-Newtonian liquid. On using a technique akin to perturbation the problem gives rise to a system of non-linear governing differential equations that are solved exactly. An analytical expression is obtained for the stream function and velocity as a function of the stretching parameters. The Clairaut equation is obtained on consideration of consistency and its solution is shown to be that of the stretching sheet boundary layer equation. The present study throws light on the analytical solution of a class of boundary layer equations arising in the stretching sheet problem
Subspace-based analysis of the ERT inverse problem
NASA Astrophysics Data System (ADS)
Ben Hadj Miled, Mohamed Khames; Miller, Eric L.
2004-05-01
In a previous work, we proposed a source-type formulation to the electrical resistance tomography (ERT) problem. Specifically, we showed that inhomogeneities in the medium can be viewed as secondary sources embedded in the homogeneous background medium and located at positions associated with variation in electrical conductivity. Assuming a piecewise constant conductivity distribution, the support of equivalent sources is equal to the boundary of the inhomogeneity. The estimation of the anomaly shape takes the form of an inverse source-type problem. In this paper, we explore the use of subspace methods to localize the secondary equivalent sources associated with discontinuities in the conductivity distribution. Our first alternative is the multiple signal classification (MUSIC) algorithm which is commonly used in the localization of multiple sources. The idea is to project a finite collection of plausible pole (or dipole) sources onto an estimated signal subspace and select those with largest correlations. In ERT, secondary sources are excited simultaneously but in different ways, i.e. with distinct amplitude patterns, depending on the locations and amplitudes of primary sources. If the number of receivers is "large enough", different source configurations can lead to a set of observation vectors that span the data subspace. However, since sources that are spatially close to each other have highly correlated signatures, seperation of such signals becomes very difficult in the presence of noise. To overcome this problem we consider iterative MUSIC algorithms like R-MUSIC and RAP-MUSIC. These recursive algorithms pose a computational burden as they require multiple large combinatorial searches. Results obtained with these algorithms using simulated data of different conductivity patterns are presented.
IPDO-2007 - Inverse Problems, Design and Optimization Symposium
2007-12-01
TRANSDUCER 107 INVERSE APPROACHES TO DRYING OF SLICED FOODS 509 108 INVERSE APPROACHES IN IMPROVEMENT OF AIR POLUTION PLUME DISPERSION MODELS FOR... Air Force Office of Scientific Research Optimization & Discrete Mathematics / NL Suite 325, Room 3112 875 Randolph Street Arlington, VA 22203-1768 11...G.S., Orlande, H.R.B., Tanaka, M. and Colaco, M.J.), Miami Beach, FL, April 16-18, 2007. 5. Inverse Approaches in Improvement of Air Pollution Plume
Explicit Solutions for a Class of Nonlinear PDE that Arise in Allocation Problems
2006-05-12
approximations for allocation and occupancy problems one must solve a deterministic optimal control problem (or equiv- alently, a calculus of variations...to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 12 MAY 2006 2. REPORT TYPE 3...significant underlying simplification. In the first example it is the fact that the value function for the control problem is expected to be quadratic
Solvability of certain inverse problems for the nonstationary kinetic transport equation
NASA Astrophysics Data System (ADS)
Volkov, N. P.
2016-09-01
Linear and nonlinear inverse problems for the nonstationary multispeed anisotropic kinetic transport equation are studied. Sufficient conditions for the existence and uniqueness of weak solutions to these problems in various function spaces are found. The proofs of the corresponding theorems imply that solutions of the inverse problems under study can be obtained by applying the method of successive approximations.
Inverse problems of combined photoacoustic and optical coherence tomography
NASA Astrophysics Data System (ADS)
Elbau, Peter; Mindrinos, Leonidas; Scherzer, Otmar
2017-02-01
Optical coherence tomography (OCT) and photoacoustic tomography (PAT) are emerging non-invasive biological and medical imaging techniques. It is a recent trend in experimental science to design experiments that perform PAT and OCT imaging at once. In this paper we present a mathematical model describing the dual experiment. Since OCT is mathematically modelled by Maxwell's equations or some simplifications of it, whereas the light propagation in quantitative photoacoustics is modelled by (simplifications of) the radiative transfer equation, the first step in the derivation of a mathematical model of the dual experiment is to obtain a unified mathematical description, which in our case are Maxwell's equations. As a by-product we therefore derive a new mathematical model of photoacoustic tomography based on Maxwell's equations. It is well known by now, that without additional assumptions on the medium, it is not possible to uniquely reconstruct all optical parameters from either one of these modalities alone. We show that in the combined approach one has additional information, compared to a single modality, and the inverse problem of reconstruction of the optical parameters becomes feasible.
Solving Inverse Detection Problems Using Passive Radiation Signatures
Favorite, Jeffrey A.; Armstrong, Jerawan C.; Vaquer, Pablo A.
2012-08-15
The ability to reconstruct an unknown radioactive object based on its passive gamma-ray and neutron signatures is very important in homeland security applications. Often in the analysis of unknown radioactive objects, for simplicity or speed or because there is no other information, they are modeled as spherically symmetric regardless of their actual geometry. In these presentation we discuss the accuracy and implications of this approximation for decay gamma rays and for neutron-induced gamma rays. We discuss an extension of spherical raytracing (for uncollided fluxes) that allows it to be used when the exterior shielding is flat or cylindrical. We revisit some early results in boundary perturbation theory, showing that the Roussopolos estimate is the correct one to use when the quantity of interest is the flux or leakage on the boundary. We apply boundary perturbation theory to problems in which spherically symmetric systems are perturbed in asymmetric nonspherical ways. We apply mesh adaptive direct search (MADS) algorithms to object reconstructions. We present a benchmark test set that may be used to quantitatively evaluate inverse detection methods.
Inverse modeling for heat conduction problem in human abdominal phantom.
Huang, Ming; Chen, Wenxi
2011-01-01
Noninvasive methods for deep body temperature measurement are based on the principle of heat equilibrium between the thermal sensor and the target location theoretically. However, the measurement position is not able to be definitely determined. In this study, a 2-dimensional mathematical model was built based upon some assumptions for the physiological condition of the human abdomen phantom. We evaluated the feasibility in estimating the internal organs temperature distribution from the readings of the temperature sensors arranged on the skin surface. It is a typical inverse heat conduction problem (IHCP), and is usually mathematically ill-posed. In this study, by integrating some physical and physiological a-priori information, we invoked the quasi-linear (QL) method to reconstruct the internal temperature distribution. The solutions of this method were improved by increasing the accuracy of the sensors and adjusting their arrangement on the outer surface, and eventually reached the state of converging at the best state accurately. This study suggests that QL method is able to reconstruct the internal temperature distribution in this phantom and might be worthy of a further study in an anatomical based model.
Beamforming through regularized inverse problems in ultrasound medical imaging.
Szasz, Teodora; Basarab, Adrian; Kouame, Denis
2016-09-13
Beamforming in ultrasound imaging has significant impact on the quality of the final image, controlling its resolution and contrast. Despite its low spatial resolution and contrast, delay-and-sum is still extensively used nowadays in clinical applications, due to its real-time capabilities. The most common alternatives are minimum variance method and its variants, which overcome the drawbacks of delay-and-sum, at the cost of higher computational complexity that limits its utilization in real-time applications. In this paper, we propose to perform beamforming in ultrasound imaging through a regularized inverse problem based on a linear model relating the reflected echoes to the signal to be recovered. Our approach presents two major advantages: i) its flexibility in the choice of statistical assumptions on the signal to be beamformed (Laplacian and Gaussian statistics are tested herein) and ii) its robustness to a reduced number of pulse emissions. The proposed framework is flexible and allows for choosing the right trade-off between noise suppression and sharpness of the resulted image. We illustrate the performance of our approach on both simulated and experimental data, with in vivo examples of carotid and thyroid. Compared to delay-and-sum, minimimum variance and two other recently published beamforming techniques, our method offers better spatial resolution, respectively contrast, when using Laplacian and Gaussian priors.
Bayesian Genomic-Enabled Prediction as an Inverse Problem
Cuevas, Jaime; Pérez-Elizalde, Sergio; Soberanis, Victor; Pérez-Rodríguez, Paulino; Gianola, Daniel; Crossa, José
2014-01-01
Genomic-enabled prediction in plant and animal breeding has become an active area of research. Many prediction models address the collinearity that arises when the number (p) of molecular markers (e.g. single-nucleotide polymorphisms) is larger than the sample size (n). Here we propose four Bayesian approaches to the problem based on commonly used data reduction methods. Specifically, we use a Gaussian linear model for an orthogonal transformation of both the observed data and the matrix of molecular markers. Because shrinkage of estimates is affected by the prior variance of transformed effects, we propose four structures of the prior variance as a way of potentially increasing the prediction accuracy of the models fitted. To evaluate our methods, maize and wheat data previously used with standard Bayesian regression models were employed for measuring prediction accuracy using the proposed models. Results indicate that, for the maize and wheat data sets, our Bayesian models yielded, on average, a prediction accuracy that is 3% greater than that of standard Bayesian regression models, with less computational effort. PMID:25155273
Bayesian genomic-enabled prediction as an inverse problem.
Cuevas, Jaime; Pérez-Elizalde, Sergio; Soberanis, Victor; Pérez-Rodríguez, Paulino; Gianola, Daniel; Crossa, José
2014-08-25
Genomic-enabled prediction in plant and animal breeding has become an active area of research. Many prediction models address the collinearity that arises when the number (p) of molecular markers (e.g. single-nucleotide polymorphisms) is larger than the sample size (n). Here we propose four Bayesian approaches to the problem based on commonly used data reduction methods. Specifically, we use a Gaussian linear model for an orthogonal transformation of both the observed data and the matrix of molecular markers. Because shrinkage of estimates is affected by the prior variance of transformed effects, we propose four structures of the prior variance as a way of potentially increasing the prediction accuracy of the models fitted. To evaluate our methods, maize and wheat data previously used with standard Bayesian regression models were employed for measuring prediction accuracy using the proposed models. Results indicate that, for the maize and wheat data sets, our Bayesian models yielded, on average, a prediction accuracy that is 3% greater than that of standard Bayesian regression models, with less computational effort.
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
Butler, T.; Graham, L.; Estep, D.; Westerink, J.J.
2015-01-01
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. PMID:25937695
Numerical methods for problems involving the Drazin inverse
NASA Technical Reports Server (NTRS)
Meyer, C. D., Jr.
1979-01-01
The objective was to try to develop a useful numerical algorithm for the Drazin inverse and to analyze the numerical aspects of the applications of the Drazin inverse relating to the study of homogeneous Markov chains and systems of linear differential equations with singular coefficient matrices. It is felt that all objectives were accomplished with a measurable degree of success.
Children's strategies to solving additive inverse problems: a preliminary analysis
NASA Astrophysics Data System (ADS)
Ding, Meixia; Auxter, Abbey E.
2017-03-01
Prior studies show that elementary school children generally "lack" formal understanding of inverse relations. This study goes beyond lack to explore what children might "have" in their existing conception. A total of 281 students, kindergarten to third grade, were recruited to respond to a questionnaire that involved both contextual and non-contextual tasks on inverse relations, requiring both computational and explanatory skills. Results showed that children demonstrated better performance in computation than explanation. However, many students' explanations indicated that they did not necessarily utilize inverse relations for computation. Rather, they appeared to possess partial understanding, as evidenced by their use of part-whole structure, which is a key to understanding inverse relations. A close inspection of children's solution strategies further revealed that the sophistication of children's conception of part-whole structure varied in representation use and unknown quantity recognition, which suggests rich opportunities to develop students' understanding of inverse relations in lower elementary classrooms.
Children's strategies to solving additive inverse problems: a preliminary analysis
NASA Astrophysics Data System (ADS)
Ding, Meixia; Auxter, Abbey E.
2017-01-01
Prior studies show that elementary school children generally "lack" formal understanding of inverse relations. This study goes beyond lack to explore what children might "have" in their existing conception. A total of 281 students, kindergarten to third grade, were recruited to respond to a questionnaire that involved both contextual and non-contextual tasks on inverse relations, requiring both computational and explanatory skills. Results showed that children demonstrated better performance in computation than explanation. However, many students' explanations indicated that they did not necessarily utilize inverse relations for computation. Rather, they appeared to possess partial understanding, as evidenced by their use of part-whole structure, which is a key to understanding inverse relations. A close inspection of children's solution strategies further revealed that the sophistication of children's conception of part-whole structure varied in representation use and unknown quantity recognition, which suggests rich opportunities to develop students' understanding of inverse relations in lower elementary classrooms.
New optimization problems arising in modelling of 2D-crystal lattices
NASA Astrophysics Data System (ADS)
Evtushenko, Yury; Lurie, Sergey; Posypkin, Mikhail
2016-10-01
The paper considers the problem of finding the structure of a fragment of two-dimensional crystal lattice with the minimal energy. Atoms in a lattice reside on parallel lines (layers). The interatomic distances are the same within one layer but can differ for distinct layers. The energy of the piece of material is computed using so-called potential functions. We used Lennard-Jones, Morse and Tersoff potentials. The proposed formulation can serve as a scalable complex non-smooth optimization test. The paper evaluates various optimization techniques for the problem under consideration, compares their performances and draws the conclusion about the best choice of optimization methods for the problem under test. As a result we were able to locate minima meaningful from the physical point of view, e.g. reproducing graphene lattice.
IPDO-2007: Inverse Problems, Design and Optimization Symposium
2007-08-01
108 INVERSE APPROACHES IN IMPROVEMENT OF AIR POLUTION PLUME DISPERSION MODELS FOR REGULATORY APPLICATIONS 517 109 USING OF THE IOSO NM SOFTWARE FOR...Dulikravich, G.S., Orlande, H.R.B., Tanaka, M. and Colaco, M.J.), Miami Beach, FL, April 16-18, 2007. 5. Inverse Approaches in Improvement of Air Pollution...A. Woodbury (USA) Prof. Anatoly G. Yagola (Russia) 5.4 SPONSORS AND PROMOTERS OF IPDO-2007 AFOSR/Numerical Mathematics (United States Air Force
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems
Marzouk, Youssef M. Najm, Habib N.
2009-04-01
We consider a Bayesian approach to nonlinear inverse problems in which the unknown quantity is a spatial or temporal field, endowed with a hierarchical Gaussian process prior. Computational challenges in this construction arise from the need for repeated evaluations of the forward model (e.g., in the context of Markov chain Monte Carlo) and are compounded by high dimensionality of the posterior. We address these challenges by introducing truncated Karhunen-Loeve expansions, based on the prior distribution, to efficiently parameterize the unknown field and to specify a stochastic forward problem whose solution captures that of the deterministic forward model over the support of the prior. We seek a solution of this problem using Galerkin projection on a polynomial chaos basis, and use the solution to construct a reduced-dimensionality surrogate posterior density that is inexpensive to evaluate. We demonstrate the formulation on a transient diffusion equation with prescribed source terms, inferring the spatially-varying diffusivity of the medium from limited and noisy data.
A variational Bayesian approach for inverse problems with skew-t error distributions
NASA Astrophysics Data System (ADS)
Guha, Nilabja; Wu, Xiaoqing; Efendiev, Yalchin; Jin, Bangti; Mallick, Bani K.
2015-11-01
In this work, we develop a novel robust Bayesian approach to inverse problems with data errors following a skew-t distribution. A hierarchical Bayesian model is developed in the inverse problem setup. The Bayesian approach contains a natural mechanism for regularization in the form of a prior distribution, and a LASSO type prior distribution is used to strongly induce sparseness. We propose a variational type algorithm by minimizing the Kullback-Leibler divergence between the true posterior distribution and a separable approximation. The proposed method is illustrated on several two-dimensional linear and nonlinear inverse problems, e.g. Cauchy problem and permeability estimation problem.
Reinforcement learning solution for HJB equation arising in constrained optimal control problem.
Luo, Biao; Wu, Huai-Ning; Huang, Tingwen; Liu, Derong
2015-11-01
The constrained optimal control problem depends on the solution of the complicated Hamilton-Jacobi-Bellman equation (HJBE). In this paper, a data-based off-policy reinforcement learning (RL) method is proposed, which learns the solution of the HJBE and the optimal control policy from real system data. One important feature of the off-policy RL is that its policy evaluation can be realized with data generated by other behavior policies, not necessarily the target policy, which solves the insufficient exploration problem. The convergence of the off-policy RL is proved by demonstrating its equivalence to the successive approximation approach. Its implementation procedure is based on the actor-critic neural networks structure, where the function approximation is conducted with linearly independent basis functions. Subsequently, the convergence of the implementation procedure with function approximation is also proved. Finally, its effectiveness is verified through computer simulations.
An optimal control problem arising from a dengue disease transmission model.
Aldila, Dipo; Götz, Thomas; Soewono, Edy
2013-03-01
An optimal control problem for a host-vector Dengue transmission model is discussed here. In the model, treatments with mosquito repellent are given to adults and children and those who undergo treatment are classified in treated compartments. With this classification, the model consists of 11 dynamic equations. The basic reproductive ratio that represents the epidemic indicator is obtained from the largest eigenvalue of the next generation matrix. The optimal control problem is designed with four control parameters, namely the treatment rates for children and adult compartments, and the drop-out rates from both compartments. The cost functional accounts for the total number of the infected persons, the cost of the treatment, and the cost related to reducing the drop-out rates. Numerical results for the optimal controls and the related dynamics are shown for the case of epidemic prevention and outbreak reduction strategies.
On complex roots of an equation arising in the oblique derivative problem
NASA Astrophysics Data System (ADS)
Kostin, A. B.; Sherstyukov, V. B.
2017-01-01
The paper is concerned with the eigenvalue problem for the Laplace operator in a disc under the condition that the oblique derivative vanishes on the disc boundary. In a famous article by V.A. Il’in and E.I. Moiseev (Differential equations, 1994) it was found, in particular, that the root of any equation of the form with the Bessel function Jn (μ) determines the eigenvalue λ = μ 2 of the problem. In our work we correct the information about the location of eigenvalues. It is specified explicit view of the corner, containing all the eigenvalues. It is shown that all the nonzero roots of the equation are simple and given a refined description of the set of their localization on the complex plane. To prove these facts we use the partial differential equations methods and also methods of entire functions theory.
NASA Astrophysics Data System (ADS)
Beretta, Elena; de Hoop, Maarten V.; Francini, Elisa; Vessella, Sergio; Zhai, Jian
2017-03-01
We consider the inverse problem of determining the Lamé parameters and the density of a three-dimensional elastic body from the local time-harmonic Dirichlet-to-Neumann map. We prove uniqueness and Lipschitz stability of this inverse problem when the Lamé parameters and the density are assumed to be piecewise constant on a given domain partition.
Application of spectral Lanczos decomposition method to large scale problems arising geophysics
Tamarchenko, T.
1996-12-31
This paper presents an application of Spectral Lanczos Decomposition Method (SLDM) to numerical modeling of electromagnetic diffusion and elastic waves propagation in inhomogeneous media. SLDM approximates an action of a matrix function as a linear combination of basis vectors in Krylov subspace. I applied the method to model electromagnetic fields in three-dimensions and elastic waves in two dimensions. The finite-difference approximation of the spatial part of differential operator reduces the initial boundary-value problem to a system of ordinary differential equations with respect to time. The solution to this system requires calculating exponential and sine/cosine functions of the stiffness matrices. Large scale numerical examples are in a good agreement with the theoretical error bounds and stability estimates given by Druskin, Knizhnerman, 1987.
Approximate Series Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology
2014-01-01
We introduce an efficient recursive scheme based on Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems. This approach is based on a modification of the ADM; here we use all the boundary conditions to derive an integral equation before establishing the recursive scheme for the solution components. In fact, we develop the recursive scheme without any undetermined coefficients while computing the solution components. Unlike the classical ADM, the proposed method avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients. The approximate solution is obtained in the form of series with easily calculable components. The uniqueness of the solution is discussed. The convergence and error analysis of the proposed method are also established. The accuracy and reliability of the proposed method are examined by four numerical examples. PMID:24707221
Model error estimation and correction by solving a inverse problem
NASA Astrophysics Data System (ADS)
Xue, Haile
2016-04-01
Nowadays, the weather forecasts and climate predictions are increasingly relied on numerical models. Yet, errors inevitably exist in model due to the imperfect numeric and parameterizations. From the practical point of view, model correction is an efficient strategy. Despite of the different complexity of forecast error correction algorithms, the general idea is to estimate the forecast errors by considering the NWP as a direct problem. Chou (1974) suggested an alternative view by considering the NWP as an inverse problem. The model error tendency term (ME) due to the model deficiency is assumed as an unknown term in NWP model, which can be discretized into short intervals (for example 6 hour) and considered as a constant or linear form in each interval. Given the past re-analyses and NWP model, the discretized MEs in the past intervals can be solved iteratively as a constant or linear-increased tendency term in each interval. These MEs can be further used as the online corrections. In this study, an iterative method for obtaining the MEs in past intervals was presented, and its convergence had been confirmed with sets of experiments in the global forecast system of the Global and Regional Assimilation and Prediction System (GRAPES-GFS) for July-August (JA) 2009 and January-February (JF) 2010. Then these MEs were used to get online model corretions based of systematic errors of GRAPES-GFS for July 2009 and January 2010. The data sets associated with initial condition and sea surface temperature (SST) used in this study are both based on NCEP final (FNL) data. According to the iterative numerical experiments, the following key conclusions can be drawn:(1) Batches of iteration test results indicated that the hour 6 forecast errors were reduced to 10% of their original value after 20 steps of iteration.(2) By offlinely comparing the error corrections estimated by MEs to the mean forecast errors, the patterns of estimated errors were considered to agree well with those
NASA Astrophysics Data System (ADS)
Senses, Begum
A state-defect constraint pairing graph coarsening method is described for improving computational efficiency during the numerical factorization of large sparse Karush-Kuhn-Tucker matrices that arise from the discretization of optimal control problems via a Legendre-Gauss-Radau orthogonal collocation method. The method takes advantage of the particular sparse structure of the Karush-Kuhn-Tucker matrix that arises from the orthogonal collocation method. The state-defect constraint pairing graph coarsening method pairs each component of the state with its corresponding defect constraint and forces paired rows to be adjacent in the reordered Karush-Kuhn-Tucker matrix. Aggregate state-defect constraint pairing results are presented using a wide variety of benchmark optimal control problems where it is found that the proposed state-defect constraint pairing graph coarsening method significantly reduces both the number of delayed pivots and the number of floating point operations and increases the computational efficiency by performing more floating point operations per unit time. It is then shown that the state-defect constraint pairing graph coarsening method is less effective on Karush-Kuhn-Tucker matrices arising from Legendre-Gauss-Radau collocation when the optimal control problem contains state and control equality path constraints because such matrices may have delayed pivots that correspond to both defect and path constraints. An unweighted alternate graph coarsening method that employs maximal matching and a weighted alternate graph coarsening method that employs Hungarian algorithm on a weighting matrix are then used to attempt to further reduce the number of delayed pivots. It is found, however, that these alternate graph coarsening methods provide no further advantage over the state-defect constraint pairing graph coarsening method.
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.
[Anaesthetic problems arising during the surgical correction of scoliosis (harrington chnique].
Hack, G; Schraudebach, T; Rommelsheim, K; Freiberger, K U; Picht, U
1976-04-01
Anaesthesia for the surgical correction of scoliosis with the Harrington technique carries serious risks on account of the impaired cardiac and pulmonary function, the length of the operation, the area involved and the post-operative problems. Based on the experience gained in 32 young persons who had this operation the anaesthetic procedure for these cases is described: it comprises detailted pre- operative examination of cardiac and pulmonary function, continuous monitoring during the operation, a careful technique that takes into account the massive blood loss and stress associated with the operation, a careful technique that takes into account the massive blood loss and stress associated with the operation and close surveillance during the post-operative stage. Controlled hypotension (60 mm Hg) succeeded in reducing the blood loss during operation to 2,500 ml, compared with 4,500 ml without hypotension. If the pre-0perative examinations have established adequate cardiac function, if surgeon and anaesthetist work in close collaboration and if the heart action, pulse, arterial and venous pressure (catheter) and body temperature are continuously monitored, then controlled hypotension offers a means to reduce the, generally massive, blood loss during the surgical correction of scoliosis.
Global solution to a hyperbolic problem arising in the modeling of blood flow in circulatory systems
NASA Astrophysics Data System (ADS)
Ruan, Weihua; Clark, M. E.; Zhao, Meide; Curcio, Anthony
2007-07-01
This paper considers a system of first-order, hyperbolic, partial differential equations in the domain of a one-dimensional network. The system models the blood flow in human circulatory systems as an initial-boundary-value problem with boundary conditions of either algebraic or differential type. The differential equations are nonhomogeneous with frictional damping terms and the state variables are coupled at internal junctions. The existence and uniqueness of the local classical solution have been established in our earlier work [W. Ruan, M.E. Clark, M. Zhao, A. Curcio, A hyperbolic system of equations of blood flow in an arterial network, J. Appl. Math. 64 (2) (2003) 637-667; W. Ruan, M.E. Clark, M. Zhao, A. Curcio, Blood flow in a network, Nonlinear Anal. Real World Appl. 5 (2004) 463-485; W. Ruan, M.E. Clark, M. Zhao, A. Curcio, A quasilinear hyperbolic system that models blood flow in a network, in: Charles V. Benton (Ed.), Focus on Mathematical Physics Research, Nova Science Publishers, Inc., New York, 2004, pp. 203-230]. This paper continues the analysis and gives sufficient conditions for the global existence of the classical solution. We prove that the solution exists globally if the boundary data satisfy the dissipative condition (2.3) or (3.2), and the norms of the initial and forcing functions in a certain Sobolev space are sufficiently small. This is only the first step toward establishing the global existence of the solution to physiologically realistic models, because, in general, the chosen dissipative conditions (2.3) and (3.2) do not appear to hold for the originally proposed boundary conditions (1.3)-(1.12).
ERIC Educational Resources Information Center
Brown, Malcolm
2009-01-01
Inversions are fascinating phenomena. They are reversals of the normal or expected order. They occur across a wide variety of contexts. What do inversions have to do with learning spaces? The author suggests that they are a useful metaphor for the process that is unfolding in higher education with respect to education. On the basis of…
Solution of an inverse scattering problem for the acoustic wave equation in three-dimensional media
NASA Astrophysics Data System (ADS)
Baev, A. V.
2016-12-01
A three-dimensional inverse scattering problem for the acoustic wave equation is studied. The task is to determine the density and acoustic impedance of a medium. A necessary and sufficient condition for the unique solvability of this problem is established in the form of an energy conservation law. The interpretation of the solution to the inverse problem and the construction of medium images are discussed.
A boundary integral method for an inverse problem in thermal imaging
NASA Technical Reports Server (NTRS)
Bryan, Kurt
1992-01-01
An inverse problem in thermal imaging involving the recovery of a void in a material from its surface temperature response to external heating is examined. Uniqueness and continuous dependence results for the inverse problem are demonstrated, and a numerical method for its solution is developed. This method is based on an optimization approach, coupled with a boundary integral equation formulation of the forward heat conduction problem. Some convergence results for the method are proved, and several examples are presented using computationally generated data.
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.
2010-03-12
denotes the state, c the speed of sound, a viscous dissipation, and S the source term. If all variables are time- harmonic with a fixed angular...for the 2008 Gordon Bell Prize. • PI Ghattas gave the keynote talk at the 10th LCI International Conference on High- Performance Clustered Computing...diagonal of the inverse, adaptivity, and integration of all of these components within a particle filter methodology. In addition, our
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.
The Inverse Source Problem for Maxwell’s Equations
2006-10-01
if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YYYY) 2. REPORT...currents from surface electroencephalographic measurements. The application is to prosthesis control . 15. SUBJECT TERMS INVERSE, MAXWELL...measurements could be used to diagnose abnormalities in the brain and also to allow the control of prosthetic limbs. From the point of view of mathematical
Adapting a truly nonlinear filter to the ocean acoustic inverse problem
NASA Astrophysics Data System (ADS)
Ganse, Andrew A.; Odom, Robert I.
2005-04-01
Nonlinear inverse problems including the ocean acoustic problem have been solved by Monte Carlo, locally-linear, and filter based techniques such as the Extended Kalman Filter (EKF). While these techniques do provide statistical information about the solution (e.g., mean and variance), each suffers from inherent limitations in their approach to nonlinear problems. Monte Carlo techniques are expensive to compute and do not contribute to intuitive interpretation of a problem, and locally-linear techniques (including the EKF) are limited by the multimodal objective landscape of nonlinear problems. A truly nonlinear filter, based on recent work in nonlinear tracking, estimates state information for a nonlinear problem in continual measurement updates and is adapted to solving nonlinear inverse problems. Additional terms derived from the system's state PDF are added to the mean and covariance of the solution to address the nonlinearities of the problem, and overall the technique offers improved performance in nonlinear inversion. [Work supported by ONR.
Collage-based approaches for elliptic partial differential equations inverse problems
NASA Astrophysics Data System (ADS)
Yodzis, Michael; Kunze, Herb
2017-01-01
The collage method for inverse problems has become well-established in the literature in recent years. Initial work developed a collage theorem, based upon Banach's fixed point theorem, for treating inverse problems for ordinary differential equations (ODEs). Amongst the subsequent work was a generalized collage theorem, based upon the Lax-Milgram representation theorem, useful for treating inverse problems for elliptic partial differential equations (PDEs). Each of these two different approaches can be applied to elliptic PDEs in one space dimension. In this paper, we explore and compare how the two different approaches perform for the estimation of the diffusivity for a steady-state heat equation.
Yu, Guoshen; Sapiro, Guillermo; Mallat, Stéphane
2012-05-01
A general framework for solving image inverse problems with piecewise linear estimations is introduced in this paper. The approach is based on Gaussian mixture models, which are estimated via a maximum a posteriori expectation-maximization algorithm. A dual mathematical interpretation of the proposed framework with a structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared with traditional sparse inverse problem techniques. We demonstrate that, in a number of image inverse problems, including interpolation, zooming, and deblurring of narrow kernels, the same simple and computationally efficient algorithm yields results in the same ballpark as that of the state of the art.
A unified approach to the helioseismic forward and inverse problems of differential rotation
NASA Technical Reports Server (NTRS)
Ritzwoller, Michael H.; Lavely, Eugene M.
1991-01-01
A general, degenerate perturbation theoretic treatment of the helioseismic forward and inverse problem for solar differential rotation is presented. For the forward problem, differential rotation is represented as the axisymmetric component of a general toroidal flow field using velocity spherical harmonics. This approach allows each degree of differential rotation to be estimated independently from all other degrees. In the inverse problem, the splitting caused by differential rotation is expressed as an expansion in a set of orthonormal polynomials that are intimately related to the solution of the forward problem. The combined use of vector spherical harmonics as basis functions for differential ratio and the Clebsch-Gordon coefficients to represent splitting provides a unified approach to the forward and inverse problems of differential rotation which greatly simplify inversion.
Application of Lead Field Theory and Computerized Thorax Modeling for the ECG Inverse Problem
2007-11-02
Takano, P. Laarne, J. Malmivuo Ragnar Granit Institute, Tampere University of Technology, Finland Abstract – The ECG inverse problem is a...Performing Organization Name(s) and Address(es) Ragnar Granit Institute, Tampere University of Technology, Finland Performing Organization Report Number...computational load for calculating ECG inverse solutions. ACKNOWLEDGMENTS This work has been kindly supported by The Ragnar Granit Foundation, The
NASA Astrophysics Data System (ADS)
Corrado, Cesare; Gerbeau, Jean-Frédéric; Moireau, Philippe
2015-02-01
This work addresses the inverse problem of electrocardiography from a new perspective, by combining electrical and mechanical measurements. Our strategy relies on the definition of a model of the electromechanical contraction which is registered on ECG data but also on measured mechanical displacements of the heart tissue typically extracted from medical images. In this respect, we establish in this work the convergence of a sequential estimator which combines for such coupled problems various state of the art sequential data assimilation methods in a unified consistent and efficient framework. Indeed, we aggregate a Luenberger observer for the mechanical state and a Reduced-Order Unscented Kalman Filter applied on the parameters to be identified and a POD projection of the electrical state. Then using synthetic data we show the benefits of our approach for the estimation of the electrical state of the ventricles along the heart beat compared with more classical strategies which only consider an electrophysiological model with ECG measurements. Our numerical results actually show that the mechanical measurements improve the identifiability of the electrical problem allowing to reconstruct the electrical state of the coupled system more precisely. Therefore, this work is intended to be a first proof of concept, with theoretical justifications and numerical investigations, of the advantage of using available multi-modal observations for the estimation and identification of an electromechanical model of the heart.
Hemmelmayr, Vera C; Cordeau, Jean-François; Crainic, Teodor Gabriel
2012-12-01
In this paper, we propose an adaptive large neighborhood search heuristic for the Two-Echelon Vehicle Routing Problem (2E-VRP) and the Location Routing Problem (LRP). The 2E-VRP arises in two-level transportation systems such as those encountered in the context of city logistics. In such systems, freight arrives at a major terminal and is shipped through intermediate satellite facilities to the final customers. The LRP can be seen as a special case of the 2E-VRP in which vehicle routing is performed only at the second level. We have developed new neighborhood search operators by exploiting the structure of the two problem classes considered and have also adapted existing operators from the literature. The operators are used in a hierarchical scheme reflecting the multi-level nature of the problem. Computational experiments conducted on several sets of instances from the literature show that our algorithm outperforms existing solution methods for the 2E-VRP and achieves excellent results on the LRP.
Hemmelmayr, Vera C.; Cordeau, Jean-François; Crainic, Teodor Gabriel
2012-01-01
In this paper, we propose an adaptive large neighborhood search heuristic for the Two-Echelon Vehicle Routing Problem (2E-VRP) and the Location Routing Problem (LRP). The 2E-VRP arises in two-level transportation systems such as those encountered in the context of city logistics. In such systems, freight arrives at a major terminal and is shipped through intermediate satellite facilities to the final customers. The LRP can be seen as a special case of the 2E-VRP in which vehicle routing is performed only at the second level. We have developed new neighborhood search operators by exploiting the structure of the two problem classes considered and have also adapted existing operators from the literature. The operators are used in a hierarchical scheme reflecting the multi-level nature of the problem. Computational experiments conducted on several sets of instances from the literature show that our algorithm outperforms existing solution methods for the 2E-VRP and achieves excellent results on the LRP. PMID:23483764
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
Comparing hard and soft prior bounds in geophysical inverse problems
NASA Technical Reports Server (NTRS)
Backus, George E.
1987-01-01
In linear inversion of a finite-dimensional data vector y to estimate a finite-dimensional prediction vector z, prior information about X sub E is essential if y is to supply useful limits for z. The one exception occurs when all the prediction functionals are linear combinations of the data functionals. Two forms of prior information are compared: a soft bound on X sub E is a probability distribution p sub x on X which describeds the observer's opinion about where X sub E is likely to be in X; a hard bound on X sub E is an inequality Q sub x(X sub E, X sub E) is equal to or less than 1, where Q sub x is a positive definite quadratic form on X. A hard bound Q sub x can be softened to many different probability distributions p sub x, but all these p sub x's carry much new information about X sub E which is absent from Q sub x, and some information which contradicts Q sub x. Both stochastic inversion (SI) and Bayesian inference (BI) estimate z from y and a soft prior bound p sub x. If that probability distribution was obtained by softening a hard prior bound Q sub x, rather than by objective statistical inference independent of y, then p sub x contains so much unsupported new information absent from Q sub x that conclusions about z obtained with SI or BI would seen to be suspect.
NASA Astrophysics Data System (ADS)
Klibanov, Michael V.; Romanov, Vladimir G.
2016-01-01
The 3D inverse scattering problem of the reconstruction of the unknown dielectric permittivity in the generalized Helmholtz equation is considered. Applications are in imaging of nanostructures and biological cells. The main difference with the conventional inverse scattering problems is that only the modulus of the scattering wave field is measured. The phase is not measured. The initializing wave field is the incident plane wave. On the other hand, in the previous recent works of the authors about the ‘phaseless topic’ the case of the point source was considered (Klibanov and Romanov 2015 J. Inverse Ill-Posed Problem 23 415-28 J. Inverse Ill-Posed Problem 23 187-93). Two reconstruction procedures are developed.
Uniqueness and stability for the inverse medium problem with internal data
NASA Astrophysics Data System (ADS)
Triki, Faouzi
2010-09-01
In this paper we study the inverse medium problem with internal data. We show that knowledge of one real internal data uniquely determines the medium. A local Lipschitz stability of the reconstruction is also derived.
The numerical solution of the boundary inverse problem for a parabolic equation
NASA Astrophysics Data System (ADS)
Vasil'ev, V. V.; Vasilyeva, M. V.; Kardashevsky, A. M.
2016-10-01
Boundary inverse problems occupy an important place among the inverse problems of mathematical physics. They are connected with the problems of diagnosis, when additional measurements on one of the borders or inside the computational domain are necessary to restore the boundary regime in the other border, inaccessible to direct measurements. The boundary inverse problems belong to a class of conditionally correct problems, and therefore, their numerical solution requires the development of special computational algorithms. The paper deals with the solution of the boundary inverse problem for one-dimensional second-order parabolic equations, consisting in the restoration of boundary regime according to measurements inside the computational domain. For the numerical solution of the inverse problem it is proposed to use an analogue of a computational algorithm, proposed and developed to meet the challenges of identification of the right side of the parabolic equations in the works P.N.Vabishchevich and his students based on a special decomposition of solving the problem at each temporal layer. We present and discuss the results of a computational experiment conducted on model problems with quasi-solutions, including with random errors in the input data.
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.
Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Haq, Ihsanul
2014-01-01
We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE) and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA), interior point algorithm (IPA), and active set algorithm (ASA). The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions.
Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Haq, Ihsanul
2014-01-01
We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE) and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA), interior point algorithm (IPA), and active set algorithm (ASA). The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions. PMID:24672381
The Use of Reciprocity in Atmospheric Source Inversion Problems
Nitao, J J
2004-10-13
The goal of the Event Reconstruction Project is to find the location and strength of atmospheric release points, both stationary and moving. Source inversion relies on observational data as input. The methodology is sufficiently general to allow various forms of data. In this report, the authors will focus primarily on concentration measurements obtained at point monitoring locations at various times. The algorithms being investigated in the Project are the MCMC (Markov Chain Monte Carlo), SMC (Sequential Monte Carlo) Methods, classical inversion methods, and hybrids of these. They refer the reader to the report by Johannesson et al. (2004) for explanations of these methods. These methods require computing the concentrations at all monitoring locations for a given ''proposed'' source characteristic (locations and strength history). It is anticipated that the largest portion of the CPU time will take place performing this computation. MCMC and SMC will require this computation to be done at least tens of thousands of times. Therefore, an efficient means of computing forward model predictions is important to making the inversion practical. In this report they show how Green's functions and reciprocal Green's functions can significantly accelerate forward model computations. First, instead of computing a plume for each possible source strength history, they can compute plumes from unit impulse sources only. By using linear superposition, they can obtain the response for any strength history. This response is given by the forward Green's function. Second, they may use the law of reciprocity. Suppose that they require the concentration at a single monitoring point x{sub m} due to a potential (unit impulse) source that is located at x{sub s}. instead of computing a plume with source location x{sub s}, they compute a ''reciprocal plume'' whose (unit impulse) source is at the monitoring locations x{sub m}. The reciprocal plume is computed using a reversed-direction wind
Proximal point methods for the inverse problem of identifying parameters in beam models
NASA Astrophysics Data System (ADS)
Jadamba, B.; Khan, A. A.; Paulhamus, M.; Sama, M.
2012-07-01
This paper studies the nonlinear inverse problem of identifying certain material parameters in the fourth-order boundary value problem representing the beam model. The inverse problem is solved by posing a convex optimization problem whose solution is an approximation of the sought parameters. The optimization problem is solved by the gradient based approaches, and in this setting, the most challenging aspect is the computation of the gradient of the objective functional. We present a detailed treatment of the adjoint stiffness matrix based approach for the gradient computation. We employ recently proposed self-adaptive inexact proximal point methods by Hager and Zhang [6] to solve the inverse problem. It is known that the regularization features of the proximal point methods are quite different from that of the Tikhonov regularization. We present a comparative analysis of the numerical efficiency of the used proximal point methods without using the Tikhonov regularization.
Sedimentary Facies Analysis Using AVIRIS Data: A Geophysical Inverse Problem
NASA Technical Reports Server (NTRS)
Boardmann, Joe W.; Goetz, Alexander F. H.
1990-01-01
AVIRIS data can be used to quantitatively analyze and map sedimentary lithofacies. The observed radiance spectra can be reduced to 'apparent reflectance' spectra by topographic and reflectance characterization of several field sites within the image. These apparent reflectance spectra correspond to the true reflectance at each pixel, multiplied by an unknown illumination factor (ranging in value from zero to one). The spatial abundance patterns of spectrally defined lithofacies and the unknown illumination factors can be simultaneously derived using constrained linear spectral unmixing methods. Estimates of the minimum uncertainty in the final results (due to noise, instrument resolutions, degree of illumination and mixing systematics) can be made by forward and inverse modeling. Specific facies studies in the Rattlesnake Hills region of Wyoming illustrate the successful application of these methods.
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
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
Computational experiment on the numerical solution of some inverse problems of mathematical physics
NASA Astrophysics Data System (ADS)
Vasil'ev, V. I.; Kardashevsky, A. M.; Sivtsev, PV
2016-11-01
In this article the computational experiment on the numerical solution of the most popular linear inverse problems for equations of mathematical physics are presented. The discretization of retrospective inverse problem for parabolic equation is performed using difference scheme with non-positive weight multiplier. Similar difference scheme is also used for the numerical solution of Cauchy problem for two-dimensional Laplace equation. The results of computational experiment, performed on model problems with exact solution, including ones with randomly perturbed input data are presented and discussed.
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
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.
Effect of head shape variations among individuals on the EEG/MEG forward and inverse problems.
von Ellenrieder, Nicolás; Muravchik, Carlos H; Wagner, Michael; Nehorai, Arye
2009-03-01
We study the effect of the head shape variations on the EEG/magnetoencephalography (MEG) forward and inverse problems. We build a random head model such that each sample represents the head shape of a different individual and solve the forward problem assuming this random head model, using a polynomial chaos expansion. The random solution of the forward problem is then used to quantify the effect of the geometry when the inverse problem is solved with a standard head model. The results derived with this approach are valid for a continuous family of head models, rather than just for a set of cases. The random model consists of three random surfaces that define layers of different electric conductivity, and we built an example based on a set of 30 deterministic models from adults. Our results show that for a dipolar source model, the effect of the head shape variations on the EEG/MEG inverse problem due to the random head model is slightly larger than the effect of the electronic noise present in the sensors. The variations in the EEG inverse problem solutions are due to the variations in the shape of the volume conductor, while the variations in the MEG inverse problem solutions, larger than the EEG ones, are caused mainly by the variations of the absolute position of the sources in a coordinate system based on anatomical landmarks, in which the magnetometers have a fixed position.
Using a derivative-free optimization method for multiple solutions of inverse transport problems
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 mesh 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.
Using a derivative-free optimization method for multiple solutions of inverse transport problems
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
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.
Globally Convergent Numerical Methods for Coefficient Inverse Problems
2008-09-23
Analysis, 39, 1863-1889, 2008. 11. M.V. Klibanov and S.E. Pamyatnykh, Lipschitz stability of a non-standard problem for the non-stationary transport...classical one. We first formulate a Lipschitz stability estimate for this problem, which is Theorem 8.1. This theorem is proven via a Carleman estimate...cmin, cmax) such that the following Lipschitz stability estimate holds ‖v‖H1(QT ) ≤ C [ ‖Lv‖L2(QT ) + ‖v |ST ‖H1(ST ) + ‖v |ST ‖L2(ST ) ] ,∀v ∈ H2 (QT
Cameron, M.K.; Fomel, S.B.; Sethian, J.A.
2009-01-01
In the present work we derive and study a nonlinear elliptic PDE coming from the problem of estimation of sound speed inside the Earth. The physical setting of the PDE allows us to pose only a Cauchy problem, and hence is ill-posed. However we are still able to solve it numerically on a long enough time interval to be of practical use. We used two approaches. The first approach is a finite difference time-marching numerical scheme inspired by the Lax-Friedrichs method. The key features of this scheme is the Lax-Friedrichs averaging and the wide stencil in space. The second approach is a spectral Chebyshev method with truncated series. We show that our schemes work because of (1) the special input corresponding to a positive finite seismic velocity, (2) special initial conditions corresponding to the image rays, (3) the fact that our finite-difference scheme contains small error terms which damp the high harmonics; truncation of the Chebyshev series, and (4) the need to compute the solution only for a short interval of time. We test our numerical scheme on a collection of analytic examples and demonstrate a dramatic improvement in accuracy in the estimation of the sound speed inside the Earth in comparison with the conventional Dix inversion. Our test on the Marmousi example confirms the effectiveness of the proposed approach.
NASA Astrophysics Data System (ADS)
Chmielewski, Arthur B.; Noca, Muriel; Ulvestad, James
2000-03-01
Supermassive black holes are among the most spectacular objects in the Universe, and are laboratories for physics in extreme conditions. Understanding the physics of massive black holes and related phenomena is a primary goal of the ARISE mission. The scientific goals of the mission are described in detail on the ARISE web site http://arise.ipl.nasa.gov and in the ARISE Science Goals document. The following paper, as the title suggests, is not intended to be a comprehensive description of ARISE, but deals only with one aspect of the ARISE mission-the inflatable antenna which is the key element of the ARISE spacecraft. This spacecraft,due to the extensive reliance on inflatables, may be considered as the first generation Gossamer spacecraft
Inverse heat conduction problem in a phase change memory device
NASA Astrophysics Data System (ADS)
Battaglia, Jean-Luc; De, Indrayush; Sousa, Véronique
2017-01-01
An invers heat conduction problem is solved considering the thermal investigation of a phase change memory device using the scanning thermal microscopy. The heat transfer model rests on system identification for the probe thermal impedance and on a finite element method for the device thermal impedance. Unknown parameters in the model are then identified using a nonlinear least square algorithm that minimizes the quadratic gap between the measured probe temperature and the simulated one.
Maximum entropy regularization of the geomagnetic core field inverse problem
NASA Astrophysics Data System (ADS)
Jackson, Andrew; Constable, Catherine; Gillet, Nicolas
2007-12-01
The maximum entropy technique is an accepted method of image reconstruction when the image is made up of pixels of unknown positive intensity (e.g. a grey-scale image). The problem of reconstructing the magnetic field at the core-mantle boundary from surface data is a problem where the target image, the value of the radial field Br, can be of either sign. We adopt a known extension of the usual maximum entropy method that can be applied to images consisting of pixels of unconstrained sign. We find that we are able to construct images which have high dynamic ranges, but which still have very simple structure. In the spherical harmonic domain they have smoothly decreasing power spectra. It is also noteworthy that these models have far less complex null flux curve topology (lines on which the radial field vanishes) than do models which are quadratically regularized. Problems such as the one addressed are ubiquitous in geophysics, and it is suggested that the applications of the method could be much more widespread than is currently the case.
Application of invariant integrals to elastostatic inverse problems
NASA Astrophysics Data System (ADS)
Goldstein, Robert; Shifrin, Efim; Shushpannikov, Pavel
2008-01-01
A problem of parameters identification for embedded defects in a linear elastic body using results of static tests is considered. A method, based on the use of invariant integrals is developed for solving this problem. A problem for the spherical inclusion parameters identification is considered as an example of the proposed approach application. It is shown that a radius, elastic moduli and coordinates of a spherical inclusion center are determined from one uniaxial tension (compression) test. The explicit formulae, expressing the spherical inclusion parameters by means of the values of corresponding invariant integrals are obtained. The values of the integrals can be calculated from the experimental data if both applied loads and displacements are measured on the surface of the body in the static test. A numerical analysis of the obtained explicit formulae is fulfilled. It is shown that the formulae give a good approximation of the spherical inclusion parameters even in the case when the inclusion is located close enough to the surface of the body. To cite this article: R. Goldstein et al., C. R. Mecanique 336 (2008).
Inverse source problem for the hyperbolic equation with a time-dependent principal part
NASA Astrophysics Data System (ADS)
Jiang, Daijun; Liu, Yikan; Yamamoto, Masahiro
2017-01-01
In this paper, we investigate the inverse problem on determining the spatial component of the source term in the hyperbolic equation with a time-dependent principal part. Based on a Carleman estimate for general hyperbolic operators, we prove a local stability result of Hölder type in both cases of partial boundary and interior observation data. Numerically, we adopt the classical Tikhonov regularization to reformulate the inverse problem into a related optimization problem, for which we develop an iterative thresholding algorithm by using the corresponding adjoint system. Numerical examples up to three spatial dimensions are presented to demonstrate the accuracy and efficiency of the proposed algorithm.
Unrealistic parameter estimates in inverse modelling: A problem or a benefit for model calibration?
Poeter, E.P.; Hill, M.C.
1996-01-01
Estimation of unrealistic parameter values by inverse modelling is useful for constructed model discrimination. This utility is demonstrated using the three-dimensional, groundwater flow inverse model MODFLOWP to estimate parameters in a simple synthetic model where the true conditions and character of the errors are completely known. When a poorly constructed model is used, unreasonable parameter values are obtained even when using error free observations and true initial parameter values. This apparent problem is actually a benefit because it differentiates accurately and inaccurately constructed models. The problems seem obvious for a synthetic problem in which the truth is known, but are obscure when working with field data. Situations in which unrealistic parameter estimates indicate constructed model problems are illustrated in applications of inverse modelling to three field sites and to complex synthetic test cases in which it is shown that prediction accuracy also suffers when constructed models are inaccurate.
NASA Astrophysics Data System (ADS)
Sbarbaro, D.; Vauhkonen, M.; Johansen, T. A.
2015-04-01
Solving electrical impedance tomography (EIT) inverse problems in real-time is a challenging task due to their dimension, the nonlinearities involved and the fact that they are ill-posed. Thus, efficient algorithms are required to address the application of tomographic technologies in process industry. In practical applications the EIT inverse problem is often linearized for fast and robust reconstruction. The aim of this paper is to analyse the solution of linearized EIT inverse problem from the perspective of a state estimation problem, providing links between regularization, observability and convergence of the algorithms. In addition, also a new way to define the fictitious outputs is proposed, leading to observers with fewer parameters than with the approach widely used in literature. Simulation of EIT examples illustrate the main ideas and algorithmic improvements of the proposed approaches.
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.
The inverse problem in electrocardiography: solutions in terms of epicardial potentials.
Rudy, Y; Messinger-Rapport, B J
1988-01-01
The objective of the inverse problem in electrocardiography is to recover noninvasively regional information about intracardiac electrical events from electrical measurements on the body surface. The choice of epicardial potentials as the solution to the inverse problem is motivated by the availability of a unique epicardial potential solution for each body surface potential distribution, by the ability to verify experimentally the inverse-recovered epicardial potentials, by the proven relationship between epicardial potentials and the details of intracardiac regional events, and by the possibility of using the inverse solution as a supplement or possible replacement to clinical epicardial potential mapping prior to surgical intervention. Although, in principle, the epicardial potential distribution can be recovered from the body surface potential distribution, the inverse problem in terms of potentials is ill-posed, and naive attempts to reconstruct the epicardial potentials result in incorrect solutions which are highly oscillatory. Large deviations from the actual solution may result from inaccuracy of the data measurement, incomplete knowledge of the potential data over the entire torso, and inaccurate description of the inhomogeneous torso volume conductor. This review begins with a mathematical and qualitative description of the inverse problem in terms of epicardial potentials. The ill-posed nature of the problem is demonstrated using a theoretical boundary value problem. Effects of inaccuracies in the body surface potential data (stability estimates) are introduced, and a sensitivity analysis of geometrical and inhomogeneity parameters is presented using an analytical eccentric spheres model. Various computational methods for relating epicardial to body surface potentials, i.e., the computation of the forward transfer matrix, are described and compared. The need for regularization of the inverse recovery of epicardial potentials, resulting from the need to
Fast and accurate analytical model to solve inverse problem in SHM using Lamb wave propagation
NASA Astrophysics Data System (ADS)
Poddar, Banibrata; Giurgiutiu, Victor
2016-04-01
Lamb wave propagation is at the center of attention of researchers for structural health monitoring of thin walled structures. This is due to the fact that Lamb wave modes are natural modes of wave propagation in these structures with long travel distances and without much attenuation. This brings the prospect of monitoring large structure with few sensors/actuators. However the problem of damage detection and identification is an "inverse problem" where we do not have the luxury to know the exact mathematical model of the system. On top of that the problem is more challenging due to the confounding factors of statistical variation of the material and geometric properties. Typically this problem may also be ill posed. Due to all these complexities the direct solution of the problem of damage detection and identification in SHM is impossible. Therefore an indirect method using the solution of the "forward problem" is popular for solving the "inverse problem". This requires a fast forward problem solver. Due to the complexities involved with the forward problem of scattering of Lamb waves from damages researchers rely primarily on numerical techniques such as FEM, BEM, etc. But these methods are slow and practically impossible to be used in structural health monitoring. We have developed a fast and accurate analytical forward problem solver for this purpose. This solver, CMEP (complex modes expansion and vector projection), can simulate scattering of Lamb waves from all types of damages in thin walled structures fast and accurately to assist the inverse problem solver.
From Bayes to Tarantola: New insights to understand uncertainty in inverse problems
NASA Astrophysics Data System (ADS)
Fernández-Martínez, J. L.; Fernández-Muñiz, Z.; Pallero, J. L. G.; Pedruelo-González, L. M.
2013-11-01
Anyone working on inverse problems is aware of their ill-posed character. In the case of inverse problems, this concept (ill-posed) proposed by J. Hadamard in 1902, admits revision since it is somehow related to their ill-conditioning and the use of local optimization methods to find their solution. A more general and interesting approach regarding risk analysis and epistemological decision making would consist in analyzing the existence of families of equivalent model parameters that are compatible with the prior information and predict the observed data within the same error bounds. Otherwise said, the ill-posed character of discrete inverse problems (ill-conditioning) originates that their solution is uncertain. Traditionally nonlinear inverse problems in discrete form have been solved via local optimization methods with regularization, but linear analysis techniques failed to account for the uncertainty in the solution that it is adopted. As a result of this fact uncertainty analysis in nonlinear inverse problems has been approached in a probabilistic framework (Bayesian approach), but these methods are hindered by the curse of dimensionality and by the high computational cost needed to solve the corresponding forward problems. Global optimization techniques are very attractive, but most of the times are heuristic and have the same limitations than Monte Carlo methods. New research is needed to provide uncertainty estimates, especially in the case of high dimensional nonlinear inverse problems with very costly forward problems. After the discredit of deterministic methods and some initial years of Bayesian fever, now the pendulum seems to return back, because practitioners are aware that the uncertainty analysis in high dimensional nonlinear inverse problems cannot (and should not be) solved via random sampling methodologies. The main reason is that the uncertainty “space” of nonlinear inverse problems has a mathematical structure that is embedded in the
NASA Astrophysics Data System (ADS)
Moses, Harry E.
1984-06-01
The object of the time-dependent inverse source problem of electromagnetic theory and acoustics is to find time-dependent sources and currents, which are turned on at a given time and then off to give rise to prescribed radiation fields. In an early paper for the three-dimensional electromagnetic case, the present writer showed that the sources and currents are not unique and gave conditions which make them so. The ideas of that paper are reformulated for the three-dimensional electromagnetic case and extended to the acoustical three-dimensional case and the one-dimensional electromagnetic and acoustic cases. The one-dimensional cases show very explicitly the nature of the ambiguity of the choice of sources and currents. This ambiguity is closely related to one which occurs in inverse scattering theory. The ambiguity in inverse scattering theory arises when one wishes to obtain the off-shell elements of the T matrix from some of the on-shell elements (i.e., from the corresponding elements of the scattering operator). In inverse scattering theory prescribing of the representation in which the potential is to be diagonal removes the ambiguity. For the inverse source problem a partial prescription of the time dependence of the sources and currents removes the ambiguity. The inverse source problem is then solved explicitly for this prescribed time dependence. The direct source problems for the one- and three-dimensional acoustic and electromagnetic cases are also given to provide a contrast with the inverse source problem and for use in later papers. Moreover, the present author's earlier work on the eigenfunctions of the curl operator is reviewed and used to simplify drastically the three-dimensional direct and inverse source problems for electromagnetic theory by splitting off the radiation field and its currents from the longitudinal field and its sources and currents. Finally, for a prescribed time dependence, the inverse source problem is solved explicitly in
Terekhov, Alexander V; Zatsiorsky, Vladimir M
2011-02-01
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.
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
Advanced model of eddy-current NDE inverse problem with sparse grid algorithm
NASA Astrophysics Data System (ADS)
Zhou, Liming; Sabbagh, Harold A.; Sabbagh, Elias H.; Murphy, R. Kim; Bernacchi, William
2017-02-01
In model-based inverse problem, some unknown parameters need to be estimated. These parameters are used not only to characterize the physical properties of cracks, but also to describe the position of the probes (such as lift off and angles) in the calibration. After considering the effect of the position of the probes in the inverse problem, the accuracy of the inverse result will be improved. With increasing the number of the parameters in the inverse problems, the burden of calculations will increase exponentially in the traditional full grid method. The sparse grid algorithm, which was introduced by Sergey A. Smolyak, was used in our work. With this algorithm, we obtain a powerful interpolation method that requires significantly fewer support nodes than conventional interpolation on a full grid. In this work, we combined sparse grid toolbox TASMANIAN, which is produced by Oak Ridge National Laboratory, and professional eddy-current NDE software, VIC-3D R◯, to solve a specific inverse problem. An advanced model based on our previous one is used to estimate length and depth of the crack, lift off and two angles of the position of probes. Considering the calibration process, pseudorandom noise is considered in the model and statistical behavior is discussed.
[Inverse problem identification of parameters in heat transfer processes of human body].
Yu, K; Ji, Z; Xie, T; Li, X
1999-06-01
In order that the distortion of the relative skin temperatures which is accompanied with the physiological destruction of an organ in the abdominal cavity and its physical-physiological mechanism may be investigated, we adopt in this paper the mathematical model for heat transfer problems in human layered tissues and a perfect parametric identification approach-inverse problem method. By utilizing the extremum method and integrating with the experimental data of an artificial thermo-focus, this difficult biophysical problem is solved.
Effects of geometric head model perturbations on the EEG forward and inverse problems.
von Ellenrieder, Nicolás; Muravchik, Carlos H; Nehorai, Arye
2006-03-01
We study the effect of geometric head model perturbations on the electroencephalography (EEG) forward and inverse problems. Small magnitude perturbations of the shape of the head could represent uncertainties in the head model due to errors on images or techniques used to construct the model. They could also represent small scale details of the shape of the surfaces not described in a deterministic model, such as the sulci and fissures of the cortical layer. We perform a first-order perturbation analysis, using a meshless method for computing the sensitivity of the solution of the forward problem to the geometry of the head model. The effect on the forward problem solution is treated as noise in the EEG measurements and the Cramér-Rao bound is computed to quantify the effect on the inverse problem performance. Our results show that, for a dipolar source, the effect of the perturbations on the inverse problem performance is under the level of the uncertainties due to the spontaneous brain activity. Thus, the results suggest that an extremely detailed model of the head may be unnecessary when solving the EEG inverse problem.
Celik, Hasan; Shaka, A J; Mandelshtam, V A
2010-09-01
We consider the harmonic inversion problem, and the associated spectral estimation problem, both of which are key numerical problems in NMR data analysis. Under certain conditions (in particular, in exact arithmetic) these problems have unique solutions. Therefore, these solutions must not depend on the inversion algorithm, as long as it is exact in principle. In this paper, we are not concerned with the algorithmic aspects of harmonic inversion, but rather with the sensitivity of the solutions of the problem to perturbations of the time-domain data. A sensitivity analysis was performed and the counterintuitive results call into question the common assumption made in "super-resolution" methods using non-uniform data sampling, namely, that the data should be sampled more often where the time signal has the largest signal-to-noise ratio. The numerical analysis herein demonstrates that the spectral parameters (such as the peak positions and amplitudes) resulting from the solution of the harmonic inversion problem are least susceptible to the perturbations in the values of data points at the edges of the time interval and most susceptible to the perturbations in the values at intermediate times.
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
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.
NASA Astrophysics Data System (ADS)
Wang, Qian; Li, Xingwen; Song, Haoyong; Rong, Mingzhe
2010-04-01
Non-contact magnetic measurement method is an effective way to study the air arc behavior experimentally One of the crucial techniques is to solve an inverse problem for the electromagnetic field. This study is devoted to investigating different algorithms for this kind of inverse problem preliminarily, including the preconditioned conjugate gradient method, penalty function method and genetic algorithm. The feasibility of each algorithm is analyzed. It is shown that the preconditioned conjugate gradient method is valid only for few arc segments, the estimation accuracy of the penalty function method is dependent on the initial conditions, and the convergence of genetic algorithm should be studied further for more segments in an arc current.
Solution of inverse heat conduction problem using the Tikhonov regularization method
NASA Astrophysics Data System (ADS)
Duda, Piotr
2017-02-01
It is hard to solve ill-posed problems, as calculated temperatures are very sensitive to errors made while calculating "measured" temperatures or performing real-time measurements. The errors can create temperature oscillation, which can be the cause of an unstable solution. In order to overcome such difficulties, a variety of techniques have been proposed in literature, including regularization, future time steps and smoothing digital filters. In this paper, the Tikhonov regularization is applied to stabilize the solution of the inverse heat conduction problem. The impact on the inverse solution stability and accuracy is demonstrated.
Uniqueness of inverse problems of isotropic incompressible three-dimensional elasticity
NASA Astrophysics Data System (ADS)
Albocher, Uri; Barbone, Paul E.; Oberai, Assad A.; Harari, Isaac
2014-12-01
The uniqueness of an inverse problem of isotropic incompressible three dimensional elasticity aimed at reconstructing material modulus distributions is considered. We show that given a single strain field and no boundary conditions, arbitrary functions may have to be prescribed to make the solution unique. On the other hand, having two linearly independent strain fields leads to a favorable solution space where a maximum of five arbitrary constants must be prescribed to guarantee a unique solution. We solve inverse problems with two strain fields given using the adjoint weighted equation method and impose five discrete constraints. The method exhibits good numerical performance with optimal rates of convergence.
Ivanov, J.; Miller, R.D.; Xia, J.; Steeples, D.; Park, C.B.
2006-01-01
We describe a possible solution to the inverse refraction-traveltime problem (IRTP) that reduces the range of possible solutions (nonuniqueness). This approach uses a reference model, derived from surface-wave shear-wave velocity estimates, as a constraint. The application of the joint analysis of refractions with surface waves (JARS) method provided a more realistic solution than the conventional refraction/tomography methods, which did not benefit from a reference model derived from real data. This confirmed our conclusion that the proposed method is an advancement in the IRTP analysis. The unique basic principles of the JARS method might be applicable to other inverse geophysical problems. ?? 2006 Society of Exploration Geophysicists.
Computational modeling of monoenergetic neutral particle inverse transport problems in slab geometry
NASA Astrophysics Data System (ADS)
Gomes, Rodrigo R.; Barros, Ricardo C.
2012-09-01
Presented here is an analytical numerical method applied to three different types of monoenergetic neutral particle inverse transport problems in the discrete ordinates (SN) formulation: (a) boundary condition estimation; (b) interior source estimation; and (c) effective slab length estimation. These three types of inverse problems governed by the linear integrodifferential transport equation in SN formulation are related respectively to medical physics (a); nuclear waste storage (b); and non-destructive testing in industry (c). Numerical results and a brief discussion are given to conclude this paper.
Application of robust Generalised Cross-Validation to the inverse problem of electrocardiology.
Barnes, Josef P; Johnston, Peter R
2016-02-01
Robust Generalised Cross-Validation was proposed recently as a method for determining near optimal regularisation parameters in inverse problems. It was introduced to overcome a problem with the regular Generalised Cross-Validation method in which the function that is minimised to obtain the regularisation parameter often has a broad, flat minimum, resulting in a poor estimate for the parameter. The robust method defines a new function to be minimised which has a narrower minimum, but at the expense of introducing a new parameter called the robustness parameter. In this study, the Robust Generalised Cross-Validation method is applied to the inverse problem of electrocardiology. It is demonstrated that, for realistic situations, the robustness parameter can be set to zero. With this choice of robustness parameter, it is shown that the robust method is able to obtain estimates of the regularisation parameter in the inverse problem of electrocardiology that are comparable to, or better than, many of the standard methods that are applied to this inverse problem.
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
Solution of the nonlinear inverse scattering problem by T -matrix completion. II. Simulations
NASA Astrophysics Data System (ADS)
Levinson, Howard W.; Markel, Vadim A.
2016-10-01
This is Part II of the paper series on data-compatible T -matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043317 (2016), 10.1103/PhysRevE.94.043317] contains theory and here we present simulations for inverse scattering of scalar waves. The underlying mathematical model is the scalar wave equation and the object function that is reconstructed is the medium susceptibility. The simulations are relevant to ultrasound tomographic imaging and seismic tomography. It is shown that DCTMC is a viable method for solving strongly nonlinear inverse problems with large data sets. It provides not only the overall shape of the object, but the quantitative contrast, which can correspond, for instance, to the variable speed of sound in the imaged medium.
A domain derivative-based method for solving elastodynamic inverse obstacle scattering problems
NASA Astrophysics Data System (ADS)
Le Louër, Frédérique
2015-11-01
The present work is concerned with the shape reconstruction problem of isotropic elastic inclusions from far-field data obtained by the scattering of a finite number of time-harmonic incident plane waves. This paper aims at completing the theoretical framework which is necessary for the application of geometric optimization tools to the inverse transmission problem in elastodynamics. The forward problem is reduced to systems of boundary integral equations following the direct and indirect methods initially developed for solving acoustic transmission problems. We establish the Fréchet differentiability of the boundary to far-field operator and give a characterization of the first Fréchet derivative and its adjoint operator. Using these results we propose an inverse scattering algorithm based on the iteratively regularized Gauß-Newton method and show numerical experiments in the special case of star-shaped obstacles.
Inverse problem for the Verhulst equation of limited population growth with discrete experiment data
NASA Astrophysics Data System (ADS)
Azimov, Anvar; Kasenov, Syrym; Nurseitov, Daniyar; Serovajsky, Simon
2016-08-01
Verhulst limited growth model with unknown parameters of growth is considered. These parameters are defined by discrete experiment data. This inverse problem is solved with using gradient method with interpolation of data and without it. Approximation of the delta-function is used for the latter case. As an example the bacteria population E.coli is considered.
New global stability estimates for the Gel'fand-Calderon inverse problem
NASA Astrophysics Data System (ADS)
Novikov, R. G.
2011-01-01
We prove new global stability estimates for the Gel'fand-Calderon inverse problem in 3D. For sufficiently regular potentials, this result of the present work is a principal improvement of the result of Alessandrini (1988 Appl. Anal. 27 153-172).
Global stability for an inverse problem in soil–structure interaction
Alessandrini, G.; Morassi, A.; Rosset, E.; Vessella, S.
2015-01-01
We consider the inverse problem of determining the Winkler subgrade reaction coefficient of a slab foundation modelled as a thin elastic plate clamped at the boundary. The plate is loaded by a concentrated force and its transversal deflection is measured at the interior points. We prove a global Hölder stability estimate under (mild) regularity assumptions on the unknown coefficient. PMID:26345082
Numerical solution of 2D-vector tomography problem using the method of approximate inverse
NASA Astrophysics Data System (ADS)
Svetov, Ivan; Maltseva, Svetlana; Polyakova, Anna
2016-08-01
We propose a numerical solution of reconstruction problem of a two-dimensional vector field in a unit disk from the known values of the longitudinal and transverse ray transforms. The algorithm is based on the method of approximate inverse. Numerical simulations confirm that the proposed method yields good results of reconstruction of vector fields.
ON THE GEOSTATISTICAL APPROACH TO THE INVERSE PROBLEM. (R825689C037)
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...
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.
Butler, Troy; Graham, L.; Estep, D.; Dawson, C.; Westerink, J. J.
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 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. 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.
2014-08-19
finite element method, performance verification on experimental data, imaging of explosive devices, comparison with the classical Krein equation method...of the globally convergent numerical method of this project and the classical Krein equation method. It was established that while the first method...of a long standing problem about uniqueness of a phaseless 3-d inverse problem of quantum scattering. This was an open question since the publication
Numerical study of the inverse problem for the diffusion-reaction equation using optimization method
NASA Astrophysics Data System (ADS)
Soboleva, O. V.; Brizitskii, R. V.
2016-04-01
The model of transfer of substance with mixed boundary condition is considered. The inverse extremum problem of identification of the main coefficient in a nonstationary diffusion-reaction equation is formulated. The numerical algorithm based on the Newton-method of nonlinear optimization and finite difference discretization for solving this extremum problem is developed and realized on computer. The results of numerical experiments are discussed.
NASA Astrophysics Data System (ADS)
Sazaklioglu, Ali Ugur; Erdogan, Abdullah Said; Ashyralyev, Allaberen
2016-08-01
This paper deals with existence and uniqueness of the solution of an inverse problem for a semilinear equation subject to a final overdetermination in a Banach space. Moreover, the first order of accuracy Rothe difference scheme is presented for the numerical solution of this problem. The existence and uniqueness result for this difference scheme is given. This difference scheme is applied on a particular example and some numerical results are given.
NASA Astrophysics Data System (ADS)
Rudowicz, Czesław; Karbowiak, Mirosław
2015-01-01
Survey of recent literature has revealed a doubly-worrying tendency concerning the treatment of the two distinct types of Hamiltonians, namely, the physical crystal field (CF), or equivalently ligand field (LF), Hamiltonians and the zero-field splitting (ZFS) Hamiltonians, which appear in the effective spin Hamiltonians (SH). The nature and properties of the CF (LF) Hamiltonians have been mixed up in various ways with those of the ZFS Hamiltonians. Such cases have been identified in a rapidly growing number of studies of the transition-ion based systems using electron magnetic resonance (EMR), optical spectroscopy, and magnetic measurements. These findings have far ranging implications since these Hamiltonians are cornerstones for interpretation of magnetic and spectroscopic properties of the single transition ions in various crystals or molecules as well as the exchange coupled systems (ECS) of transition ions, e.g. single molecule magnets (SMM) or single ion magnets (SIM). The seriousness of the consequences of such conceptual problems and related terminological confusions has reached a level that goes far beyond simple semantic issues or misleading keyword classifications of papers in journals and scientific databases. The prevailing confusion, denoted as the CF=ZFS confusion, pertains to the cases of labeling the true ZFS quantities as purportedly the CF (LF) quantities. Here we consider the inverse confusion between the CF (LF) quantities and the SH (ZFS) ones, denoted the ZFS=CF confusion, which consists in referring to the parameters (or Hamiltonians), which are the true CF (LF) quantities, as purportedly the ZFS (or SH) quantities. Specific cases of the ZFS=CF confusion identified in recent textbooks, reviews and papers, especially SMM- and SIM-related ones, are surveyed and the pertinent misconceptions are clarified. The serious consequences of the terminological confusions include misinterpretation of data from a wide range of experimental techniques and
Analysis of forward and inverse problems in chemical dynamics and spectroscopy
Rabitz, H.
1993-12-01
The overall scope of this research concerns the development and application of forward and inverse analysis tools for problems in chemical dynamics and chemical kinetics. The chemical dynamics work is specifically associated with relating features in potential surfaces and resultant dynamical behavior. The analogous inverse research aims to provide stable algorithms for extracting potential surfaces from laboratory data. In the case of chemical kinetics, the focus is on the development of systematic means to reduce the complexity of chemical kinetic models. Recent progress in these directions is summarized below.
Scattering and inverse scattering for a left-definite Sturm-Liouville problem
NASA Astrophysics Data System (ADS)
Bennewitz, C.; Brown, B. M.; Weikard, R.
This work develops a scattering and an inverse scattering theory for the Sturm-Liouville equation -u″+qu=λwu where w may change sign but q⩾0. Thus the left-hand side of the equation gives rise to a positive quadratic form and one is led to a left-definite spectral problem. The crucial ingredient of the approach is a generalized transform built on the Jost solutions of the problem and hence termed the Jost transform and the associated Paley-Wiener theorem linking growth properties of transforms with support properties of functions. One motivation for this investigation comes from the Camassa-Holm equation for which the solution of the Cauchy problem can be achieved by the inverse scattering transform for -u″+1/4u=λwu.
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.
A neural network approach for the solution of electric and magnetic inverse problems
Coccorese, E.; Morabito, F.C. . Istituto di Ingegneria Elettronica); Martone, R. . Dipartimento di Ingegneria Elettronica)
1994-09-01
Multilayer neural networks, trained via the back-propagation rule, are proved to provide an efficient means for solving electric and/or magnetic inverse problems. The underlying model of the system is learned by the network by means of a dataset defining the relationship between input and output parameters. The merits of the method are illustrated at the light of three example cases. The first two samples deal with inverse electrostatic problems which are relevant for nondestructive testing applications. In a first problem, a boss on an earthed plane is identified on the basis of the map of potential produced by a point charge. In the second problem, the geometric parameters of an ellipsoid carrying an electric charge are identified. In both cases, database of simulated measurements has been generated thanks to the available analytical solutions. As a sample magnetic inverse problem, the identification of a circular plasma in a tokamak device from external flux measurements is carried out. The results achieved show that the method here proposed is promising for technically meaningful applications.
NASA Astrophysics Data System (ADS)
Menke, William
2017-02-01
We prove that the problem of inverting Rayleigh wave phase velocity functions c( k ) , where k is wavenumber, for density ρ ( z ) , rigidity μ ( z ) and Lamé parameter λ ( z ) , where z is depth, is fully non-unique, at least in the highly-idealized case where the base Earth model is an isotropic half space. The model functions completely trade off. This is one special case of a common inversion scenario in which one seeks to determine several model functions from a single data function. We explore the circumstances under which this broad class of problems is unique, starting with very simple scenarios, building up to the somewhat more complicated (and common) case where data and model functions are related by convolutions, and then finally, to scale-independent problems (which include the Rayleigh wave problem). The idealized cases that we examine analytically provide insight into the kinds of nonuniqueness that are inherent in the much more complicated problems encountered in modern geophysical imaging (though they do not necessarily provide methods for solving those problems). We also define what is meant by a Backus and Gilbert resolution kernel in this kind of inversion and show under what circumstances a unique localized average of a single model function can be constructed.
Inverse reference in subtraction performance: an analysis from arithmetic word problems.
Orrantia, Josetxu; Rodríguez, Laura; Múñez, David; Vicente, Santiago
2012-01-01
Studies of elementary calculation have shown that adults solve basic subtraction problems faster with problems presented in addition format (e.g., 6 ± = 13) than in standard subtraction format (e.g., 13 - 6 = ). Therefore, it is considered that adults solve subtraction problems by reference to the inverse operation (e.g., for 13 - 6 = 7, "I know that 13 is 6 + 7") because presenting the subtraction problem in addition format does not require the mental rearrangement of the problem elements into the addition format. In two experiments, we examine whether adults' use of addition to solve subtractions is modulated by the arrangement of minuend and subtrahend, regardless of format. To this end, we used arithmetic word problems since single-digit problems in subtraction format would not allow the subtrahend to appear before the minuend. In Experiment 1, subtractions were presented by arranging minuend and subtrahend according to previous research. In Experiment 2, operands were reversed. The overall results showed that participants benefited from word problems where the subtrahend appears before the minuend, including subtractions in standard subtraction format. These findings add to a growing body of literature that emphasizes the role of inverse reference in adults' performance on subtractions.
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.
On the new approach to solving the inverse problem of gravimetry
NASA Astrophysics Data System (ADS)
Arsanukaev, Z. Z.
2017-01-01
The results of the studies within the new approach to solving the inverse problem of gravimetry are considered. This approach consists in direct (analytical) continuation of the anomalous gravitational field specified on the Earth's surface into the lower half-space with the use of the method of discrete approximations. The solution of the problem of analytical continuation is demonstrated by the model example. In the solution of the problem of analytical continuation, the developed algorithms and computer programs were implemented in two program packages which are used both in the model computations and in practice.
Solving Large-Scale Inverse Magnetostatic Problems using the Adjoint Method
NASA Astrophysics Data System (ADS)
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.
Solving Large-Scale Inverse Magnetostatic Problems using the Adjoint Method
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
NASA Astrophysics Data System (ADS)
Gross, Lutz; Altinay, Cihan; Fenwick, Joel; Smith, Troy
2014-05-01
The program package escript has been designed for solving mathematical modeling problems using python, see Gross et al. (2013). Its development and maintenance has been funded by the Australian Commonwealth to provide open source software infrastructure for the Australian Earth Science community (recent funding by the Australian Geophysical Observing System EIF (AGOS) and the AuScope Collaborative Research Infrastructure Scheme (CRIS)). The key concepts of escript are based on the terminology of spatial functions and partial differential equations (PDEs) - an approach providing abstraction from the underlying spatial discretization method (i.e. the finite element method (FEM)). This feature presents a programming environment to the user which is easy to use even for complex models. Due to the fact that implementations are independent from data structures simulations are easily portable across desktop computers and scalable compute clusters without modifications to the program code. escript has been successfully applied in a variety of applications including modeling mantel convection, melting processes, volcanic flow, earthquakes, faulting, multi-phase flow, block caving and mineralization (see Poulet et al. 2013). The recent escript release (see Gross et al. (2013)) provides an open framework for solving joint inversion problems for geophysical data sets (potential field, seismic and electro-magnetic). The strategy bases on the idea to formulate the inversion problem as an optimization problem with PDE constraints where the cost function is defined by the data defect and the regularization term for the rock properties, see Gross & Kemp (2013). This approach of first-optimize-then-discretize avoids the assemblage of the - in general- dense sensitivity matrix as used in conventional approaches where discrete programming techniques are applied to the discretized problem (first-discretize-then-optimize). In this paper we will discuss the mathematical framework for
Investigation of one inverse problem in case of modeling water areas with "liquid" boundaries
NASA Astrophysics Data System (ADS)
Sheloput, Tatiana; Agoshkov, Valery
2015-04-01
In hydrodynamics often appears the problem of modeling water areas (oceans, seas, rivers, etc.) with "liquid" boundaries. "Liquid" boundary means set of those parts of boundary where impermeability condition is broken (for example, straits, bays borders, estuaries, interfaces of oceans). Frequently such effects are ignored: for "liquid" boundaries the same conditions are used as for "solid" ones, "material boundary" approximation is applied [1]. Sometimes it is possible to interpolate the results received from models of bigger areas. Moreover, approximate estimates for boundary conditions are often used. However, those approximations are not always valid. Sometimes errors in boundary condition determination could lead to a significant decrease in the accuracy of the simulation results. In this work one way of considering the problem mentioned above is described. According to this way one inverse problem on reconstruction of boundary function in convection-reaction-diffusion equations which describe transfer of heat and salinity is solved. The work is based on theory of adjoint equations [2] and optimal control, as well as on common methodology of investigation inverse problems [3]. The work contains theoretical investigation and the results of computer simulation applied for the Baltic Sea. Moreover, conditions and restrictions that should be satisfied for solvability of the problem are entered and justified in the work. Submitted work could be applied for the solution of more complicated inverse problems and data assimilation problems in the areas with "liquid" boundaries; also it is a step for developing algorithms on computing level, speed, temperature and salinity that could be applied for real objects. References 1. A. E. Gill. Atmosphere-ocean dynamics. // London: Academic Press, 1982. 2. G. I. Marchuk. Adjoint equations. // Moscow: INM RAS, 2000, 175 p. (in Russian). 3. V.I. Agoshkov. The methods of optimal control and adjoint equations in problems of
A hierarchical Bayesian-MAP approach to inverse problems in imaging
NASA Astrophysics Data System (ADS)
Raj, Raghu G.
2016-07-01
We present a novel approach to inverse problems in imaging based on a hierarchical Bayesian-MAP (HB-MAP) formulation. In this paper we specifically focus on the difficult and basic inverse problem of multi-sensor (tomographic) imaging wherein the source object of interest is viewed from multiple directions by independent sensors. Given the measurements recorded by these sensors, the problem is to reconstruct the image (of the object) with a high degree of fidelity. We employ a probabilistic graphical modeling extension of the compound Gaussian distribution as a global image prior into a hierarchical Bayesian inference procedure. Since the prior employed by our HB-MAP algorithm is general enough to subsume a wide class of priors including those typically employed in compressive sensing (CS) algorithms, HB-MAP algorithm offers a vehicle to extend the capabilities of current CS algorithms to include truly global priors. After rigorously deriving the regression algorithm for solving our inverse problem from first principles, we demonstrate the performance of the HB-MAP algorithm on Monte Carlo trials and on real empirical data (natural scenes). In all cases we find that our algorithm outperforms previous approaches in the literature including filtered back-projection and a variety of state-of-the-art CS algorithms. We conclude with directions of future research emanating from this work.
Group-sparsity regularization for ill-posed subsurface flow inverse problems
NASA Astrophysics Data System (ADS)
Golmohammadi, Azarang; Khaninezhad, Mohammad-Reza M.; Jafarpour, Behnam
2015-10-01
Sparse representations provide a flexible and parsimonious description of high-dimensional model parameters for reconstructing subsurface flow property distributions from limited data. To further constrain ill-posed inverse problems, group-sparsity regularization can take advantage of possible relations among the entries of unknown sparse parameters when: (i) groups of sparse elements are either collectively active or inactive and (ii) only a small subset of the groups is needed to approximate the parameters of interest. Since subsurface properties exhibit strong spatial connectivity patterns they may lead to sparse descriptions that satisfy the above conditions. When these conditions are established, a group-sparsity regularization can be invoked to facilitate the solution of the resulting inverse problem by promoting sparsity across the groups. The proposed regularization penalizes the number of groups that are active without promoting sparsity within each group. Two implementations are presented in this paper: one based on the multiresolution tree structure of Wavelet decomposition, without a need for explicit prior models, and another learned from explicit prior model realizations using sparse principal component analysis (SPCA). In each case, the approach first classifies the parameters of the inverse problem into groups with specific connectivity features, and then takes advantage of the grouped structure to recover the relevant patterns in the solution from the flow data. Several numerical experiments are presented to demonstrate the advantages of additional constraining power of group-sparsity in solving ill-posed subsurface model calibration problems.
Berrier, Keith L; Sorensen, Danny C; Khoury, Dirar S
2004-03-01
Numeric regularization methods most often used to solve the ill-posed inverse problem of electrocardiography are spatial and ignore the temporal nature of the problem. In this paper, a Kalman filter reformulation incorporated temporal information to regularize the inverse problem, and was applied to reconstruct left ventricular endocardial electrograms based on cavitary electrograms measured by a noncontact, multielectrode probe. These results were validated against in situ electrograms measured with an integrated, multielectrode basket-catheter. A three-dimensional, probe-endocardium model was determined from multiplane fluoroscopic images. The boundary element method was applied to solve the boundary value problem and determine a linear relationship between endocardial and probe potentials. The Duncan and Horn formulation of the Kalman filter was employed and was compared to the commonly used zero- and first-order Tikhonov spatial regularization as well as the Twomey temporal regularization method. Endocardial electrograms were reconstructed during both sinus and paced rhythms. The Paige and Saunders solution of the Duncan and Horn formulation reconstructed endocardial electrograms at an amplitude relative error of 13% (potential amplitude) which was superior to solutions obtained with zero-order Tikhonov (relative error, 31%), first-order Tikhonov (relative error, 19%), and Twomey regularization (relative error, 44%). Likewise, activation time error in the inverse solution using the Duncan and Horn formulation (2.9 ms) was smaller than that of zero-order Tikhonov (4.8 ms), first-order Tikhonov (5.4 ms), and Twomey regularization (5.8 ms). Therefore, temporal regularization based on the Duncan and Horn formulation of the Kalman filter improves the solution of the inverse problem of electrocardiography.
The \\bar\\partial-equation in the multidimensional inverse scattering problem
NASA Astrophysics Data System (ADS)
Novikov, R. G.; Khenkin, G. M.
1987-06-01
CONTENTSChapter I. A survey of the results § 1.1. The method of Faddeev in the inverse scattering problem for the Schrödinger equation -\\Delta\\psi+v\\cdot\\psi=k^2\\psi § 1.2. The results of Newton, Ablowitz, and Nachman § 1.3. Necessary and sufficient properties of the scattering data. Generalized dispersion relations § 1.4. Methods of solution of the inverse problem with non-overdetermined data. The results of Moses and Prosser and their generalizations § 1.5. The inverse problem on a fixed energy level for the two-dimensional Schrödinger operator and non-linear equations. The methods of S. P. Novikov and Manakov and their further development § 1.6. The inverse problem on a fixed energy level for the three-dimensional Schrödinger operator. The results of Beals and Coifman. New resultsChapter II. Necessary properties of the scattering data § 2.1. The Green-Faddeev function G(x, k) and its properties. Analysis of the integral equation \\mu=1+G*\\mu\\cdot v § 2.2. Generalized scattering data h(k,l). The non-linear \\bar\\partial-equation \\bar\\partial h=\\{h,h\\}. Corollaries § 2.3. Properties of zeros of the Fredholm determinant \\Delta(k) for the equation \\mu=1+G*\\mu\\cdot v § 2.4. Solution of the inverse problem on the basis of generalized dispersion relationsChapter III. Characterization of scattering data. Preliminary results § 3.1. Liouville's theorem for solutions of the non-linear \\bar\\partial-equation § 3.2. Formulae for solutions of the \\bar\\partial-equation in a concave domain of \\mathbf{C}^n § 3.3. Estimates for the form \\{h, h\\} § 3.4. Estimates for solutions of the \\bar\\partial-equation § 3.5. Proof of Liouville's theorem for the non-linear \\bar\\partial-equation Chapter IV. Characterization of scattering data. Final results § 4.1. Theorems concerning the characterization of scattering data in "physical" and "non-physical" domains § 4.2. A separate analyticity theorem for the non-linear \\bar\\partial-equation § 4
Variational approach to direct and inverse problems of atmospheric pollution studies
NASA Astrophysics Data System (ADS)
Penenko, Vladimir; Tsvetova, Elena; Penenko, Alexey
2016-04-01
We present the development of a variational approach for solving interrelated problems of atmospheric hydrodynamics and chemistry concerning air pollution transport and transformations. The proposed approach allows us to carry out complex studies of different-scale physical and chemical processes using the methods of direct and inverse modeling [1-3]. We formulate the problems of risk/vulnerability and uncertainty assessment, sensitivity studies, variational data assimilation procedures [4], etc. A computational technology of constructing consistent mathematical models and methods of their numerical implementation is based on the variational principle in the weak constraint formulation specifically designed to account for uncertainties in models and observations. Algorithms for direct and inverse modeling are designed with the use of global and local adjoint problems. Implementing the idea of adjoint integrating factors provides unconditionally monotone and stable discrete-analytic approximations for convection-diffusion-reaction problems [5,6]. The general framework is applied to the direct and inverse problems for the models of transport and transformation of pollutants in Siberian and Arctic regions. The work has been partially supported by the RFBR grant 14-01-00125 and RAS Presidium Program I.33P. 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. V. V. Penenko, E. A. Tsvetova, and A. V. Penenko Development of variational approach for direct and inverse problems of atmospheric hydrodynamics and chemistry, Izvestiya, Atmospheric and Oceanic Physics, 2015, Vol. 51, No. 3, p. 311-319, DOI: 10.1134/S0001433815030093. 3. V.V. Penenko, E.A. Tsvetova, A.V. Penenko. Methods based on the joint use of models and observational data in the framework of variational approach to forecasting weather and atmospheric composition
Inverse problem for shape control of flexible space reflectors using distributed solar pressure
NASA Astrophysics Data System (ADS)
Borggräfe, A.; Heiligers, J.; Ceriotti, M.; McInnes, C. R.
2014-07-01
This paper investigates controlled elastic deflection of thin circular space reflectors using an inverse problem approach to non-linear thin membrane theory. When changing the surface reflectivity across the membrane, the distributed loads due to ambient solar radiation pressure can be manipulated optically, thus controlling the surface shape without using mechanical or piezo-electric systems. The surface reflectivity can in principle be modulated using uniformly distributed thin-film electro-chromic coatings. We present an analytic solution to the inverse problem of finding the necessary reflectivity distribution that creates a specific membrane deflection, for example that of a parabolic reflector. Importantly, the reflectivity distribution across the surface is found to be independent of membrane size, thickness and solar distance, enabling engineering of the reflectivity distribution directly during the manufacture of the membrane.
Inverse acoustic scattering problem in half-space with anisotropic random impedance
NASA Astrophysics Data System (ADS)
Helin, Tapio; Lassas, Matti; Päivärinta, Lassi
2017-02-01
We study an inverse acoustic scattering problem in half-space with a probabilistic impedance boundary value condition. The Robin coefficient (surface impedance) is assumed to be a Gaussian random function with a pseudodifferential operator describing the covariance. We measure the amplitude of the backscattered field averaged over the frequency band and assume that the data is generated by a single realization of λ. Our main result is to show that under certain conditions the principal symbol of the covariance operator of λ is uniquely determined. Most importantly, no approximations are needed and we can solve the full non-linear inverse problem. We concentrate on anisotropic models for the principal symbol, which leads to the analysis of a novel anisotropic spherical Radon transform and its invertibility.
A multiple-scale Pascal polynomial for 2D Stokes and inverse Cauchy-Stokes problems
NASA Astrophysics Data System (ADS)
Liu, Chein-Shan; Young, D. L.
2016-05-01
The polynomial expansion method is a useful tool for solving both the direct and inverse Stokes problems, which together with the pointwise collocation technique is easy to derive the algebraic equations for satisfying the Stokes differential equations and the specified boundary conditions. In this paper we propose two novel numerical algorithms, based on a third-first order system and a third-third order system, to solve the direct and the inverse Cauchy problems in Stokes flows by developing a multiple-scale Pascal polynomial method, of which the scales are determined a priori by the collocation points. To assess the performance through numerical experiments, we find that the multiple-scale Pascal polynomial expansion method (MSPEM) is accurate and stable against large noise.
Inverse problem for multiple scattering of fast charged particles in a mesoscopic medium
Ramm, A.G. C-3 Division, Los Alamos National Laboratory, Los Alamos, New Mexcio 87545 ); Berman, G.P. Kirensky Institute of Physics, Research Educational Center for Nonlinear Processes, The Krasnoyarsk Technical University, 660036 Krasnoyarsk Theoretical Department, The Krasnoyarsk State University, 660036 Krasnoyarsk )
1995-01-15
We consider an inverse problem of multiple scattering for fast charged particles propagating in an inhomogeneous medium. The scattering processes are described by the diffusion-type equation in the small-angle approximation. It is shown that by using the scattering data given on some small interval, it is possible to recover the spatial dependence of the density of the medium. This inverse problem is ill posed in the sense that small noise in the data may lead to large perturbations in [epsilon]([ital z]) if no [ital a] priori assumptions are made about [epsilon]([ital z]). This is clear from our presentation, since an analytic continuation of [epsilon]([ital z]) is involved. One hopes that the proposed method can be applied to thin foils and to mesoscopic systems.
Meyer, J C; Needham, D J
2015-03-08
In this paper, we examine a semi-linear parabolic Cauchy problem with non-Lipschitz nonlinearity which arises as a generic form in a significant number of applications. Specifically, we obtain a well-posedness result and examine the qualitative structure of the solution in detail. The standard classical approach to establishing well-posedness is precluded owing to the lack of Lipschitz continuity for the nonlinearity. Here, existence and uniqueness of solutions is established via the recently developed generic approach to this class of problem (Meyer & Needham 2015 The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations. London Mathematical Society Lecture Note Series, vol. 419) which examines the difference of the maximal and minimal solutions to the problem. From this uniqueness result, the approach of Meyer & Needham allows for development of a comparison result which is then used to exhibit global continuous dependence of solutions to the problem on a suitable initial dataset. The comparison and continuous dependence results obtained here are novel to this class of problem. This class of problem arises specifically in the study of a one-step autocatalytic reaction, which is schematically given by A→B at rate a(p)b(q) (where a and b are the concentrations of A and B, respectively, with 0
problem has been lacking up to the present.
Adaptive Thouless-Anderson-Palmer approach to inverse Ising problems with quenched random fields
NASA Astrophysics Data System (ADS)
Huang, Haiping; Kabashima, Yoshiyuki
2013-06-01
The adaptive Thouless-Anderson-Palmer equation is derived for inverse Ising problems in the presence of quenched random fields. We test the proposed scheme on Sherrington-Kirkpatrick, Hopfield, and random orthogonal models and find that the adaptive Thouless-Anderson-Palmer approach allows accurate inference of quenched random fields whose distribution can be either Gaussian or bimodal. In particular, another competitive method for inferring external fields, namely, the naive mean field method with diagonal weights, is compared and discussed.
NASA Astrophysics Data System (ADS)
Koepke, C.; Irving, J.; Roubinet, D.
2014-12-01
Geophysical methods have gained much interest in hydrology over the past two decades because of their ability to provide estimates of the spatial distribution of subsurface properties at a scale that is often relevant to key hydrological processes. Because of an increased desire to quantify uncertainty in hydrological predictions, many hydrogeophysical inverse problems have recently been posed within a Bayesian framework, such that estimates of hydrological properties and their corresponding uncertainties can be obtained. With the Bayesian approach, it is often necessary to make significant approximations to the associated hydrological and geophysical forward models such that stochastic sampling from the posterior distribution, for example using Markov-chain-Monte-Carlo (MCMC) methods, is computationally feasible. These approximations lead to model structural errors, which, so far, have not been properly treated in hydrogeophysical inverse problems. Here, we study the inverse problem of estimating unsaturated hydraulic properties, namely the van Genuchten-Mualem (VGM) parameters, in a layered subsurface from time-lapse, zero-offset-profile (ZOP) ground penetrating radar (GPR) data, collected over the course of an infiltration experiment. In particular, we investigate the effects of assumptions made for computational tractability of the stochastic inversion on model prediction errors as a function of depth and time. These assumptions are that (i) infiltration is purely vertical and can be modeled by the 1D Richards equation, and (ii) the petrophysical relationship between water content and relative dielectric permittivity is known. Results indicate that model errors for this problem are far from Gaussian and independently identically distributed, which has been the common assumption in previous efforts in this domain. In order to develop a more appropriate likelihood formulation, we use (i) a stochastic description of the model error that is obtained through
2009-02-28
each one), as governed by a for- mally tractable source-energy cost function that is physically motivated by ohmic loss control . The derived theory ...The main accomplishments of this work are: • The development of a new theory of the full vector electromagnetic inverse source problem in non...plus reactive power tun- ing). • The demonstration, via many computer simulations, of the effective- ness of this theory as a tool for antenna
NASA Astrophysics Data System (ADS)
Goncharsky, Alexander V.; Romanov, Sergey Y.
2017-02-01
We develop efficient iterative methods for solving inverse problems of wave tomography in models incorporating both diffraction effects and attenuation. In the inverse problem the aim is to reconstruct the velocity structure and the function that characterizes the distribution of attenuation properties in the object studied. We prove mathematically and rigorously the differentiability of the residual functional in normed spaces, and derive the corresponding formula for the Fréchet derivative. The computation of the Fréchet derivative includes solving both the direct problem with the Neumann boundary condition and the reversed-time conjugate problem. We develop efficient methods for numerical computations where the approximate solution is found using the detector measurements of the wave field and its normal derivative. The wave field derivative values at detector locations are found by solving the exterior boundary value problem with the Dirichlet boundary conditions. We illustrate the efficiency of this approach by applying it to model problems. The algorithms developed are highly parallelizable and designed to be run on supercomputers. Among the most promising medical applications of our results is the development of ultrasonic tomographs for differential diagnosis of breast cancer.
Using the Schwinger variational functional for the solution of inverse transport problems
Favorite, J. A.
2002-01-01
A new iterative inverse method for gama-ray transport problems is presented. The method, based on a novel application of the Schwinger variational functional, is developed as a perturbation problem in which the current model (in the iterative process) is considered the initial, unperturbed system, and the actual model is considered the perturbed system. The new method requires the solution of a set of uncoupled one-group forward and adjoint transport equations in each iteration. Four inverse problems are considered: determination of (1) interface locations in a multilayer sourcehhield system; (2) the isotopic composition of an unknown source (including inert elements); (3) interface locations and the source composition simultaneously; and (4) the composition of an unknown layer in the shield. Only the first two problems were actually solved in numerical one-dimensional (spherical) test cases. The method worked well for the unknown interface location problem and extremely well for the unknown source composition problem. Convergence of the method was heavily dependent on the initial guess.
On parameterization of the inverse problem for estimating aquifer properties using tracer data
Kowalsky, M. B.; Finsterle, Stefan A.; Williams, Kenneth H.; Murray, Christopher J.; Commer, Michael; Newcomer, Darrell R.; Englert, Andreas L.; Steefel, Carl I.; Hubbard, Susan
2012-06-11
We consider a field-scale tracer experiment conducted in 2007 in a shallow uranium-contaminated aquifer at Rifle, Colorado. In developing a reliable approach for inferring hydrological properties at the site through inverse modeling of the tracer data, decisions made on how to parameterize heterogeneity (i.e., how to represent a heterogeneous distribution using a limited number of parameters that are amenable to estimation) are of paramount importance. We present an approach for hydrological inversion of the tracer data and explore, using a 2D synthetic example at first, how parameterization affects the solution, and how additional characterization data could be incorporated to reduce uncertainty. Specifically, we examine sensitivity of the results to the configuration of pilot points used in a geostatistical parameterization, and to the sampling frequency and measurement error of the concentration data. A reliable solution of the inverse problem is found when the pilot point configuration is carefully implemented. In addition, we examine the use of a zonation parameterization, in which the geometry of the geological facies is known (e.g., from geophysical data or core data), to reduce the non-uniqueness of the solution and the number of unknown parameters to be estimated. When zonation information is only available for a limited region, special treatment in the remainder of the model is necessary, such as using a geostatistical parameterization. Finally, inversion of the actual field data is performed using 2D and 3D models, and results are compared with slug test data.
NASA Astrophysics Data System (ADS)
Völl, Annika; Stollenwerk, Jochen; Loosen, Peter
2016-03-01
Laser beam intensity distribution profiles for material processing techniques are most of the time restricted to be either of Gaussian or tophat shape. This often leads to different kind of problems especially at the edges of the laser-heated tracks, examples are energy losses or unnecessary overlaps. Thus, machining quality and process efficiency could be much improved by using application specific intensity profiles to generate optimal temperature distributions in the processed material. In this work, we present a numerical method to derive a specific intensity profile for a given temperature distribution. As this problem belongs to the set of inverse heat conduction problems, which are ill-posed, special regularization algorithms are needed. The only method to solve this inverse problem in reasonable time is the conjugate gradient method which we extend to the given problem of laser material processing applications. This method is an iterative approach where in each step the actual temperature distribution is calculated by using the finite element method. In general, the proposed method is applicable for materials with constant or temperature dependent coefficients, for static and dynamic distributions as well as for plane or complex geometries. However, restricting ourselves to plane geometries, intensity distributions that create tophat- or stepped temperature distributions on the plane surface of the processed material are derived and will be presented. In future work, we intend to verify these results using freeform optics as well as singly addressable V(E)CSEL arrays.
NASA Astrophysics Data System (ADS)
Dong, Li; Wijesinghe, Philip; Dantuono, James T.; Sampson, David D.; Munro, Peter R. T.; Kennedy, Brendan F.; Oberai, Assad A.
2016-03-01
Quantitative elasticity imaging, which retrieves elastic modulus maps from tissue, is preferred to qualitative strain imaging for acquiring system- and operator-independent images and longitudinal and multi-site diagnoses. Quantitative elasticity imaging has already been demonstrated in optical elastography by relating surface-acoustic and shear wave speed to Young's modulus via a simple algebraic relationship. Such approaches assume largely homogeneous samples and neglect the effect of boundary conditions. We present a general approach to quantitative elasticity imaging based upon the solution of the inverse elasticity problem using an iterative technique and apply it to compression optical coherence elastography. The inverse problem is one of finding the distribution of Young's modulus within a sample, that in response to an applied load, and a given displacement and traction boundary conditions, can produce a displacement field matching one measured in experiment. Key to our solution of the inverse elasticity problem is the use of the adjoint equations that allow the very efficient evaluation of the gradient of the objective function to be minimized with respect to the unknown values of Young's modulus within the sample. Although we present the approach for the case of linear elastic, isotropic, incompressible solids, this method can be employed for arbitrarily complex mechanical models. We present the details of the method and quantitative elastograms of phantoms and tissues. We demonstrate that by using the inverse approach, we can decouple the artefacts produced by mechanical tissue heterogeneity from the true distribution of Young's modulus, which are often evident in techniques that employ first-order algebraic relationships.
A method of fast, sequential experimental design for linearized geophysical inverse problems
NASA Astrophysics Data System (ADS)
Coles, Darrell A.; Morgan, Frank Dale
2009-07-01
An algorithm for linear(ized) experimental design is developed for a determinant-based design objective function. This objective function is common in design theory and is used to design experiments that minimize the model entropy, a measure of posterior model uncertainty. Of primary significance in design problems is computational expediency. Several earlier papers have focused attention on posing design objective functions and opted to use global search methods for finding the critical points of these functions, but these algorithms are too slow to be practical. The proposed technique is distinguished primarily for its computational efficiency, which derives partly from a greedy optimization approach, termed sequential design. Computational efficiency is further enhanced through formulae for updating determinants and matrix inverses without need for direct calculation. The design approach is orders of magnitude faster than a genetic algorithm applied to the same design problem. However, greedy optimization often trades global optimality for increased computational speed; the ramifications of this tradeoff are discussed. The design methodology is demonstrated on a simple, single-borehole DC electrical resistivity problem. Designed surveys are compared with random and standard surveys, both with and without prior information. All surveys were compared with respect to a `relative quality' measure, the post-inversion model per cent rms error. The issue of design for inherently ill-posed inverse problems is considered and an approach for circumventing such problems is proposed. The design algorithm is also applied in an adaptive manner, with excellent results suggesting that smart, compact experiments can be designed in real time.
NASA Astrophysics Data System (ADS)
Beretta, Elena; Manzoni, Andrea; Ratti, Luca
2017-03-01
In this paper we develop a reconstruction algorithm for the solution of an inverse boundary value problem dealing with a semilinear elliptic partial differential equation of interest in cardiac electrophysiology. The goal is the detection of small inhomogeneities located inside a domain Ω , where the coefficients of the equation are altered, starting from observations of the solution of the equation on the boundary \\partial Ω . Exploiting theoretical results recently achieved in [13], we implement a reconstruction procedure based on the computation of the topological gradient of a suitable cost functional. Numerical results obtained for several test cases finally assess the feasibility and the accuracy of the proposed technique.
Method of Minimax Optimization in the Coefficient Inverse Heat-Conduction Problem
NASA Astrophysics Data System (ADS)
Diligenskaya, A. N.; Rapoport, É. Ya.
2016-07-01
Consideration has been given to the inverse problem on identification of a temperature-dependent thermal-conductivity coefficient. The problem was formulated in an extremum statement as a problem of search for a quantity considered as the optimum control of an object with distributed parameters, which is described by a nonlinear homogeneous spatially one-dimensional Fourier partial equation with boundary conditions of the second kind. As the optimality criterion, the authors used the error (minimized on the time interval of observation) of uniform approximation of the temperature computed on the object's model at an assigned point of the segment of variation in the spatial variable to its directly measured value. Pre-parametrization of the sought control action, which a priori records its description accurate to assigning parameters of representation in the class of polynomial temperature functions, ensured the reduction of the problem under study to a problem of parametric optimization. To solve the formulated problem, the authors used an analytical minimax-optimization method taking account of the alternance properties of the sought optimum solutions based on which the algorithm of computation of the optimum values of the sought parameters is reduced to a system (closed for these unknowns) of equations fixing minimax deviations of the calculated values of temperature from those observed on the time interval of identification. The obtained results confirm the efficiency of the proposed method for solution of a certain range of applied problems. The authors have studied the influence of the coordinate of a point of temperature measurement on the exactness of solution of the inverse problem.
Cheng, Leo K; Bodley, John M; Pullan, Andrew J
2003-01-01
Two predominant source formulations for the inverse problem of electrocardiology currently exist. They involve the reconstruction of epicardial potentials or myocardial activation times from noninvasively recorded torso surface potentials. Each of these formulations have their advantages, however, they have not been systematically compared against each other. We present results from a simulation study which compared a number of epicardial potential (Tikhonov, Truncated singular value decomposition (TSVD), Greensite-Tikhonov and Greensite-TSVD), and a myocardial activation time formulation for the inverse problem of electrocardiology. A number of different methods were also used to determine the appropriate level of regularization (optimal, L-curve, zero-crossing, and composite residual and smoothing operator) to apply to each formulation. The simulation study was conducted using an anatomically based boundary element porcine model with a variety of cardiac sources. Varying levels of geometric error were introduced to the system and solutions were computed using each of the inverse algorithms. Results show that under pure Gaussian noise potential-based methods performed best at low noise levels while the activation-based method was less effected by higher noise levels. In the presence of correlated geometric error, the activation-based method out performed the potential methods, with the Greensite-Tikhonov method being the most favored potential-based method when using the L-curve or zero-crossing method to determine the regularization parameter.
Model-based elastography: a survey of approaches to the inverse elasticity problem.
Doyley, M M
2012-02-07
Elastography is emerging as an imaging modality that can distinguish normal versus diseased tissues via their biomechanical properties. This paper reviews current approaches to elastography in three areas--quasi-static, harmonic and transient--and describes inversion schemes for each elastographic imaging approach. Approaches include first-order approximation methods; direct and iterative inversion schemes for linear elastic; isotropic materials and advanced reconstruction methods for recovering parameters that characterize complex mechanical behavior. The paper's objective is to document efforts to develop elastography within the framework of solving an inverse problem, so that elastography may provide reliable estimates of shear modulus and other mechanical parameters. We discuss issues that must be addressed if model-based elastography is to become the prevailing approach to quasi-static, harmonic and transient elastography: (1) developing practical techniques to transform the ill-posed problem with a well-posed one; (2) devising better forward models to capture the complex mechanical behavior of soft tissues and (3) developing better test procedures to evaluate the performance of modulus elastograms.
On the Optimization of the Inverse Problem for Bouguer Gravity Anomalies
NASA Astrophysics Data System (ADS)
Zamora, A.; Velasco, A. A.; Gutierrez, A. E.
2013-12-01
Inverse modeling of gravity data presents a very ill-posed mathematical problem, given that solutions are non-unique and small changes in parameters (position and density contrast of an anomalous body) can highly impact the resulting Earth's model. Although implementing 2- and 3-Dimensional gravitational inverse problems can determine the structural composition of the Earth, traditional inverse modeling approaches can be very unstable. A model of the shallow substructure is based on the density contrasts of anomalous bodies -with different densities with respect to a uniform region- or the boundaries between layers in a layered environment. We implement an interior-point method constrained optimization technique to improve the 2-D model of the Earth's structure through the use of known density constraints for transitional areas obtained from previous geological observations (e.g. core samples, seismic surveys, etc.). The proposed technique is applied to both synthetic data and gravitational data previously obtained from the Rio Grande Rift and the Cooper Flat Mine region located in Sierra County, New Mexico. We find improvements on the models obtained from this optimization scheme given that getting rid of geologically unacceptable models that would otherwise meet the required geophysical properties reduces the solution space.
Model-based elastography: a survey of approaches to the inverse elasticity problem
NASA Astrophysics Data System (ADS)
Doyley, M. M.
2012-02-01
Elastography is emerging as an imaging modality that can distinguish normal versus diseased tissues via their biomechanical properties. This paper reviews current approaches to elastography in three areas—quasi-static, harmonic and transient—and describes inversion schemes for each elastographic imaging approach. Approaches include first-order approximation methods; direct and iterative inversion schemes for linear elastic; isotropic materials and advanced reconstruction methods for recovering parameters that characterize complex mechanical behavior. The paper's objective is to document efforts to develop elastography within the framework of solving an inverse problem, so that elastography may provide reliable estimates of shear modulus and other mechanical parameters. We discuss issues that must be addressed if model-based elastography is to become the prevailing approach to quasi-static, harmonic and transient elastography: (1) developing practical techniques to transform the ill-posed problem with a well-posed one; (2) devising better forward models to capture the complex mechanical behavior of soft tissues and (3) developing better test procedures to evaluate the performance of modulus elastograms.
Direct and inverse problems in radiation of sound from discrete random sources on two coaxial rings
NASA Technical Reports Server (NTRS)
Maestrello, L.
1979-01-01
An analytical model consisting of two ring sources of sound is developed to study the direct radiation in terms of correlation, coherence, and phase and also to aid in solving the inverse-radiation problem of determining the noise source in terms of farfield measurements. The rings consist of discrete sources which are either monopoles or quadrupoles with Gaussian autocorrelations. Only adjacent sources, both within and between the rings, are correlated. Results show that from the farfield information one can determine when the sources are compact or noncompact with respect to the acoustic wavelength and distinguish between the types of sources. In addition, from the inverse-radiation approach one can recover the center of mass, the location and separation distance of the ring, and the respective diameters.
Solving the Linear Balance Equation on the Globe as a Generalized Inverse Problem
NASA Technical Reports Server (NTRS)
Lu, Huei-Iin; Robertson, Franklin R.
1999-01-01
A generalized (pseudo) inverse technique was developed to facilitate a better understanding of the numerical effects of tropical singularities inherent in the spectral linear balance equation (LBE). Depending upon the truncation, various levels of determinancy are manifest. The traditional fully-determined (FD) systems give rise to a strong response, while the under-determined (UD) systems yield a weak response to the tropical singularities. The over-determined (OD) systems result in a modest response and a large residual in the tropics. The FD and OD systems can be alternatively solved by the iterative method. Differences in the solutions of an UD system exist between the inverse technique and the iterative method owing to the non- uniqueness of the problem. A realistic balanced wind was obtained by solving the principal components of the spectral LBE in terms of vorticity in an intermediate resolution. Improved solutions were achieved by including the singular-component solutions which best fit the observed wind data.
Inverse problem theory in the optical depth profilometry of thin films
NASA Astrophysics Data System (ADS)
Power, J. F.
2002-12-01
The problem of nondestructive measurement of composition with depth on the scale of ˜0.1-500 μm, in polymers and related materials, has many applications in traditional and recent areas of thin film processing. This article reviews the optical depth profilometry techniques operating on this scale based on optical absorption, photoluminescence, elastic, and inelastic scattering. These methods include photoacoustic and photothermal imaging (including pulsed laser opto-acoustic profiling), attenuated total reflectance infrared, integrated optical spectroscopy methods (based on excitation of planar waveguide structures), confocal scanning microscopy, and the recent technique of light profile microscopy. The profiling of planar structures is emphasized. A common element of all of these methods is that depth mapping requires the solution of a linear inverse problem, where a map of the sample properties is mathematically reconstructed from a set of experimental measurements. This problem is to some extent ill conditioned in some or all regimes of measurement, with the result that depth maps may show sensitivity to data errors. A method is presented for assessing performance of the above experimental depth profilometry techniques in terms of ill conditioning as indicated by: spatial resolution, sensitivity to data errors, and apparent multiplicity of solutions. This method is applied a priori given a knowledge of the linear response theory and measurement parameters Application is made to individual profiling techniques, the performance of each in applications is reviewed, and an inter-comparison is made based on the conditioning of the inverse problem.
A new reconstruction method for the inverse source problem from partial boundary measurements
NASA Astrophysics Data System (ADS)
Canelas, Alfredo; Laurain, Antoine; Novotny, Antonio A.
2015-07-01
The inverse source problem consists of reconstructing a mass distribution in a geometrical domain from boundary measurements of the associated potential and its normal derivative. In this paper the inverse source problem is reformulated as a topology optimization problem, where the support of the mass distribution is the unknown variable. The Kohn-Vogelius functional is minimized. It measures the misfit between the solutions of two auxiliary problems containing information about the boundary measurements. The Newtonian potential is used to complement the unavailable information on the hidden boundary. The resulting topology optimization algorithm is based on an analytic formula for the variation of the Kohn-Vogelius functional with respect to a class of mass distributions consisting of a finite number of ball-shaped trial anomalies. The proposed reconstruction algorithm is non-iterative and very robust with respect to noisy data. Finally, in order to show the effectiveness of the devised reconstruction algorithm, some numerical experiments in two and three spatial dimensions are presented.
Numerical solution of an inverse obstacle scattering problem with near-field data
NASA Astrophysics Data System (ADS)
Li, Peijun; Wang, Yuliang
2015-06-01
Consider the scattering of an arbitrary time-harmonic incident wave by a sound soft obstacle. In this paper, a novel method is presented for solving the inverse obstacle scattering problem of the two-dimensional Helmholtz equation, which is to reconstruct the obstacle surface by using the near-field data. The obstacle is assumed to be a small and smooth perturbation of a disc. The method uses the transformed field expansion to reduce the boundary value problem into a successive sequence of one-dimensional problems which are solved in closed forms. By dropping the higher order terms in the power series expansion and truncating the infinite linear system for the first order term, the inverse problem is linearized and an approximate but explicit formula is obtained between the Fourier coefficients of the solution and data. A nonlinear correction algorithm is introduced to improve the accuracy of the reconstructions for large deformations. Numerical examples show that the method is simple, efficient, and stable to reconstruct the obstacle with subwavelength resolution.
A numerical method for the inverse problem of cell traction in 3D
NASA Astrophysics Data System (ADS)
Vitale, G.; Preziosi, L.; Ambrosi, D.
2012-09-01
Force traction microscopy is an inversion method that allows us to obtain the stress field applied by a living cell on the environment on the basis of a pointwise knowledge of the displacement produced by the cell itself. This classical biophysical problem, usually addressed in terms of Green’s functions, can be alternatively tackled in a variational framework. In such a case, a variation of the error functional under suitable regularization is operated in view of its minimization. This setting naturally suggests the introduction of a new equation, based on the adjoint operator of the elasticity problem. In this paper, we illustrate a numerical strategy of the inversion method that discretizes the partial differential equations associated with the optimal control problem by finite elements. A detailed discussion of the numerical approximation of a test problem (with known solution) that contains most of the mathematical difficulties of the real one allows a precise evaluation of the degree of confidence that one can achieve in the numerical results.
Mroczka, Janusz; Szczuczyński, Damian
2012-04-10
We present further results of the simulation research on the constrained regularized least squares (CRLS) solution of the ill-conditioned inverse problem in spectral extinction (turbidimetric) measurements, which we originally presented in this journal [Appl. Opt. 49, 4591 (2010)]. The inverse problem consists of determining the particle size distribution (PSD) function of a particulate system on the basis of a measured extinction coefficient as a function of wavelength. In our previous paper, it was shown that under assumed conditions the problem can be formulated in terms of the discretized Fredholm integral equation of the first kind. The CRLS method incorporates two constraints, which the PSD sought will satisfy: nonnegativity of the PSD values and normalization of the PSD to unity when integrated over the whole range of particle size, into the regularized least squares (RLS) method. This leads to the quadratic programming problem, which is solved by means of the active set algorithm within the research. The simulation research that is the subject of the present paper is a continuation and extension of the research described in our previous paper. In the present research, the performance of the CRLS method variants is compared not only to the corresponding RLS method variants but also to other regularization techniques: the truncated generalized singular value decomposition and the filtered generalized singular value decomposition, as well as nonlinear iterative algorithms: The Twomey algorithm and the Twomey-Markowski algorithm. Moreover, two methods of selecting the optimum value of the regularization parameter are considered: The L-curve method and the generalized cross validation method. The results of our simulation research provide even stronger proof that the CRLS method performs considerably better with reconstruction of PSD than other inversing methods, in terms of better fidelity and smaller uncertainty.
Solutions to the Inverse LQR Problem with Application to Biological Systems Analysis.
Priess, M Cody; Conway, Richard; Choi, Jongeun; Popovich, John M; Radcliffe, Clark
2015-03-01
In this paper, we present a set of techniques for finding a cost function to the time-invariant Linear Quadratic Regulator (LQR) problem in both continuous- and discrete-time cases. Our methodology is based on the solution to the inverse LQR problem, which can be stated as: does a given controller K describe the solution to a time-invariant LQR problem, and if so, what weights Q and R produce K as the optimal solution? Our motivation for investigating this problem is the analysis of motion goals in biological systems. We first describe an efficient Linear Matrix Inequality (LMI) method for determining a solution to the general case of this inverse LQR problem when both the weighting matrices Q and R are unknown. Our first LMI-based formulation provides a unique solution when it is feasible. Additionally, we propose a gradient-based, least-squares minimization method that can be applied to approximate a solution in cases when the LMIs are infeasible. This new method is very useful in practice since the estimated gain matrix K from the noisy experimental data could be perturbed by the estimation error, which may result in the infeasibility of the LMIs. We also provide an LMI minimization problem to find a good initial point for the minimization using the proposed gradient descent algorithm. We then provide a set of examples to illustrate how to apply our approaches to several different types of problems. An important result is the application of the technique to human subject posture control when seated on a moving robot. Results show that we can recover a cost function which may provide a useful insight on the human motor control goal.
Solutions to the Inverse LQR Problem with Application to Biological Systems Analysis
Priess, M Cody; Conway, Richard; Choi, Jongeun; Popovich, John M; Radcliffe, Clark
2015-01-01
In this paper, we present a set of techniques for finding a cost function to the time-invariant Linear Quadratic Regulator (LQR) problem in both continuous- and discrete-time cases. Our methodology is based on the solution to the inverse LQR problem, which can be stated as: does a given controller K describe the solution to a time-invariant LQR problem, and if so, what weights Q and R produce K as the optimal solution? Our motivation for investigating this problem is the analysis of motion goals in biological systems. We first describe an efficient Linear Matrix Inequality (LMI) method for determining a solution to the general case of this inverse LQR problem when both the weighting matrices Q and R are unknown. Our first LMI-based formulation provides a unique solution when it is feasible. Additionally, we propose a gradient-based, least-squares minimization method that can be applied to approximate a solution in cases when the LMIs are infeasible. This new method is very useful in practice since the estimated gain matrix K from the noisy experimental data could be perturbed by the estimation error, which may result in the infeasibility of the LMIs. We also provide an LMI minimization problem to find a good initial point for the minimization using the proposed gradient descent algorithm. We then provide a set of examples to illustrate how to apply our approaches to several different types of problems. An important result is the application of the technique to human subject posture control when seated on a moving robot. Results show that we can recover a cost function which may provide a useful insight on the human motor control goal. PMID:26640359
Electrostatic point charge fitting as an inverse problem: Revealing the underlying ill-conditioning
Ivanov, Maxim V.; Talipov, Marat R.; Timerghazin, Qadir K.
2015-10-07
Atom-centered point charge (PC) model of the molecular electrostatics—a major workhorse of the atomistic biomolecular simulations—is usually parameterized by least-squares (LS) fitting of the point charge values to a reference electrostatic potential, a procedure that suffers from numerical instabilities due to the ill-conditioned nature of the LS problem. To reveal the origins of this ill-conditioning, we start with a general treatment of the point charge fitting problem as an inverse problem and construct an analytical model with the point charges spherically arranged according to Lebedev quadrature which is naturally suited for the inverse electrostatic problem. This analytical model is contrasted to the atom-centered point-charge model that can be viewed as an irregular quadrature poorly suited for the problem. This analysis shows that the numerical problems of the point charge fitting are due to the decay of the curvatures corresponding to the eigenvectors of LS sum Hessian matrix. In part, this ill-conditioning is intrinsic to the problem and is related to decreasing electrostatic contribution of the higher multipole moments, that are, in the case of Lebedev grid model, directly associated with the Hessian eigenvectors. For the atom-centered model, this association breaks down beyond the first few eigenvectors related to the high-curvature monopole and dipole terms; this leads to even wider spread-out of the Hessian curvature values. Using these insights, it is possible to alleviate the ill-conditioning of the LS point-charge fitting without introducing external restraints and/or constraints. Also, as the analytical Lebedev grid PC model proposed here can reproduce multipole moments up to a given rank, it may provide a promising alternative to including explicit multipole terms in a force field.
Eskin, G.
2008-02-15
We consider the inverse boundary value problem for the Schroedinger operator with time-dependent electromagnetic potentials in domains with obstacles. We extend the resuls of the author's works [Inverse Probl. 19, 49 (2003); 19, 985 (2003); 20, 1497 (2004)] to the case of time-dependent potentials. We relate our results to the Aharonov-Bohm effect caused by magnetic and electric fluxes.
FOREWORD: 3rd International Workshop on New Computational Methods for Inverse Problems (NCMIP 2013)
NASA Astrophysics Data System (ADS)
Blanc-Féraud, Laure; Joubert, Pierre-Yves
2013-10-01
Conference logo This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 3rd International Workshop on New Computational Methods for Inverse Problems, NCMIP 2013 (http://www.farman.ens-cachan.fr/NCMIP_2013.html). This workshop took place at Ecole Normale Supérieure de Cachan, in Cachan, France, on 22 May 2013, at the initiative of Institut Farman. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of the ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/), and secondly at the initiative of Institut Farman, in May 2012 (http://www.farman.ens-cachan.fr/NCMIP_2012.html). The 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
FOREWORD: 2nd International Workshop on New Computational Methods for Inverse Problems (NCMIP 2012)
NASA Astrophysics Data System (ADS)
Blanc-Féraud, Laure; Joubert, Pierre-Yves
2012-09-01
Conference logo This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 2nd International Workshop on New Computational Methods for Inverse Problems, (NCMIP 2012). This workshop took place at Ecole Normale Supérieure de Cachan, in Cachan, France, on 15 May 2012, at the initiative of Institut Farman. The first edition of NCMIP also took place in Cachan, France, within the scope of the ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/). The 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 finance. 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
Klinke, David J.; Birtwistle, Marc R.
2015-01-01
Identifying the network of biochemical interactions that underpin disease pathophysiology is a key hurdle in drug discovery. While many components involved in these biological processes are identified, how components organize differently in health and disease remains unclear. In chemical engineering, mechanistic modeling provides a quantitative framework to capture our understanding of a reactive system and test this knowledge against data. Here, we describe an emerging approach to test this knowledge against data that leverages concepts from probability, Bayesian statistics, and chemical kinetics by focusing on two related inverse problems. The first problem is to identify the causal structure of the reaction network, given uncertainty as to how the reactive components interact. The second problem is to identify the values of the model parameters, when a network is known a priori. PMID:26309811
An Augmented Lagrangian Method for a Class of Inverse Quadratic Programming Problems
Zhang Jianzhong; Zhang Liwei
2010-02-15
We consider an inverse quadratic programming (QP) problem in which the parameters in the objective function of a given QP problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a minimization problem with a positive semidefinite cone constraint and its dual is a linearly constrained semismoothly differentiable (SC{sup 1}) convex programming problem with fewer variables than the original one. We demonstrate the global convergence of the augmented Lagrangian method for the dual problem and prove that the convergence rate of primal iterates, generated by the augmented Lagrange method, is proportional to 1/r, and the rate of multiplier iterates is proportional to 1/{radical}r, where r is the penalty parameter in the augmented Lagrangian. As the objective function of the dual problem is a SC{sup 1} function involving the projection operator onto the cone of symmetrically semi-definite matrices, the analysis requires extensive tools such as the singular value decomposition of matrices, an implicit function theorem for semismooth functions, and properties of the projection operator in the symmetric-matrix space. Furthermore, the semismooth Newton method with Armijo line search is applied to solve the subproblems in the augmented Lagrange approach, which is proven to have global convergence and local quadratic rate. Finally numerical results, implemented by the augmented Lagrangian method, are reported.
An inverse problem solution to the flow of tracers in naturally fractured reservoirs
Jetzabeth Ramirez S.; Fernando Samaniego V.; Fernando Rodriguez; Jesus Rivera R.
1994-01-20
This paper presents a solution for the inverse problem to the flow of tracers in naturally fractured reservoirs. The models considered include linear flow in vertical fractures, radial flow in horizontal fractures, and cubic block matrix-fracture geometry. The Rosenbrock method for nonlinear regression used in this study, allowed the estimation of up to six parameters for the cubic block matrix fracture geometry. The nonlinear regression for the three cases was carefully tested against syntetical tracer concentration responses affected by random noise, with the objective of simulating as close as possible step injection field data. Results were obtained within 95 percent confidence limits. The sensitivity of the inverse problem solution on the main parameters that describe this flow problem was investigated. The main features of the nonlinear regression program used in this study are also discussed. The procedure of this study can be applied to interpret tracer tests in naturally fractured reservoirs, allowing the estimation of fracture and matrix parameters of practical interest (longitudinal fracture dispersivity alpha, matrix porosity phi2, fracture half-width w, matrix block size d, matrix diffusion coefficient D2 and the adsorption constant kd). The methodology of this work offers a practical alternative for tracer flow tests interpretation to other techniques.
A Hybrid Optimization Method for Solving Bayesian Inverse Problems under Uncertainty
Zhang, Kai; Wang, Zengfei; Zhang, Liming; Yao, Jun; Yan, Xia
2015-01-01
In this paper, we investigate the application of a new method, the Finite Difference and Stochastic Gradient (Hybrid method), for history matching in reservoir models. History matching is one of the processes of solving an inverse problem by calibrating reservoir models to dynamic behaviour of the reservoir in which an objective function is formulated based on a Bayesian approach for optimization. The goal of history matching is to identify the minimum value of an objective function that expresses the misfit between the predicted and measured data of a reservoir. To address the optimization problem, we present a novel application using a combination of the stochastic gradient and finite difference methods for solving inverse problems. The optimization is constrained by a linear equation that contains the reservoir parameters. We reformulate the reservoir model’s parameters and dynamic data by operating the objective function, the approximate gradient of which can guarantee convergence. At each iteration step, we obtain the relatively ‘important’ elements of the gradient, which are subsequently substituted by the values from the Finite Difference method through comparing the magnitude of the components of the stochastic gradient, which forms a new gradient, and we subsequently iterate with the new gradient. Through the application of the Hybrid method, we efficiently and accurately optimize the objective function. We present a number numerical simulations in this paper that show that the method is accurate and computationally efficient. PMID:26252392
Implementation of probabilistic approach in solving inverse problems as a grid-backed web service.
NASA Astrophysics Data System (ADS)
Kholodkov, K. I.; Aleshin, I. M.; Koryagin, V. N.; Shogin, A. N.; Sukhoroslov, O. V.
2012-04-01
In this work probabilistic approach to inverse problem was adopted. It leads to definition and sampling of a posteriori probability density function (APDF), which combines a priori system information with information, derived from observation data. Use of APDF implies significant computational resourses consumption, even for moderate model parameter count. However the computation of APDF value at different points is carried out completely independently, therefore this problem is considered ideal for loosely coupled distributed computing system. Globus Toolkit middleware was used, including the GridFTP for data transfer and GRAM for execution control, as well as TORQUE resource manager for each computing node. To reduce the hardware cost all grid services, except for GridFTP, run as virtual guests on execution nodes. Due to very insignificant resources utilization the guests make no footprint on node's computation power. To hide complex middleware interface from scientific users, user friendly web interface was created, which provides restricted but sufficient tool set. Determination of seismic anisotropy by wave form inversion was implemented as model problem. The interface allows user to edit model parameters, estimate execution time for specified parameter set, run calculation and perform result visualization. Details of start-up, management and results acquisition are hidden from user. This work was supported by Russian Foundation of Basic Research, grants 10-07-00491-a, 11-05-00988-a and 11-07-12045-ofi-m-2011
SimPEG: An open-source framework for geophysical simulations and inverse problems
NASA Astrophysics Data System (ADS)
Cockett, R.; Kang, S.; Heagy, L.
2014-12-01
Geophysical surveys are powerful tools for obtaining information about the subsurface. Inverse modelling provides a mathematical framework for constructing a model of physical property distributions that are consistent with the data collected by these surveys. The geosciences are increasingly moving towards the integration of geological, geophysical, and hydrological information to better characterize the subsurface. This integration must span disciplines and is not only challenging scientifically, but the inconsistencies between conventions often makes implementations complicated, non-reproducible, or inefficient. We have developed an open source software package for Simulation and Parameter Estimation in Geophysics (SimPEG), which provides a generalized framework for solving geophysical forward and inverse problems. SimPEG is written entirely in Python with minimal dependencies in the hopes that it can be used both as a research tool and for education. SimPEG includes finite volume discretizations on structured and unstructured meshes, interfaces to standard numerical solver packages, convex optimization algorithms, model parameterizations, and tailored visualization routines. The framework is modular and object-oriented, which promotes real time experimentation and combination of geophysical problems and inversion methodologies. In this presentation, we will highlight a few geophysical examples, including direct-current resistivity and electromagnetics, and discuss some of the challenges and successes we encountered in developing a flexible and extensible framework. Throughout development of SimPEG we have focused on simplicity, usability, documentation, and extensive testing. By embracing a fully open source development paradigm, we hope to encourage reproducible research, cooperation, and communication to help tackle some of the inherently multidisciplinary problems that face integrated geophysical methods.
A Subspace Pursuit–based Iterative Greedy Hierarchical Solution to the Neuromagnetic Inverse Problem
Babadi, Behtash; Obregon-Henao, Gabriel; Lamus, Camilo; Hämäläinen, Matti S.; Brown, Emery N.; Purdon, Patrick L.
2013-01-01
Magnetoencephalography (MEG) is an important non-invasive method for studying activity within the human brain. Source localization methods can be used to estimate spatiotemporal activity from MEG measurements with high temporal resolution, but the spatial resolution of these estimates is poor due to the ill-posed nature of the MEG inverse problem. Recent developments in source localization methodology have emphasized temporal as well as spatial constraints to improve source localization accuracy, but these methods can be computationally intense. Solutions emphasizing spatial sparsity hold tremendous promise, since the underlying neurophysiological processes generating MEG signals are often sparse in nature, whether in the form of focal sources, or distributed sources representing large-scale functional networks. Recent developments in the theory of compressed sensing (CS) provide a rigorous framework to estimate signals with sparse structure. In particular, a class of CS algorithms referred to as greedy pursuit algorithms can provide both high recovery accuracy and low computational complexity. Greedy pursuit algorithms are difficult to apply directly to the MEG inverse problem because of the high-dimensional structure of the MEG source space and the high spatial correlation in MEG measurements. In this paper, we develop a novel greedy pursuit algorithm for sparse MEG source localization that overcomes these fundamental problems. This algorithm, which we refer to as the Subspace Pursuit-based Iterative Greedy Hierarchical (SPIGH) inverse solution, exhibits very low computational complexity while achieving very high localization accuracy. We evaluate the performance of the proposed algorithm using comprehensive simulations, as well as the analysis of human MEG data during spontaneous brain activity and somatosensory stimuli. These studies reveal substantial performance gains provided by the SPIGH algorithm in terms of computational complexity, localization accuracy
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.
An optimization approach to multi-dimensional time domain acoustic inverse problems.
Gustafsson, M; He, S
2000-10-01
An optimization approach to a multi-dimensional acoustic inverse problem in the time domain is considered. The density and/or the sound speed are reconstructed by minimizing an objective functional. By introducing dual functions and using the Gauss divergence theorem, the gradient of the objective functional is found as an explicit expression. The parameters are then reconstructed by an iterative algorithm (the conjugate gradient method). The reconstruction algorithm is tested with noisy data, and these tests indicate that the algorithm is stable and robust. The computation time for the reconstruction is greatly improved when the analytic gradient is used.
NASA Astrophysics Data System (ADS)
Lisin, E. A.; Lisina, I. I.; Vaulina, O. S.; Petrov, O. F.
2015-03-01
Solution of the inverse Langevin problem is presented for open dissipative systems with anisotropic interparticle interaction. Possibility of applying this solution for experimental determining the anisotropic interaction forces between dust particles in complex plasmas with ion flow is considered. For this purpose, we have tested the method on the results of numerical simulation of chain structures of particles with quasidipole-dipole interaction, similar to the one occurring due to effects of ion focusing in gas discharges. Influence of charge spatial inhomogeneity and fluctuations on the results of recovery is also discussed.
Zhang, Yang; Liu, Guoqiang; Tao, Chunjing; Wang, Hao; He, Wenjing
2009-01-01
The analysis of electromagnetic forward and inverse problems is very important in the process of image reconstruction for magnetoacoustic tomography with magnetic induction (MAT-MI). A new analysis method was introduced in this paper. It breaks through some illogical supposes that the existing methods applied and can improve the spatial resolution of the image availably. Besides it can avoid rotating the static magnetic field which is very difficult to come true in application, therefore the development of MAT-MI technique can be promoted greatly. To test the validity of the new method, two test models were analyzed, and the availability of the method was demonstrated.
Limitations of polynomial chaos expansions in the Bayesian solution of inverse problems
Lu, Fei; Morzfeld, Matthias; Tu, Xuemin; Chorin, Alexandre J.
2015-02-01
Polynomial chaos expansions are used to reduce the computational cost in the Bayesian solutions of inverse problems by creating a surrogate posterior that can be evaluated inexpensively. We show, by analysis and example, that when the data contain significant information beyond what is assumed in the prior, the surrogate posterior can be very different from the posterior, and the resulting estimates become inaccurate. One can improve the accuracy by adaptively increasing the order of the polynomial chaos, but the cost may increase too fast for this to be cost effective compared to Monte Carlo sampling without a surrogate posterior.
Automatic Processing of Digital Ionograms and Full Wave Solutions for the Profile Inversion Problem.
1981-11-01
Korteweg - deVries Equation ," J. Math. Phys., 18, 2445 (1977). Kay, I., "The Inverse Scattering Problem," Report No. EM-74 of the Institute of Mathematical...3.2 Comparison of the IWKB Method with the Full-Wave Method for Profiles for Which the Full-Wave Equation can be Solved for Exactly 45 3.2.1 General...Section 2 describes the automatic scaling of Digisonde ionograms, and Section 3 investigates the possibility of solving the Schroedinger wave equation for
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...backscattering data for a Coefficient Inverse Problem (CIP) for a hyperbolic PDE are generated by a single location of the point source. We develop a new...98) Prescribed by ANSI Std Z39-18 2 we model the most suitable arrangement for this case, which is to use a single position of the point source and
Inverse problem for extragalactic transport of ultra-high energy cosmic rays
Ptuskin, V.S.; Rogovaya, S.I.; Zirakashvili, V.N. E-mail: rogovaya@izmiran.ru
2015-03-01
The energy spectra and composition of ultra-high energy cosmic rays are changing in a course of propagation in the expanding Universe filled with background radiation. We developed a numerical code for solution of inverse problem for cosmic-ray transport equations that allows the determination of average source spectra of different nuclei from the cosmic ray spectra observed at the Earth. Employing this approach, the injection spectra of protons and Iron nuclei in extragalactic sources are found assuming that only these species are accelerated at the source. The data from the Auger experiment and the combined data from the Telescope Array + HiRes experiments are used to illustrate the method.
An efficient numerical method for solving inverse conduction problem in a hollow cylinder
NASA Astrophysics Data System (ADS)
Mehta, R. C.
1984-06-01
A simple numerical scheme for solving the inverse conduction problem in a hollow cylinder is presented using transient temperature data for estimating the unknown surface conditions. A general digital program is discussed that can treat a variety of boundary conditions using a single set of equations. As an example, the method is applied to estimate the wall heat flux, surface temperature, convective heat transfer coefficient, and combustion gas temperature for a typical divergent rocket nozzle made of mild steel, and the results are compared with experimentally measured outer surface temperature data.
A necessary condition for applying MUSIC algorithm in limited-view inverse scattering problem
NASA Astrophysics Data System (ADS)
Park, Taehoon; Park, Won-Kwang
2015-09-01
Throughout various results of numerical simulations, it is well-known that MUltiple SIgnal Classification (MUSIC) algorithm can be applied in the limited-view inverse scattering problems. However, the application is somehow heuristic. In this contribution, we identify a necessary condition of MUSIC for imaging of collection of small, perfectly conducting cracks. This is based on the fact that MUSIC imaging functional can be represented as an infinite series of Bessel function of integer order of the first kind. Numerical experiments from noisy synthetic data supports our investigation.
NASA Astrophysics Data System (ADS)
Bellassoued, M.; Jellali, D.; Yamamoto, M.
2008-07-01
In this paper we consider the stability of the inverse problem of determining a function q(x) in a wave equation in a bounded smooth domain in from boundary observations. This information is enclosed in the hyperbolic (dynamic) Dirichlet-to-Neumann map associated to the solutions to the wave equation. We prove in the case of n[greater-or-equal, slanted]2 that q(x) is uniquely determined by the range restricted to a subboundary of the Dirichlet-to-Neumann map whose stability is a type of double logarithm.
NASA Technical Reports Server (NTRS)
Nitsche, Ludwig C.; Nitsche, Johannes M.; Brenner, Howard
1988-01-01
The sedimentation and diffusion of a nonneutrally buoyant Brownian particle in vertical fluid-filled cylinder of finite length which is instantaneously inverted at regular intervals are investigated analytically. A one-dimensional convective-diffusive equation is derived to describe the temporal and spatial evolution of the probability density; a periodicity condition is formulated; the applicability of Fredholm theory is established; and the parameter-space regions are determined within which the existence and uniqueness of solutions are guaranteed. Numerical results for sample problems are presented graphically and briefly characterized.
Ultrasonic focusing through inhomogeneous media by application of the inverse scattering problem
Haddadin, Osama S.; Ebbini, Emad S.
2010-01-01
A new approach is introduced for self-focusing phased arrays through inhomogeneous media for therapeutic and imaging applications. This algorithm utilizes solutions to the inverse scattering problem to estimate the impulse response (Green’s function) of the desired focal point(s) at the elements of the array. This approach is a two-stage procedure, where in the first stage the Green’s functions is estimated from measurements of the scattered field taken outside the region of interest. In the second stage, these estimates are used in the pseudoinverse method to compute excitation weights satisfying predefined set of constraints on the structure of the field at the focus points. These scalar, complex valued excitation weights are used to modulate the incident field for retransmission. The pseudoinverse pattern synthesis method requires knowing the Green’s function between the focus points and the array, which is difficult to attain for an unknown inhomogeneous medium. However, the solution to the inverse scattering problem, the scattering function, can be used directly to compute the required inhomogeneous Green’s function. This inverse scattering based self-focusing is noninvasive and does not require a strong point scatterer at or near the desired focus point. It simply requires measurements of the scattered field outside the region of interest. It can be used for high resolution imaging and enhanced therapeutic effects through inhomogeneous media without making any assumptions on the shape, size, or location of the inhomogeneity. This technique is outlined and numerical simulations are shown which validate this technique for single and multiple focusing using a circular array. PMID:9670525
Generalized Uncertainty Quantification for Linear Inverse Problems in X-ray Imaging
Fowler, Michael James
2014-04-25
In industrial and engineering applications, X-ray radiography has attained wide use as a data collection protocol for the assessment of material properties in cases where direct observation is not possible. The direct measurement of nuclear materials, particularly when they are under explosive or implosive loading, is not feasible, and radiography can serve as a useful tool for obtaining indirect measurements. In such experiments, high energy X-rays are pulsed through a scene containing material of interest, and a detector records a radiograph by measuring the radiation that is not attenuated in the scene. One approach to the analysis of these radiographs is to model the imaging system as an operator that acts upon the object being imaged to produce a radiograph. In this model, the goal is to solve an inverse problem to reconstruct the values of interest in the object, which are typically material properties such as density or areal density. The primary objective in this work is to provide quantitative solutions with uncertainty estimates for three separate applications in X-ray radiography: deconvolution, Abel inversion, and radiation spot shape reconstruction. For each problem, we introduce a new hierarchical Bayesian model for determining a posterior distribution on the unknowns and develop efficient Markov chain Monte Carlo (MCMC) methods for sampling from the posterior. A Poisson likelihood, based on a noise model for photon counts at the detector, is combined with a prior tailored to each application: an edge-localizing prior for deconvolution; a smoothing prior with non-negativity constraints for spot reconstruction; and a full covariance sampling prior based on a Wishart hyperprior for Abel inversion. After developing our methods in a general setting, we demonstrate each model on both synthetically generated datasets, including those from a well known radiation transport code, and real high energy radiographs taken at two U. S. Department of Energy
NASA Astrophysics Data System (ADS)
Khan, Junaid Ali; Zahoor Raja, Muhammad Asif; Rashidi, Mohammad Mehdi; Syam, Muhammad Ibrahim; Majid Wazwaz, Abdul
2015-10-01
In this research, the well-known non-linear Lane-Emden-Fowler (LEF) equations are approximated by developing a nature-inspired stochastic computational intelligence algorithm. A trial solution of the model is formulated as an artificial feed-forward neural network model containing unknown adjustable parameters. From the LEF equation and its initial conditions, an energy function is constructed that is used in the algorithm for the optimisation of the networks in an unsupervised way. The proposed scheme is tested successfully by applying it on various test cases of initial value problems of LEF equations. The reliability and effectiveness of the scheme are validated through comprehensive statistical analysis. The obtained numerical results are in a good agreement with their corresponding exact solutions, which confirms the enhancement made by the proposed approach.
Mature red blood cells: from optical model to inverse light-scattering problem
Gilev, Konstantin V.; Yurkin, Maxim A.; Chernyshova, Ekaterina S.; Strokotov, Dmitry I.; Chernyshev, Andrei V.; Maltsev, Valeri P.
2016-01-01
We propose a method for characterization of mature red blood cells (RBCs) morphology, based on measurement of light-scattering patterns (LSPs) of individual RBCs with the scanning flow cytometer and on solution of the inverse light-scattering (ILS) problem for each LSP. We considered a RBC shape model, corresponding to the minimal bending energy of the membrane with isotropic elasticity, and constructed an analytical approximation, which allows rapid simulation of the shape, given the diameter and minimal and maximal thicknesses. The ILS problem was solved by the nearest-neighbor interpolation using a preliminary calculated database of 250,000 theoretical LSPs. For each RBC in blood sample we determined three abovementioned shape characteristics and refractive index, which also allows us to calculate volume, surface area, sphericity index, spontaneous curvature, hemoglobin concentration and content. PMID:27446656
A hybrid differential evolution/Levenberg-Marquardt method for solving inverse transport problems
Bledsoe, Keith C; Favorite, Jeffrey A
2010-01-01
Recently, the Differential Evolution (DE) optimization method was applied to solve inverse transport problems in finite cylindrical geometries and was shown to be far superior to the Levenberg-Marquardt optimization method at finding a global optimum for problems with several unknowns. However, while extremely adept at finding a global optimum solution, the DE method often requires a large number (hundreds or thousands) of transport calculations, making it much slower than the Levenberg-Marquardt method. In this paper, a hybridization of the Differential Evolution and Levenberg-Marquardt approaches is presented. This hybrid method takes advantage of the robust search capability of the Differential Evolution method and the speed of the Levenberg-Marquardt technique.
SEMI-DEFINITE PROGRAMMING TECHNIQUES FOR STRUCTURED QUADRATIC INVERSE EIGENVALUE PROBLEMS
LIN, MATTHEW M.; DONG, BO; CHU, MOODY T.
2014-01-01
In the past decade or so, semi-definite programming (SDP) has emerged as a powerful tool capable of handling a remarkably wide range of problems. This article describes an innovative application of SDP techniques to quadratic inverse eigenvalue problems (QIEPs). The notion of QIEPs is of fundamental importance because its ultimate goal of constructing or updating a vibration system from some observed or desirable dynamical behaviors while respecting some inherent feasibility constraints well suits many engineering applications. Thus far, however, QIEPs have remained challenging both theoretically and computationally due to the great variations of structural constraints that must be addressed. Of notable interest and significance are the uniformity and the simplicity in the SDP formulation that solves effectively many otherwise very difficult QIEPs. PMID:25392603
NASA Astrophysics Data System (ADS)
Gharsalli, Leila; Mohammad-Djafari, Ali; Fraysse, Aurélia; Rodet, Thomas
2013-08-01
Our aim is to solve a linear inverse problem using various methods based on the Variational Bayesian Approximation (VBA). We choose to take sparsity into account via a scale mixture prior, more precisely a student-t model. The joint posterior of the unknown and hidden variable of the mixtures is approximated via the VBA. To do this approximation, classically the alternate algorithm is used. But this method is not the most efficient. Recently other optimization algorithms have been proposed; indeed classical iterative algorithms of optimization such as the steepest descent method and the conjugate gradient have been studied in the space of the probability densities involved in the Bayesian methodology to treat this problem. The main object of this work is to present these three algorithms and a numerical comparison of their performances.
NASA Technical Reports Server (NTRS)
Murio, Diego A.
1991-01-01
An explicit and unconditionally stable finite difference method for the solution of the transient inverse heat conduction problem in a semi-infinite or finite slab mediums subject to nonlinear radiation boundary conditions is presented. After measuring two interior temperature histories, the mollification method is used to determine the surface transient heat source if the energy radiation law is known. Alternatively, if the active surface is heated by a source at a rate proportional to a given function, the nonlinear surface radiation law is then recovered as a function of the interface temperature when the problem is feasible. Two typical examples corresponding to Newton cooling law and Stefan-Boltzmann radiation law respectively are illustrated. In all cases, the method predicts the surface conditions with an accuracy suitable for many practical purposes.
Emulation of higher-order tensors in manifold Monte Carlo methods for Bayesian Inverse Problems
NASA Astrophysics Data System (ADS)
Lan, Shiwei; Bui-Thanh, Tan; Christie, Mike; Girolami, Mark
2016-03-01
The Bayesian approach to Inverse Problems relies predominantly on Markov Chain Monte Carlo methods for posterior inference. The typical nonlinear concentration of posterior measure observed in many such Inverse Problems presents severe challenges to existing simulation based inference methods. Motivated by these challenges the exploitation of local geometric information in the form of covariant gradients, metric tensors, Levi-Civita connections, and local geodesic flows have been introduced to more effectively locally explore the configuration space of the posterior measure. However, obtaining such geometric quantities usually requires extensive computational effort and despite their effectiveness affects the applicability of these geometrically-based Monte Carlo methods. In this paper we explore one way to address this issue by the construction of an emulator of the model from which all geometric objects can be obtained in a much more computationally feasible manner. The main concept is to approximate the geometric quantities using a Gaussian Process emulator which is conditioned on a carefully chosen design set of configuration points, which also determines the quality of the emulator. To this end we propose the use of statistical experiment design methods to refine a potentially arbitrarily initialized design online without destroying the convergence of the resulting Markov chain to the desired invariant measure. The practical examples considered in this paper provide a demonstration of the significant improvement possible in terms of computational loading suggesting this is a promising avenue of further development.
A Bayesian approach to Fourier Synthesis inverse problem with application in SAR imaging
NASA Astrophysics Data System (ADS)
Zhu, Sha; Mohammad-Djafari, Ali
2011-03-01
In this paper we propose a Bayesian approach to the ill-posed inverse problem of Fourier synthesis (FS) which consists in reconstructing a function from partial knowledge of its Fourier Transform (FT) with application in SAR (Synthetic Aperture Radar) imaging. The function to be estimated represents an image of the observed scene. Considering this observed scene is mainly composed of point sources, we propose to use a Generalized Gaussian (GG) prior model, and then the Maximum A posterior (MAP) estimator as the desired solution. In particular, we are interested in bi-static case of spotlight-mode SAR data. In a first step, we consider real valued reflectivities but we account for the complex value of the measured data. The relation between the Fourier transform of the measured data and the unknown scene reflectivity is modeled by a 2D spatial FT. The inverse problem becomes then a FS and depending on the geometry of the data acquisition, only the set of locations in the Fourier space are different. We give a detailed modeling of the data acquisition process that we simulated, then apply the proposed method on those synthetic data to measure its performances compared to some other classical methods. Finally, we demonstrate the performance of the method on experimental SAR data obtained in a collaborative work by ONERA.
NASA Astrophysics Data System (ADS)
Al-Ma'shumah, Fathimah; Permana, Dony; Sidarto, Kuntjoro Adji
2015-12-01
Customer Lifetime Value is an important and useful concept in marketing. One of its benefits is to help a company for budgeting marketing expenditure for customer acquisition and customer retention. Many mathematical models have been introduced to calculate CLV considering the customer retention/migration classification scheme. A fairly new class of these models which will be described in this paper uses Markov Chain Models (MCM). This class of models has the major advantage for its flexibility to be modified to several different cases/classification schemes. In this model, the probabilities of customer retention and acquisition play an important role. From Pfeifer and Carraway, 2000, the final formula of CLV obtained from MCM usually contains nonlinear form of the transition probability matrix. This nonlinearity makes the inverse problem of CLV difficult to solve. This paper aims to solve this inverse problem, yielding the approximate transition probabilities for the customers, by applying metaheuristic optimization algorithm developed by Yang, 2013, Flower Pollination Algorithm. The major interpretation of obtaining the transition probabilities are to set goals for marketing teams in keeping the relative frequencies of customer acquisition and customer retention.
NASA Astrophysics Data System (ADS)
Lawrence, Chris C.; Febbraro, Michael; Flaska, Marek; Pozzi, Sara A.; Becchetti, F. D.
2016-08-01
Verification of future warhead-dismantlement treaties will require detection of certain warhead attributes without the disclosure of sensitive design information, and this presents an unusual measurement challenge. Neutron spectroscopy—commonly eschewed as an ill-posed inverse problem—may hold special advantages for warhead verification by virtue of its insensitivity to certain neutron-source parameters like plutonium isotopics. In this article, we investigate the usefulness of unfolded neutron spectra obtained from organic-scintillator data for verifying a particular treaty-relevant warhead attribute: the presence of high-explosive and neutron-reflecting materials. Toward this end, several improvements on current unfolding capabilities are demonstrated: deuterated detectors are shown to have superior response-matrix condition to that of standard hydrogen-base scintintillators; a novel data-discretization scheme is proposed which removes important detector nonlinearities; and a technique is described for re-parameterizing the unfolding problem in order to constrain the parameter space of solutions sought, sidestepping the inverse problem altogether. These improvements are demonstrated with trial measurements and verified using accelerator-based time-of-flight calculation of reference spectra. Then, a demonstration is presented in which the elemental compositions of low-Z neutron-attenuating materials are estimated to within 10%. These techniques could have direct application in verifying the presence of high-explosive materials in a neutron-emitting test item, as well as other for treaty verification challenges.
Sparse deconvolution for the large-scale ill-posed inverse problem of impact force reconstruction
NASA Astrophysics Data System (ADS)
Qiao, Baijie; Zhang, Xingwu; Gao, Jiawei; Liu, Ruonan; Chen, Xuefeng
2017-01-01
Most previous regularization methods for solving the inverse problem of force reconstruction are to minimize the l2-norm of the desired force. However, these traditional regularization methods such as Tikhonov regularization and truncated singular value decomposition, commonly fail to solve the large-scale ill-posed inverse problem in moderate computational cost. In this paper, taking into account the sparse characteristic of impact force, the idea of sparse deconvolution is first introduced to the field of impact force reconstruction and a general sparse deconvolution model of impact force is constructed. Second, a novel impact force reconstruction method based on the primal-dual interior point method (PDIPM) is proposed to solve such a large-scale sparse deconvolution model, where minimizing the l2-norm is replaced by minimizing the l1-norm. Meanwhile, the preconditioned conjugate gradient algorithm is used to compute the search direction of PDIPM with high computational efficiency. Finally, two experiments including the small-scale or medium-scale single impact force reconstruction and the relatively large-scale consecutive impact force reconstruction are conducted on a composite wind turbine blade and a shell structure to illustrate the advantage of PDIPM. Compared with Tikhonov regularization, PDIPM is more efficient, accurate and robust whether in the single impact force reconstruction or in the consecutive impact force reconstruction.
Inverse transport problem solvers based on regularized and compressive sensing techniques
Cheng, Y.; Cao, L.; Wu, H.; Zhang, H.
2012-07-01
According to the direct exposure measurements from flash radiographic image, regularized-based method and compressive sensing (CS)-based method for inverse transport equation are presented. The linear absorption coefficients and interface locations of objects are reconstructed directly at the same time. With a large number of measurements, least-square method is utilized to complete the reconstruction. Owing to the ill-posedness of the inverse problems, regularized algorithm is employed. Tikhonov method is applied with an appropriate posterior regularization parameter to get a meaningful solution. However, it's always very costly to obtain enough measurements. With limited measurements, CS sparse reconstruction technique Orthogonal Matching Pursuit (OMP) is applied to obtain the sparse coefficients by solving an optimization problem. This paper constructs and takes the forward projection matrix rather than Gauss matrix as measurement matrix. In the CS-based algorithm, Fourier expansion and wavelet expansion are adopted to convert an underdetermined system to a well-posed system. Simulations and numerical results of regularized method with appropriate regularization parameter and that of CS-based agree well with the reference value, furthermore, both methods avoid amplifying the noise. (authors)
NASA Technical Reports Server (NTRS)
Parker, Peter A.; Geoffrey, Vining G.; Wilson, Sara R.; Szarka, John L., III; Johnson, Nels G.
2010-01-01
The calibration of measurement systems is a fundamental but under-studied problem within industrial statistics. The origins of this problem go back to basic chemical analysis based on NIST standards. In today's world these issues extend to mechanical, electrical, and materials engineering. Often, these new scenarios do not provide "gold standards" such as the standard weights provided by NIST. This paper considers the classic "forward regression followed by inverse regression" approach. In this approach the initial experiment treats the "standards" as the regressor and the observed values as the response to calibrate the instrument. The analyst then must invert the resulting regression model in order to use the instrument to make actual measurements in practice. This paper compares this classical approach to "reverse regression," which treats the standards as the response and the observed measurements as the regressor in the calibration experiment. Such an approach is intuitively appealing because it avoids the need for the inverse regression. However, it also violates some of the basic regression assumptions.
NASA Astrophysics Data System (ADS)
Pontes, P. C.; Naveira-Cotta, C. P.
2016-09-01
The theoretical analysis for the design of microreactors in biodiesel production is a complicated task due to the complex liquid-liquid flow and mass transfer processes, and the transesterification reaction that takes place within these microsystems. Thus, computational simulation is an important tool that aids in understanding the physical-chemical phenomenon and, consequently, in determining the suitable conditions that maximize the conversion of triglycerides during the biodiesel synthesis. A diffusive-convective-reactive coupled nonlinear mathematical model, that governs the mass transfer process during the transesterification reaction in parallel plates microreactors, under isothermal conditions, is here described. A hybrid numerical-analytical solution via the Generalized Integral Transform Technique (GITT) for this partial differential system is developed and the eigenfunction expansions convergence rates are extensively analyzed and illustrated. The heuristic method of Particle Swarm Optimization (PSO) is applied in the inverse analysis of the proposed direct problem, to estimate the reaction kinetics constants, which is a critical step in the design of such microsystems. The results present a good agreement with the limited experimental data in the literature, but indicate that the GITT methodology combined with the PSO approach provide a reliable computational algorithm for direct-inverse analysis in such reactive mass transfer problems.
A hybrid algorithm for solving the EEG inverse problem from spatio-temporal EEG data.
Crevecoeur, Guillaume; Hallez, Hans; Van Hese, Peter; D'Asseler, Yves; Dupré, Luc; Van de Walle, Rik
2008-08-01
Epilepsy is a neurological disorder caused by intense electrical activity in the brain. The electrical activity, which can be modelled through the superposition of several electrical dipoles, can be determined in a non-invasive way by analysing the electro-encephalogram. This source localization requires the solution of an inverse problem. Locally convergent optimization algorithms may be trapped in local solutions and when using global optimization techniques, the computational effort can become expensive. Fast recovery of the electrical sources becomes difficult that way. Therefore, there is a need to solve the inverse problem in an accurate and fast way. This paper performs the localization of multiple dipoles using a global-local hybrid algorithm. Global convergence is guaranteed by using space mapping techniques and independent component analysis in a computationally efficient way. The accuracy is locally obtained by using the Recursively Applied and Projected-MUltiple Signal Classification (RAP-MUSIC) algorithm. When using this hybrid algorithm, a four times faster solution is obtained.
A GRASP-based Heuristic for the Sorting by Length-Weighted Inversions Problem.
da Silva Arruda, Thiago; Dias, Ulisses; Dias, Zanoni
2015-08-28
Genome Rearrangements are large-scale mutational events that affect genomes during the evolutionary process. Therefore, these mutations differ from punctual mutations. They can move genes from one place to the other, change the orientation of some genes, or even change the number of chromosomes. In this work, we deal with inversion events which occur when a segment of DNA sequence in the genome is reversed. In our model, each inversion costs the number of elements in the reversed segment. We present a new algorithm for this problem based on the metaheuristic called Greedy Randomized Adaptive Search Procedure (GRASP) that has been routinely used to find solutions for combinatorial optimization problems. In essence, we implemented an iterative process in which each iteration receives a feasible solution whose neighborhood is investigated. Our analysis shows that we outperform any other approach by significant margin. We also use our algorithm to build phylogenetic trees for a subset of species in the Yersinia genus and we compared our trees to other results in the literature.
A linear model approach for ultrasonic inverse problems with attenuation and dispersion.
Carcreff, Ewen; Bourguignon, Sébastien; Idier, Jérôme; Simon, Laurent
2014-07-01
Ultrasonic inverse problems such as spike train deconvolution, synthetic aperture focusing, or tomography attempt to reconstruct spatial properties of an object (discontinuities, delaminations, flaws, etc.) from noisy and incomplete measurements. They require an accurate description of the data acquisition process. Dealing with frequency-dependent attenuation and dispersion is therefore crucial because both phenomena modify the wave shape as the travel distance increases. In an inversion context, this paper proposes to exploit a linear model of ultrasonic data taking into account attenuation and dispersion. The propagation distance is discretized to build a finite set of radiation impulse responses. Attenuation is modeled with a frequency power law and then dispersion is computed to yield physically consistent responses. Using experimental data acquired from attenuative materials, this model outperforms the standard attenuation-free model and other models of the literature. Because of model linearity, robust estimation methods can be implemented. When matched filtering is employed for single echo detection, the model that we propose yields precise estimation of the attenuation coefficient and of the sound velocity. A thickness estimation problem is also addressed through spike deconvolution, for which the proposed model also achieves accurate results.
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.
Baker, J.R.; Budinger, T.F.; Huesman, R.H.
1992-10-01
A major limitation in tomographic inverse problems is inadequate computation speed, which frequently impedes the application of engineering ideas and principles in medical science more than in the physical and engineering sciences. Medical problems are computationally taxing because a minimum description of the system often involves 5 dimensions (3 space, 1 energy, 1 time), with the range of each space coordinate requiring up to 512 samples. The computational tasks for this problem can be simply expressed by posing the problem as one in which the tomograph system response function is spatially invariant, and the noise is additive and Gaussian. Under these assumptions, a number of reconstruction methods have been implemented with generally satisfactory results for general medical imaging purposes. However, if the system response function of the tomograph is assumed more realistically to be spatially variant and the noise to be Poisson, the computational problem becomes much more difficult. Some of the algorithms being studied to compensate for position dependent resolution and statistical fluctuations in the data acquisition process, when expressed in canonical form, are not practical for clinical applications because the number of computations necessary exceeds the capabilities of high performance computer systems currently available. Reconstruction methods based on natural pixels, specifically orthonormal natural pixels, preserve symmetries in the data acquisition process. Fast implementations of orthonormal natural pixel algorithms can achieve orders of magnitude speedup relative to general implementations. Thus, specialized thought in algorithm development can lead to more significant increases in performance than can be achieved through hardware improvements alone.
Davidson, Susan E; Gillespie, Catherine; Allum, William H; Swarbrick, Edwin
2011-01-01
Backgound The number of patients with chronic gastrointestinal (GI) symptoms after cancer therapies which have a moderate or severe impact on quality of life is similar to the number diagnosed with inflammatory bowel disease annually. However, in contrast to patients with inflammatory bowel disease, most of these patients are not referred for gastroenterological assessment. Clinicians who do see these patients are often unaware of the benefits of targeted investigation (which differ from those required to exclude recurrent cancer), the range of available treatments and how the pathological processes underlying side effects of cancer treatment differ from those in benign GI disorders. This paper aims to help clinicians become aware of the problem and suggests ways in which the panoply of syndromes can be managed. Methods A multidisciplinary literature review was performed to develop guidance to facilitate clinical management of GI side effects of cancer treatments. Results Different pathological processes within the GI tract may produce identical symptoms. Optimal management requires appropriate investigations and coordinated multidisciplinary working. Lactose intolerance, small bowel bacterial overgrowth and bile acid malabsorption frequently develop during or after chemotherapy. Toxin-negative Clostridium difficile and cytomegalovirus infection may be fulminant in immunosuppressed patients and require rapid diagnosis and treatment. Hepatic side effects include reactivation of viral hepatitis, sinusoidal obstruction syndrome, steatosis and steatohepatitis. Anticancer biological agents have multiple interactions with conventional drugs. Colonoscopy is contraindicated in neutropenic enterocolitis but endoscopy may be life-saving in other patients with GI bleeding. After cancer treatment, simple questions can identify patients who need referral for specialist management of GI symptoms. Other troublesome pelvic problems (eg, urinary, sexual, nutritional) are frequent
NASA Astrophysics Data System (ADS)
Liu, Boda; Liang, Yan
2017-04-01
Markov chain Monte Carlo (MCMC) simulation is a powerful statistical method in solving inverse problems that arise from a wide range of applications. In Earth sciences applications of MCMC simulations are primarily in the field of geophysics. The purpose of this study is to introduce MCMC methods to geochemical inverse problems related to trace element fractionation during mantle melting. MCMC methods have several advantages over least squares methods in deciphering melting processes from trace element abundances in basalts and mantle rocks. Here we use an MCMC method to invert for extent of melting, fraction of melt present during melting, and extent of chemical disequilibrium between the melt and residual solid from REE abundances in clinopyroxene in abyssal peridotites from Mid-Atlantic Ridge, Central Indian Ridge, Southwest Indian Ridge, Lena Trough, and American-Antarctic Ridge. We consider two melting models: one with exact analytical solution and the other without. We solve the latter numerically in a chain of melting models according to the Metropolis-Hastings algorithm. The probability distribution of inverted melting parameters depends on assumptions of the physical model, knowledge of mantle source composition, and constraints from the REE data. Results from MCMC inversion are consistent with and provide more reliable uncertainty estimates than results based on nonlinear least squares inversion. We show that chemical disequilibrium is likely to play an important role in fractionating LREE in residual peridotites during partial melting beneath mid-ocean ridge spreading centers. MCMC simulation is well suited for more complicated but physically more realistic melting problems that do not have analytical solutions.
NASA Astrophysics Data System (ADS)
Bui-Thanh, T.; Girolami, M.
2014-11-01
We consider the Riemann manifold Hamiltonian Monte Carlo (RMHMC) method for solving statistical inverse problems governed by partial differential equations (PDEs). The Bayesian framework is employed to cast the inverse problem into the task of statistical inference whose solution is the posterior distribution in infinite dimensional parameter space conditional upon observation data and Gaussian prior measure. We discretize both the likelihood and the prior using the H1-conforming finite element method together with a matrix transfer technique. The power of the RMHMC method is that it exploits the geometric structure induced by the PDE constraints of the underlying inverse problem. Consequently, each RMHMC posterior sample is almost uncorrelated/independent from the others providing statistically efficient Markov chain simulation. However this statistical efficiency comes at a computational cost. This motivates us to consider computationally more efficient strategies for RMHMC. At the heart of our construction is the fact that for Gaussian error structures the Fisher information matrix coincides with the Gauss-Newton Hessian. We exploit this fact in considering a computationally simplified RMHMC method combining state-of-the-art adjoint techniques and the superiority of the RMHMC method. Specifically, we first form the Gauss-Newton Hessian at the maximum a posteriori point and then use it as a fixed constant metric tensor throughout RMHMC simulation. This eliminates the need for the computationally costly differential geometric Christoffel symbols, which in turn greatly reduces computational effort at a corresponding loss of sampling efficiency. We further reduce the cost of forming the Fisher information matrix by using a low rank approximation via a randomized singular value decomposition technique. This is efficient since a small number of Hessian-vector products are required. The Hessian-vector product in turn requires only two extra PDE solves using the adjoint
NASA Astrophysics Data System (ADS)
Rudenko, O. V.; Gurbatov, S. N.
2016-07-01
Inverse problems of nonlinear acoustics have important applied significance. On the one hand, they are necessary for nonlinear diagnostics of media, materials, manufactured articles, building units, and biological and geological structures. On the other hand, they are needed for creating devices that ensure optimal action of acoustic radiation on a target. However, despite the many promising applications, this direction remains underdeveloped, especially for strongly distorted high-intensity waves containing shock fronts. An example of such an inverse problem is synthesis of the spatiotemporal structure of a field in a radiating system that ensures the highest possible energy density in the focal region. This problem is also related to the urgent problems of localizing wave energy and the theory of strongly nonlinear waves. Below we analyze some quite general and simple inverse nonlinear problems.
Solution of the nonlinear elasticity imaging inverse problem: The incompressible case.
Goenezen, Sevan; Barbone, Paul; Oberai, Assad A
2011-03-01
We have recently developed and tested an efficient algorithm for solving the nonlinear inverse elasticity problem for a compressible hyperelastic material. The data for this problem are the quasi-static deformation fields within the solid measured at two distinct overall strain levels. The main ingredients of our algorithm are a gradient based quasi-Newton minimization strategy, the use of adjoint equations and a novel strategy for continuation in the material parameters. In this paper we present several extensions to this algorithm. First, we extend it to incompressible media thereby extending its applicability to tissues which are nearly incompressible under slow deformation. We achieve this by solving the forward problem using a residual-based, stabilized, mixed finite element formulation which circumvents the Ladyzenskaya-Babuska-Brezzi condition. Second, we demonstrate how the recovery of the spatial distribution of the nonlinear parameter can be improved either by preconditioning the system of equations for the material parameters, or by splitting the problem into two distinct steps. Finally, we present a new strain energy density function with an exponential stress-strain behavior that yields a deviatoric stress tensor, thereby simplifying the interpretation of pressure when compared with other exponential functions. We test the overall approach by solving for the spatial distribution of material parameters from noisy, synthetic deformation fields.
A fast nonstationary iterative method with convex penalty for inverse problems in Hilbert spaces
NASA Astrophysics Data System (ADS)
Jin, Qinian; Lu, Xiliang
2014-04-01
In this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex functions are introduced as penalty terms. By exploiting the Hilbert space structure of the underlying problems, we propose a fast iterative regularization method which reduces to the classical nonstationary iterated Tikhonov regularization when the penalty term is chosen to be the square of norm. Each iteration of the method consists of two steps: the first step involves only the operator from the problem while the second step involves only the penalty term. This splitting character has the advantage of making the computation efficient. In case the data is corrupted by noise, a stopping rule is proposed to terminate the method and the corresponding regularization property is established. Finally, we test the performance of the method by reporting various numerical simulations, including the image deblurring, the determination of source term in Poisson equation, and the de-autoconvolution problem.
Identification of dynamic characteristics of flexible rotors as dynamic inverse problem
NASA Technical Reports Server (NTRS)
Roisman, W. P.; Vajingortin, L. D.
1991-01-01
The problem of dynamic and balancing of flexible rotors were considered, which were set and solved as the problem of the identification of flexible rotor systems, which is the same as the inverse problem of the oscillation theory dealing with the task of the identifying the outside influences and system parameters on the basis of the known laws of motion. This approach to the problem allows the disclosure the picture of disbalances throughout the rotor-under-test (which traditional methods of flexible rotor balancing, based on natural oscillations, could not provide), and identify dynamic characteristics of the system, which correspond to a selected mathematical model. Eventually, various methods of balancing were developed depending on the special features of the machines as to their design, technology, and operation specifications. Also, theoretical and practical methods are given for the flexible rotor balancing at far from critical rotation frequencies, which does not necessarily require the knowledge forms of oscillation, dissipation, and elasticity and inertia characteristics, and to use testing masses.
Hayakawa, Yoshihiro; Nakajima, Koji
2010-02-01
We have already proposed the inverse function delayed (ID) model as a novel neuron model. The ID model has a negative resistance similar to Bonhoeffer-van der Pol (BVP) model and the network has an energy function similar to Hopfield model. The neural network having an energy can converge on a solution of the combinatorial optimization problem and the computation is in parallel and hence fast. However, the existence of local minima is a serious problem. The negative resistance of the ID model can make the network state free from such local minima by selective destabilization. Hence, we expect that it has a potential to overcome the local minimum problems. In computer simulations, we have already shown that the ID network can be free from local minima and that it converges on the optimal solutions. However, the theoretical analysis has not been presented yet. In this paper, we redefine three types of constraints for the particular problems, then we analytically estimate the appropriate network parameters giving the global minimum states only. Moreover, we demonstrate the validity of estimated network parameters by computer simulations.
On the possibility of control restoration in some inverse problems of heat and mass transfer
NASA Astrophysics Data System (ADS)
Bilchenko, G. G.; Bilchenko, N. G.
2016-11-01
The hypersonic aircraft permeable surfaces effective heat protection problems are considered. The physic-chemical processes (the dissociation and the ionization) in laminar boundary layer of compressible gas are appreciated in mathematical model. The statements of direct problems of heat and mass transfer are given: according to preset given controls it is necessary to compute the boundary layer mathematical model parameters and determinate the local and total heat flows and friction forces and the power of blowing system. The A.A.Dorodnicyn's generalized integral relations method has been used as calculation basis. The optimal control - the blowing into boundary layer (for continuous functions) was constructed as the solution of direct problem in extreme statement with the use of this approach. The statement of inverse problems are given: the control laws ensuring the preset given local heat flow and local tangent friction are restored. The differences between the interpolation and the approximation statements are discussed. The possibility of unique control restoration is established and proved (in the stagnation point). The computational experiments results are presented.
Rosetta Consert Radio Sounding Experiment: A Numerical Method for the Inverse Problem
NASA Astrophysics Data System (ADS)
Cardiet, M.; Herique, A.; Rogez, Y.; Douté, S.; Kofman, W. W.
2014-12-01
Rosetta's module Philae will soon land on 67P CG nucleus, giving unprecedented insight about a comet nucleus, its composition and interior. The CONSERT instrument is one of the 20 scientific instruments of the mission. It's a bistatic two-modules radar, one on the orbiter, one on the lander. They generate EM waves that are transmitted through the nucleus. The signal is therefore delayed and attenuated by the nucleus materials and possible inhomogeneities. An accurate measurement and processing of these signals, repeated along the orbit, will allow us to perform a tomography, and for the first time, map the dielectric properties of a comet nucleus internal structures .Our approach for the resolution of this inverse problem is to use a custom built software called SIMSERT, which simulates the end-to-end experiment, using a ray-tracing algorithm. This tool is the key to prepare CONSERT operation and perform signal analysis. Given a comet shape and a landing site, we have conducted simulations to understand, quantify and get rid of the biases due to the discretization of the shape model.The first inversion using the comet shape model given by OSIRIS and NavCam teams , will assume a propagation in an homogeneous medium. The first goal is to identify and correct artefacts due to the surface interface. The second goal is to evaluate the coherency of the different permittivity estimations given by inverting the latter model on the signal measured at different positions along the orbit. Then it is likely that, based on the first investigations, more sophisticated models (rubble pile, strata) and inversions will be required. A comparative approach between the simulated data and the CONSERT data, will lead to permittivity maps of the nucleus, that are coherent with the observation, with a certain probability. These maps, the first of this type, will provide unprecedented information about the internal structure, the accretion history and the nucleus time evolution.
SU-E-J-161: Inverse Problems for Optical Parameters in Laser Induced Thermal Therapy
Fahrenholtz, SJ; Stafford, RJ; Fuentes, DT
2014-06-01
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 physics 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 MRg
Improving landscape inference by integrating heterogeneous data in the inverse Ising problem
Barrat-Charlaix, Pierre; Figliuzzi, Matteo; Weigt, Martin
2016-01-01
The inverse Ising problem and its generalizations to Potts and continuous spin models have recently attracted much attention thanks to their successful applications in the statistical modeling of biological data. In the standard setting, the parameters of an Ising model (couplings and fields) are inferred using a sample of equilibrium configurations drawn from the Boltzmann distribution. However, in the context of biological applications, quantitative information for a limited number of microscopic spins configurations has recently become available. In this paper, we extend the usual setting of the inverse Ising model by developing an integrative approach combining the equilibrium sample with (possibly noisy) measurements of the energy performed for a number of arbitrary configurations. Using simulated data, we show that our integrative approach outperforms standard inference based only on the equilibrium sample or the energy measurements, including error correction of noisy energy measurements. As a biological proof-of-concept application, we show that mutational fitness landscapes in proteins can be better described when combining evolutionary sequence data with complementary structural information about mutant sequences. PMID:27886273
Hybrid modeling of spatial continuity for application to numerical inverse problems
Friedel, Michael J.; Iwashita, Fabio
2013-01-01
A novel two-step modeling approach is presented to obtain optimal starting values and geostatistical constraints for numerical inverse problems otherwise characterized by spatially-limited field data. First, a type of unsupervised neural network, called the self-organizing map (SOM), is trained to recognize nonlinear relations among environmental variables (covariates) occurring at various scales. The values of these variables are then estimated at random locations across the model domain by iterative minimization of SOM topographic error vectors. Cross-validation is used to ensure unbiasedness and compute prediction uncertainty for select subsets of the data. Second, analytical functions are fit to experimental variograms derived from original plus resampled SOM estimates producing model variograms. Sequential Gaussian simulation is used to evaluate spatial uncertainty associated with the analytical functions and probable range for constraining variables. The hybrid modeling of spatial continuity is demonstrated using spatially-limited hydrologic measurements at different scales in Brazil: (1) physical soil properties (sand, silt, clay, hydraulic conductivity) in the 42 km2 Vargem de Caldas basin; (2) well yield and electrical conductivity of groundwater in the 132 km2 fractured crystalline aquifer; and (3) specific capacity, hydraulic head, and major ions in a 100,000 km2 transboundary fractured-basalt aquifer. These results illustrate the benefits of exploiting nonlinear relations among sparse and disparate data sets for modeling spatial continuity, but the actual application of these spatial data to improve numerical inverse modeling requires testing.
Improving landscape inference by integrating heterogeneous data in the inverse Ising problem
NASA Astrophysics Data System (ADS)
Barrat-Charlaix, Pierre; Figliuzzi, Matteo; Weigt, Martin
2016-11-01
The inverse Ising problem and its generalizations to Potts and continuous spin models have recently attracted much attention thanks to their successful applications in the statistical modeling of biological data. In the standard setting, the parameters of an Ising model (couplings and fields) are inferred using a sample of equilibrium configurations drawn from the Boltzmann distribution. However, in the context of biological applications, quantitative information for a limited number of microscopic spins configurations has recently become available. In this paper, we extend the usual setting of the inverse Ising model by developing an integrative approach combining the equilibrium sample with (possibly noisy) measurements of the energy performed for a number of arbitrary configurations. Using simulated data, we show that our integrative approach outperforms standard inference based only on the equilibrium sample or the energy measurements, including error correction of noisy energy measurements. As a biological proof-of-concept application, we show that mutational fitness landscapes in proteins can be better described when combining evolutionary sequence data with complementary structural information about mutant sequences.
NASA Astrophysics Data System (ADS)
Gauthier, P.-A.; Gérard, A.; Camier, C.; Berry, A.
2014-02-01
Acoustic imaging aims at localization and characterization of sound sources using microphone arrays. In this paper a new regularization method for acoustic imaging by inverse approach is proposed. The method first relies on the singular value decomposition of the plant matrix and on the projection of the measured data on the corresponding singular vectors. In place of regularization using classical methods such as truncated singular value decomposition and Tikhonov regularization, the proposed method involves the direct definition of the filter factors on the basis of a thresholding operation, defined from the estimated measurement noise. The thresholding operation is achieved using modified filter functions. The originality of the approach is to propose the definition of a filter factor which provides more damping to the singular components dominated by noise than that given by the Tikhonov filter. This has the advantage of potentially simplifying the selection of the best regularization amount in inverse problems. Theoretical results show that this method is comparatively more accurate than Tikhonov regularization and truncated singular value decomposition.
NASA Astrophysics Data System (ADS)
Rizzuti, G.; Gisolf, A.
2017-03-01
We study a reconstruction algorithm for the general inverse scattering problem based on the estimate of not only medium properties, as in more conventional approaches, but also wavefields propagating inside the computational domain. This extended set of unknowns is justified as a way to prevent local minimum stagnation, which is a common issue for standard methods. At each iteration of the algorithm, (i) the model parameters are obtained by solution of a convex problem, formulated from a special bilinear relationship of the data with respect to properties and wavefields (where the wavefield is kept fixed), and (ii) a better estimate of the wavefield is calculated, based on the previously reconstructed properties. The resulting scheme is computationally convenient since step (i) can greatly benefit from parallelization and the wavefield update (ii) requires modeling only in the known background model, which can be sped up considerably by factorization-based direct methods. The inversion method is successfully tested on synthetic elastic datasets.
NASA Astrophysics Data System (ADS)
Hetmaniok, Edyta
2016-07-01
In this paper the procedure for solving the inverse problem for the binary alloy solidification in the casting mould is presented. Proposed approach is based on the mathematical model suitable for describing the investigated solidification process, the lever arm model describing the macrosegregation process, the finite element method for solving the direct problem and the artificial bee colony algorithm for minimizing the functional expressing the error of approximate solution. Goal of the discussed inverse problem is the reconstruction of heat transfer coefficient and distribution of temperature in investigated region on the basis of known measurements of temperature.
Thomas, Edward V.; Stork, Christopher L.; Mattingly, John K.
2015-07-01
Inverse radiation transport focuses on identifying the configuration of an unknown radiation source given its observed radiation signatures. The inverse problem is traditionally solved by finding the set of transport model parameter values that minimizes a weighted sum of the squared differences by channel between the observed signature and the signature pre dicted by the hypothesized model parameters. The weights are inversely proportional to the sum of the variances of the measurement and model errors at a given channel. The traditional implicit (often inaccurate) assumption is that the errors (differences between the modeled and observed radiation signatures) are independent across channels. Here, an alternative method that accounts for correlated errors between channels is described and illustrated using an inverse problem based on the combination of gam ma and neutron multiplicity counting measurements.
The inverse problem of brain energetics: ketone bodies as alternative substrates
NASA Astrophysics Data System (ADS)
Calvetti, D.; Occhipinti, R.; Somersalo, E.
2008-07-01
Little is known about brain energy metabolism under ketosis, although there is evidence that ketone bodies have a neuroprotective role in several neurological disorders. We investigate the inverse problem of estimating reaction fluxes and transport rates in the different cellular compartments of the brain, when the data amounts to a few measured arterial venous concentration differences. By using a recently developed methodology to perform Bayesian Flux Balance Analysis and a new five compartment model of the astrocyte-glutamatergic neuron cellular complex, we are able to identify the preferred biochemical pathways during shortage of glucose and in the presence of ketone bodies in the arterial blood. The analysis is performed in a minimally biased way, therefore revealing the potential of this methodology for hypothesis testing.
A numerical method for inverse source problems for Poisson and Helmholtz equations
NASA Astrophysics Data System (ADS)
Hamad, A.; Tadi, M.
2016-11-01
This paper is concerned with an iterative algorithm for inverse evaluation of the source function for two elliptic systems. The algorithm starts with an initial guess for the unknown source function, obtains a background field and, obtains the working equations for the error field. The correction to the assumed value appears as a source term for the error field. It formulates two well-posed problems for the error field which makes it possible to obtain the correction term. The algorithm can also recover the source function with partial data at the boundary. We consider 2-D as well as 3-D domains. The method can be applied to both Poisson and Helmholtz operators. Numerical results indicate that the algorithm can recover close estimates of the unknown source functions based on measurements collected at the boundary.
Adaptive use of prior information in inverse problems: an application to neutron depth profiling
NASA Astrophysics Data System (ADS)
Levenson, Mark S.; Coakley, Kevin J.
2000-03-01
A flexible class of Bayesian models is proposed to solve linear inverse problems. The models generalize linear regularization methods such as Tikhonov regularization and are motivated by the ideas of the image restoration model of Johnson et al (1991 IEEE Trans. Pattern Anal. Machine Intell. 13 413-25). The models allow for the existence of sharp boundaries between regions of different intensities in the signal, as well as the incorporation of prior information on the locations of the boundaries. The use of the prior boundary information is adaptive to the data. The models are applied to data collected to study a multilayer diamond-like carbon film sample using a nondestructive testing procedure known as neutron depth profiling.
Presymplectic current and the inverse problem of the calculus of variations
Khavkine, Igor
2013-11-15
The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when horizontally closed on solutions, allows us to construct a variational formulation for a subsystem of the given PDE. No constraints on the differential order or number of dependent or independent variables are assumed. The proof follows a recent observation of Bridges, Hydon, and Lawson [Math. Proc. Cambridge Philos. Soc. 148(01), 159–178 (2010)] and generalizes an older result of Henneaux [Ann. Phys. 140(1), 45–64 (1982)] from ordinary differential equations (ODEs) to PDEs. Uniqueness of the variational formulation is also discussed.
Lorentz-Lorenz Model for the Inverse Problem of Inhomogeneous Layer Spectrometry
NASA Astrophysics Data System (ADS)
Sotsky, A. B.; Krivetskii, K. N.; Parashkov, S. O.; Sotskaya, L. I.
2016-11-01
A spectrophotometric method is developed for recovery of the dispersion and spatial distribution of the refractive index of inhomogeneous layers using a complete set of experimental data for the reflection spectra of s- and p-polarized waves recorded at several angles of incidence. A Lorentz-Lorenz model is used to solve the inverse problem with the spatial density function and refractive index of the layer material represented by polynomials that are obtained by minimizing the discrepancy between the computed and experimental reflection spectra. The optimum order of the spatial polynomial is found using a criterion based on estimating the errors in the solutions. The effectiveness of this approach is tested experimentally and by numerical simulation.
The relative entropy is fundamental to multiscale and inverse thermodynamic problems
NASA Astrophysics Data System (ADS)
Shell, M. Scott
2008-10-01
We show that the relative entropy, Srel≡∑pT ln(pT/pM), provides a fundamental and unifying framework for multiscale analysis and for inverse molecular-thermodynamic problems involving optimization of a model system (M) to reproduce the properties of a target one (T). We demonstrate that the relative entropy serves as a generating function for principles in variational mean-field theory and uniqueness and gives intuitive results for simple case scenarios in model development. Moreover, we suggest that the relative entropy provides a rigorous framework for multiscale simulations and offers new numerical techniques for linking models at different scales. Finally, we show that Srel carries physical significance by using it to quantify the deviations of a three-site model of water from simple liquids, finding that the relative entropy, a thermodynamic concept, even predicts water's kinetic anomalies.
Preconditioned alternating direction method of multipliers for inverse problems with constraints
NASA Astrophysics Data System (ADS)
Jiao, Yuling; Jin, Qinian; Lu, Xiliang; Wang, Weijie
2017-02-01
We propose a preconditioned alternating direction method of multipliers (ADMM) to solve linear inverse problems in Hilbert spaces with constraints, where the feature of the sought solution under a linear transformation is captured by a possibly non-smooth convex function. During each iteration step, our method avoids solving large linear systems by choosing a suitable preconditioning operator. In case the data is given exactly, we prove the convergence of our preconditioned ADMM without assuming the existence of a Lagrange multiplier. In case the data is corrupted by noise, we propose a stopping rule using information on noise level and show that our preconditioned ADMM is a regularization method; we also propose a heuristic rule when the information on noise level is unavailable or unreliable and give its detailed analysis. Numerical examples are presented to test the performance of the proposed method.
NASA Astrophysics Data System (ADS)
Barbone, Paul E.; Gokhale, Nachiket H.
2004-02-01
We examine the uniqueness of an N-field generalization of a 2D inverse problem associated with elastic modulus imaging: given N linearly independent displacement fields in an incompressible elastic material, determine the shear modulus. We show that for the standard case, N=1, the general solution contains two arbitrary functions which must be prescribed to make the solution unique. In practice, the data required to evaluate the necessary functions are impossible to obtain. For N=2, on the other hand, the general solution contains at most four arbitrary constants, and so very few data are required to find the unique solution. For N=4, the general solution contains only one arbitrary constant. Our results apply to both quasistatic and dynamic deformations.
NASA Astrophysics Data System (ADS)
Ebtehaj, Mohammad
The past decades have witnessed a remarkable emergence of new spaceborne and ground-based sources of multiscale remotely sensed geophysical data. Apart from applications related to the study of short-term climatic shifts, availability of these sources of information has improved dramatically our real-time hydro-meteorological forecast skills. Obtaining improved estimates of hydro-meteorological states from a single or multiple low-resolution observations and assimilating them into the background knowledge of a prognostic model have been a subject of growing research in the past decades. In this thesis, with particular emphasis on precipitation data, statistical structure of rainfall images have been thoroughly studied in transform domains (i.e., Fourier and Wavelet). It is mainly found that despite different underlying physical structure of storm events, there are general statistical signatures that can be robustly characterized and exploited as a prior knowledge for solving hydro-meteorological inverse problems such rainfall downscaling, data fusion, retrieval and data assimilation. In particular, it is observed that in the wavelet domain or derivative space, rainfall images are sparse. In other words, a large number of the rainfall expansion coefficients are very close to zero and only a small number of them are significantly non-zero, a manifestation of the non-Gaussian probabilistic structure of rainfall data. To explain this signature, relevant family of probability models including Generalized Gaussian Density (GGD) and a specific class of conditionally linear Gaussian Scale Mixtures (GSM) are studied. Capitalizing on this important but overlooked property of precipitation, new methodologies are proposed to optimally integrate and improve resolution of spaceborne and ground-based precipitation data. In particular, a unified framework is proposed that ties together the problems of downscaling, data fusion and data assimilation via a regularized variational
NASA Astrophysics Data System (ADS)
Gallovic, F.; Ampuero, J. P.
2015-12-01
Slip inversion methods differ in how the rupture model is parameterized and which regularizations or constraints are applied. However, there is still no consensus about which of the slip inversion methods are preferable and how reliable the inferred source models are due to the non-uniqueness or ill-posedness of the inverse problem. The 'Source Inversion Validation' (SIV) initiative aims to characterize and understand the performance of slip inversion methods (http://equake-rc.info/SIV/). Up to now, four benchmark test cases have been proposed, some of which were even conducted as blind tests. The next step is performing quantitative comparisons of the inverted rupture models. To this aim, we introduce a new comparison technique based on a Singular Value Decomposition (SVD) of the design matrix of the continuum inverse problem. We separate the range and null sub-spaces (representing resolved and unresolved features, respectively) by a selected 'cut-off' singular value, and compare different inverted models to the target (exact) model after projecting them on the range sub-space. This procedure effectively quantifies the ability of an inversion result to reproduce the resolvable features of the source. We find that even with perfect Green's functions the quality of an inverted model deteriorates with decreasing cut-off singular value due to applied regularization (smoothing and positivity constraints). Applying this approach to the inversion results of the SIV2a benchmark from various authors shows that the inferred source images are very similar to the target model when we consider a cut-off at ~1/10 of the largest singular value. Although the truncated model captures the overall rupture propagation, the final slip is biased significantly, showing distinct peaks below the stations lying above the rupture. We also show synthetic experiments to assess the role of station coverage, crustal velocity model, etc. on the conditioning of the slip inversion.
Solution of the nonlinear inverse scattering problem by T -matrix completion. I. Theory
NASA Astrophysics Data System (ADS)
Levinson, Howard W.; Markel, Vadim A.
2016-10-01
We propose a conceptually different method for solving nonlinear inverse scattering problems (ISPs) such as are commonly encountered in tomographic ultrasound imaging, seismology, and other applications. The method is inspired by the theory of nonlocality of physical interactions and utilizes the relevant formalism. We formulate the ISP as a problem whose goal is to determine an unknown interaction potential V from external scattering data. Although we seek a local (diagonally dominated) V as the solution to the posed problem, we allow V to be nonlocal at the intermediate stages of iterations. This allows us to utilize the one-to-one correspondence between V and the T matrix of the problem. Here it is important to realize that not every T corresponds to a diagonal V and we, therefore, relax the usual condition of strict diagonality (locality) of V . An iterative algorithm is proposed in which we seek T that is (i) compatible with the measured scattering data and (ii) corresponds to an interaction potential V that is as diagonally dominated as possible. We refer to this algorithm as to the data-compatible T -matrix completion. This paper is Part I in a two-part series and contains theory only. Numerical examples of image reconstruction in a strongly nonlinear regime are given in Part II [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043318 (2016), 10.1103/PhysRevE.94.043318]. The method described in this paper is particularly well suited for very large data sets that become increasingly available with the use of modern measurement techniques and instrumentation.
NASA Astrophysics Data System (ADS)
Pham, H. V.; Elshall, A. S.; Tsai, F. T.; Yan, L.
2012-12-01
The inverse problem in groundwater modeling deals with a rugged (i.e. ill-conditioned and multimodal), nonseparable and noisy function since it involves solving second order nonlinear partial deferential equations with forcing terms. Derivative-based optimization algorithms may fail to reach a near global solution due to their stagnation at a local minimum solution. To avoid entrapment in a local optimum and enhance search efficiency, this study introduces the covariance matrix adaptation-evolution strategy (CMA-ES) as a local derivative-free optimization method. In the first part of the study, we compare CMA-ES with five commonly used heuristic methods and the traditional derivative-based Gauss-Newton method on a hypothetical problem. This problem involves four different cases to allow a rigorous assessment against ten criterions: ruggedness in terms of nonsmooth and multimodal, ruggedness in terms of ill-conditioning and high nonlinearity, nonseparablity, high dimensionality, noise, algorithm adaptation, algorithm tuning, performance, consistency, parallelization (scaling with number of cores) and invariance (solution vector and function values). The CMA-ES adapts a covariance matrix representing the pair-wise dependency between decision variables, which approximates the inverse of the Hessian matrix up to a certain factor. The solution is updated with the covariance matrix and an adaptable step size, which are adapted through two conjugates that implement heuristic control terms. The covariance matrix adaptation uses information from the current population of solutions and from the previous search path. Since such an elaborate search mechanism is not common in the other heuristic methods, CMA-ES proves to be more robust than other population-based heuristic methods in terms of reaching a near-optimal solution for a rugged, nonseparable and noisy inverse problem. Other favorable properties that the CMA-ES exhibits are the consistency of the solution for repeated
On the ill-conditioned nature of the intracardiac inverse problem.
Bates, Jason H T; Spector, Peter S
2009-01-01
Multi-electrode catheters can be placed transvenously and positioned on the atrial endocardial surface in order to sample the chaotic electrical activity taking place during atrial fibrillation. We consider here the possibility of placing an array of electrodes over a relatively small, and hence roughly planar, region of the atrial surface in order to examine local activity patterns. This provides a spatially coarse but temporally fine sampling of electrical activity that can be expressed at each point in time as the convolution of the true electrical excitation of the tissue with a hyperbolic point spread function. We demonstrate the deconvolution of sampled signals using a polynomial approximation of the true electrical activity. When the deconvolution is unconstrained the inverse problem is poorly conditioned, showing that a high spatial sampling rate is required for accurate reconstructions of atrial activity in the vicinity of the electrode array. We discuss ways in which the conditioning of the problem might be improved through the application of constraints on the solution.
A 2D inverse problem of predicting boiling heat transfer in a long fin
NASA Astrophysics Data System (ADS)
Orzechowski, Tadeusz
2016-10-01
A method for the determination of local values of the heat transfer coefficient on non-isothermal surfaces was analyzed on the example of a long smooth-surfaced fin made of aluminium. On the basis of the experimental data, two cases were taken into consideration: one-dimensional model for Bi < 0.1 and two-dimensional model for thicker elements. In the case when the drop in temperature over the thickness could be omitted, the rejected local values of heat fluxes were calculated from the integral of the equation describing temperature distribution on the fin. The corresponding boiling curve was plotted on the basis of temperature gradient distribution as a function of superheat. For thicker specimens, where Bi > 0.1, the problem was modelled using a 2-D heat conduction equation, for which the boundary conditions were posed on the surface observed with a thermovision camera. The ill-conditioned inverse problem was solved using a method of heat polynomials, which required validation.
Cao, Jianping; Du, Zhengjian; Mo, Jinhan; Li, Xinxiao; Xu, Qiujian; Zhang, Yinping
2016-12-20
Passive sampling is an alternative to active sampling for measuring concentrations of gas-phase volatile organic compounds (VOCs). However, the uncertainty or relative error of the measurements have not been minimized due to the limitations of existing design methods. In this paper, we have developed a novel method, the inverse problem optimization method, to address the problems associated with designing accurate passive samplers. The principle is to determine the most appropriate physical properties of the materials, and the optimal geometry of a passive sampler, by minimizing the relative sampling error based on the mass transfer model of VOCs for a passive sampler. As an example application, we used our proposed method to optimize radial passive samplers for the sampling of benzene and formaldehyde in a normal indoor environment. A new passive sampler, which we have called the Tsinghua Passive Diffusive Sampler (THPDS), for indoor benzene measurement was developed according to the optimized results. Silica zeolite was selected as the sorbent for the THPDS. The measured overall uncertainty of THPDS (22% for benzene) is lower than that of most commercially available passive samplers but is quite a bit larger than the modeled uncertainty (4.8% for benzene, the optimized result), suggesting that further research is required.
Assessment of Tikhonov-type regularization methods for solving atmospheric inverse problems
NASA Astrophysics Data System (ADS)
Xu, Jian; Schreier, Franz; Doicu, Adrian; Trautmann, Thomas
2016-11-01
Inverse problems occurring in atmospheric science aim to estimate state parameters (e.g. temperature or constituent concentration) from observations. To cope with nonlinear ill-posed problems, both direct and iterative Tikhonov-type regularization methods can be used. The major challenge in the framework of direct Tikhonov regularization (TR) concerns the choice of the regularization parameter λ, while iterative regularization methods require an appropriate stopping rule and a flexible λ-sequence. In the framework of TR, a suitable value of the regularization parameter can be generally determined based on a priori, a posteriori, and error-free selection rules. In this study, five practical regularization parameter selection methods, i.e. the expected error estimation (EEE), the discrepancy principle (DP), the generalized cross-validation (GCV), the maximum likelihood estimation (MLE), and the L-curve (LC), have been assessed. As a representative of iterative methods, the iteratively regularized Gauss-Newton (IRGN) algorithm has been compared with TR. This algorithm uses a monotonically decreasing λ-sequence and DP as an a posteriori stopping criterion. Practical implementations pertaining to retrievals of vertically distributed temperature and trace gas profiles from synthetic microwave emission measurements and from real far infrared data, respectively, have been conducted. Our numerical analysis demonstrates that none of the parameter selection methods dedicated to TR appear to be perfect and each has its own advantages and disadvantages. Alternatively, IRGN is capable of producing plausible retrieval results, allowing a more efficient manner for estimating λ.
Inverse scattering for an exterior Dirichlet problem. [due to metallic cylinder
NASA Technical Reports Server (NTRS)
Hariharan, S. I.
1982-01-01
Scattering caused by a metallic cylinder in the field of a wire carrying a periodic current is studied, with a view to determining the location and shape of the cylinder in light of far field measurements between the cylinder and the wire. The associated direct problem is the exterior Dirichlet problem for the Helmholtz equation in two dimensions, and an improved low frequency estimate for its solution by integral equation methods is shown by inverse scattering calculations to be accurate to this estimate. The far field measurements are related to low frequency boundary integral equations whose solutions may be expressed in terms of a mapping function for the exterior of the unknown curve onto the exterior of a unit disk. The conformal transformation's Laurent expansion coefficients can be related to those of the far field, the first of which leads to the calculation of the distance between the source and the cylinder, while the other coefficients are determined by placing the source in a different location.
NASA Astrophysics Data System (ADS)
Ramezanpour, A.
2016-06-01
We study the inverse problem of constructing an appropriate Hamiltonian from a physically reasonable set of orthogonal wave functions for a quantum spin system. Usually, we are given a local Hamiltonian and our goal is to characterize the relevant wave functions and energies (the spectrum) of the system. Here, we take the opposite approach; starting from a reasonable collection of orthogonal wave functions, we try to characterize the associated parent Hamiltonians, to see how the wave functions and the energy values affect the structure of the parent Hamiltonian. Specifically, we obtain (quasi) local Hamiltonians by a complete set of (multilayer) product states and a local mapping of the energy values to the wave functions. On the other hand, a complete set of tree wave functions (having a tree structure) results to nonlocal Hamiltonians and operators which flip simultaneously all the spins in a single branch of the tree graph. We observe that even for a given set of basis states, the energy spectrum can significantly change the nature of interactions in the Hamiltonian. These effects can be exploited in a quantum engineering problem optimizing an objective functional of the Hamiltonian.
Radiative transport in plant canopies: Forward and inverse problem for UAV applications
NASA Astrophysics Data System (ADS)
Furfaro, Roberto
This dissertation deals with modeling the radiative regime in vegetation canopies and the possible remote sensing applications derived by solving the forward and inverse canopy transport equation. The aim of the research is to develop a methodology (called "end-to-end problem solution") that, starting from first principles describing the interaction between light and vegetation, constructs, as the final product, a tool that analyzes remote sensing data for precision agriculture (ripeness prediction). The procedure begins by defining the equations that describe the transport of photons inside the leaf and within the canopy. The resulting integro-differential equations are numerically integrated by adapting the conventional discrete-ordinate methods to compute the reflectance at the top of the canopy. The canopy transport equation is also analyzed to explore its spectral properties. The goal here is to apply Case's method to determine eigenvalues and eigenfunctions and to prove completeness. A model inversion is attempted by using neural network algorithms. Using input-outputs generated by running the forward model, a neural network is trained to learn the inverse map. The model-based neural network represents the end product of the overall procedure. During Oct 2002, an Unmanned Aerial Vehicles (UAVs) equipped with a camera system, flew over Kauai to take images of coffee field plantations. Our goal is to predict the amount of ripe coffee cherries for optimal harvesting. The Leaf-Canopy model was modified to include cherries as absorbing and scattering elements and two classes of neural networks were trained on the model to learn the relationship between reflectance and percentage of ripe, over-ripe and under-ripe cherries. The neural networks are interfaced with images coming from Kauai to predict ripeness percentage. Both ground and airborne images are considered. The latter were taken from the on-board Helios UAV camera system flying over the Kauai coffee field
On the inverse seismic problem for horizontally layered media: Subsidiary study
NASA Astrophysics Data System (ADS)
Cuer, Michel; Petit, Jean Louis
The starting point of this work is the inversion of vertical seismic profiling (VSP) data. The usual processing of VSP data by inverse techniques is restricted to 1D propagation model. In this case, the parameters to identify are the acoustic impedance as function of travel time and the seismic source so that we have as unknowns two functions of one variable and as data a function of two variables, the time and the depth positions of geophones. The problem is thus largely overdetermined and an elementary mathematical analysis can be made. The source is modelled as a boundary condition at the top of the geophones zone. So this boundary condition replaces the true source function and the medium parameters above the geophones zone. The question asked by V. Richard from IFP was the "management" of this unknown source when 3D propagation effects are taken into account in horizontally layered medium where the propagation equations are parametrized by the k parameter of the Hankel transform. Now we think that the answer is that it is impossible to work round the fact that there are at least two unknown functions, the source and the medium parameters above the geophones zone. During this study, we have searched for some non local boundary conditions and this was the opportunity to obtain some results on exact transparent conditions for 3D propagation in 1D media (preliminary communication was made by Petit and Cuer (1994)) and on the discretization of such conditions in the acoustic case (preliminary communication was made by Cuer and Petit (1995)). This is the mathematical substance of this work in which the Poisson summation formula is used to prove the stability of a discrete non local boundary condition.
Circulation of the Carribean Sea: a well-resolved inverse problem
Roemmich, D.
1981-09-20
The Caribbean Sea is selected as a region where the large-scale circulation is well determined by historical hydrographic measurements through application of the inverse method. A simple example is used to illustrate the technique and to demonstrate how some physically relevant quantities may be well determined in the formally underdetermined inverse problem. The geostrophic flow field in the Caribbean is found by imposing mass and salt conservation constraints in seven layers separated by surfaces of constant potential density. An unsmoothed solution is displayed that has weak dependence on an initial choice of reference level. In addition, a unique smoothed solution is shown. Above sigma/sub theta/ = 27.4, the total flow leaving the western Caribbean is estimated to be 29 x 10/sup 6/ m/sup 3/ s/sup -1/, in agreement with direct measurements. This flow is made up of 22 x 10/sup 6/ m/sup 3/s /sup -1/ entering the Caribbean from the east and flowing across the southern half of the basin as the Caribbean Current, and 7 x 10/sup 6/ m/sup 3/ s/sup -1/, in agreement with direct measurements. This flow is made up of 22 x 10/sup 6/ m/sup 3/ s/sup -1/ entering the Caribbean from the east and flowing across the southern half of the basin as the Caribbean Current, and 7 x 10/sup 7/ m/sup 3/ s/sup -1/ entering from the north through Windward Passage. Both of these currents show small-scale variability that diminishes with distance from the respective passages. The deep flow has no net transport, as required by the shallow exit, but a well organized clockwise recirculation is found in the deep eastern Caribbean.
NASA Astrophysics Data System (ADS)
Nazarov, L. A.; Nazarova, L. A.; Romenskii, E. I.; Tcheverda, V. A.; Epov, M. I.
2016-02-01
A method for estimating the stress-strain state of a rock massif in the vicinity of underground facilities is substantiated. This method is based on solution of the boundary inverse problem of defining the components of an external stress field from the acoustic sounding data. The acoustic sounding data used are the arrival times of diving head longitudinal waves, recorded in a long mine shaft. Numerical experiments have revealed the optimal arrangement of the recording network and the limited relative error in the input data, which, taken together, provide for solvability of the inverse problem.
Simplified Solution of the Inverse Problem for Instantaneous Cometary Dust Size Distribution
NASA Astrophysics Data System (ADS)
Kocifaj, M.; Klačka, J.; Kundracek, F.; Videen, G.
Available optical measurements indicate that the modal radius rm of a cometary dust population is in the submicron range and that the dust refractive index m changes slightly in the visible region of the spectrum. A realistic instantaneous particle size distribution f(r) may be determined by processing the measured intensity of continuum at several wavelengths. The solution of the inverse problem for particle size distribution is based on rigorous Mie theory. Additionally, an application of the Rayleigh-Gans approximation enables to construct an accelerated solution scheme since the total intensity of the scattered radiation can then be expressed in an analytical form. However, the range of validity of the approximation is strongly limited to very small submicron-sized particles. The numerical simulations of light scattering by Mie cometary dust particles are performed for two model size distributions - power function f(r) µ r-n and modified gamma function f(r) µ ra e-br, which are commonly used to represent real dust populations. It is shown that the cometary dust size distribution may easily be reproduced analysing the spectral behaviour of measured intensity of the scattered radiation IJ(l). The more rapid increasing of continuum with the wavelength of incident radiation the larger particles are contained in cometary dusty environment.
The multi-scale 3D-1D compatibility scoring for inverse protein folding problem
Oniuka, Kentaro; Asai, Kiyoshi
1994-12-31
The applicability of the Multi-Scale Structure Description (MSSD) scheme to the inverse-folding problems was investigated. An MSSD represents a 3D protein structure with multiple symbolic sequences, where fine structures are represented with the sequence at low levels, the middle scale structural motifs at middle levels, and global topology at high levels. Each symbol in the symbolic sequence denotes a type of local structure of the level scale. The structure fragments are classified at each scale level respectively according to the shape and the environment around the fragments: how the structure is exposed to the solvent or buried in the molecule. I modeled the propensity of an amino-acid sequence to the structure fragment type (i.e., primary constraint) at each scale level. The local propensity is, therefore, modeled at small scale (low) levels, while the global propensity modeled at large scale (high) levels. Thus, superposing all the primary constraints, a 3D protein structure yields an amino-acid sequence profile. Evaluating the fit of an amino acid sequence to the profile derived from the known 3D protein structure, we can identify which 3D structure the given amino-acid sequence would fold into. I checked whether a sequence identifies its own structure over two hundred protein sequences. In many cases, an amino acid sequence identified its own 3D protein structure.
Extraction of skin-friction fields from surface flow visualizations as an inverse problem
NASA Astrophysics Data System (ADS)
Liu, Tianshu
2013-12-01
Extraction of high-resolution skin-friction fields from surface flow visualization images as an inverse problem is discussed from a unified perspective. The surface flow visualizations used in this study are luminescent oil-film visualization and heat-transfer and mass-transfer visualizations with temperature- and pressure-sensitive paints (TSPs and PSPs). The theoretical foundations of these global methods are the thin-oil-film equation and the limiting forms of the energy- and mass-transport equations at a wall, which are projected onto the image plane to provide the relationships between a skin-friction field and the relevant quantities measured by using an imaging system. Since these equations can be re-cast in the same mathematical form as the optical flow equation, they can be solved by using the variational method in the image plane to extract relative or normalized skin-friction fields from images. Furthermore, in terms of instrumentation, essentially the same imaging system for measurements of luminescence can be used in these surface flow visualizations. Examples are given to demonstrate the applications of these methods in global skin-friction diagnostics of complex flows.
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.
NASA Astrophysics Data System (ADS)
Bao, Xingxian; Cao, Aixia; Zhang, Jing
2016-07-01
Modal parameters estimation plays an important role for structural health monitoring. Accurately estimating the modal parameters of structures is more challenging as the measured vibration response signals are contaminated with noise. This study develops a mathematical algorithm of solving the partially described inverse singular value problem (PDISVP) combined with the complex exponential (CE) method to estimate the modal parameters. The PDISVP solving method is to reconstruct an L2-norm optimized (filtered) data matrix from the measured (noisy) data matrix, when the prescribed data constraints are one or several sets of singular triplets of the matrix. The measured data matrix is Hankel structured, which is constructed based on the measured impulse response function (IRF). The reconstructed matrix must maintain the Hankel structure, and be lowered in rank as well. Once the filtered IRF is obtained, the CE method can be applied to extract the modal parameters. Two physical experiments, including a steel cantilever beam with 10 accelerometers mounted, and a steel plate with 30 accelerometers mounted, excited by an impulsive load, respectively, are investigated to test the applicability of the proposed scheme. In addition, the consistency diagram is proposed to exam the agreement among the modal parameters estimated from those different accelerometers. Results indicate that the PDISVP-CE method can significantly remove noise from measured signals and accurately estimate the modal frequencies and damping ratios.
Inverse Problem for Color Doppler Ultrasound-Assisted Intracardiac Blood Flow Imaging
Jang, Jaeseong
2016-01-01
For the assessment of the left ventricle (LV), echocardiography has been widely used to visualize and quantify geometrical variations of LV. However, echocardiographic image itself is not sufficient to describe a swirling pattern which is a characteristic blood flow pattern inside LV without any treatment on the image. We propose a mathematical framework based on an inverse problem for three-dimensional (3D) LV blood flow reconstruction. The reconstruction model combines the incompressible Navier-Stokes equations with one-direction velocity component of the synthetic flow data (or color Doppler data) from the forward simulation (or measurement). Moreover, time-varying LV boundaries are extracted from the intensity data to determine boundary conditions of the reconstruction model. Forward simulations of intracardiac blood flow are performed using a fluid-structure interaction model in order to obtain synthetic flow data. The proposed model significantly reduces the local and global errors of the reconstructed flow fields. We demonstrate the feasibility and potential usefulness of the proposed reconstruction model in predicting dynamic swirling patterns inside the LV over a cardiac cycle. PMID:27313657
NASA Astrophysics Data System (ADS)
Sjöberg, L. E.
2012-11-01
We derive computational formulas for determining the Clairaut constant, i.e. the cosine of the maximum latitude of the geodesic arc, from two given points on the oblate ellipsoid of revolution. In all cases the Clairaut constant is unique. The inverse geodetic problem on the ellipsoid is to determine the geodesic arc between and the azimuths of the arc at the given points. We present the solution for the fixed Clairaut constant. If the given points are not(nearly) antipodal, each azimuth and location of the geodesic is unique, while for the fixed points in the ”antipodal region”, roughly within 36”.2 from the antipode, there are two geodesics mirrored in the equator and with complementary azimuths at each point. In the special case with the given points located at the poles of the ellipsoid, all meridians are geodesics. The special role played by the Clairaut constant and the numerical integration make this method different from others available in the literature.
An algorithmic framework for Mumford-Shah regularization of inverse problems in imaging
NASA Astrophysics Data System (ADS)
Hohm, Kilian; Storath, Martin; Weinmann, Andreas
2015-11-01
The Mumford-Shah model is a very powerful variational approach for edge preserving regularization of image reconstruction processes. However, it is algorithmically challenging because one has to deal with a non-smooth and non-convex functional. In this paper, we propose a new efficient algorithmic framework for Mumford-Shah regularization of inverse problems in imaging. It is based on a splitting into specific subproblems that can be solved exactly. We derive fast solvers for the subproblems which are key for an efficient overall algorithm. Our method neither requires a priori knowledge of the gray or color levels nor of the shape of the discontinuity set. We demonstrate the wide applicability of the method for different modalities. In particular, we consider the reconstruction from Radon data, inpainting, and deconvolution. Our method can be easily adapted to many further imaging setups. The relevant condition is that the proximal mapping of the data fidelity can be evaluated a within reasonable time. In other words, it can be used whenever classical Tikhonov regularization is possible.
An analytical approach to estimate the number of small scatterers in 2D inverse scattering problems
NASA Astrophysics Data System (ADS)
Fazli, Roohallah; Nakhkash, Mansor
2012-07-01
This paper presents an analytical method to estimate the location and number of actual small targets in 2D inverse scattering problems. This method is motivated from the exact maximum likelihood estimation of signal parameters in white Gaussian noise for the linear data model. In the first stage, the method uses the MUSIC algorithm to acquire all possible target locations and in the next stage, it employs an analytical formula that works as a spatial filter to determine which target locations are associated to the actual ones. The ability of the method is examined for both the Born and multiple scattering cases and for the cases of well-resolved and non-resolved targets. Many numerical simulations using both the coincident and non-coincident arrays demonstrate that the proposed method can detect the number of actual targets even in the case of very noisy data and when the targets are closely located. Using the experimental microwave data sets, we further show that this method is successful in specifying the number of small inclusions.
Using eigenmodes to perform the inverse problem associated with resonant ultrasound spectroscopy
David Hurley; Farhad Farzbod
2012-11-01
In principle, resonant ultrasonic spectroscopy (RUS) can be used to characterize any parameter that influences the mechanical resonant response of a sample. Examples include the elastic constants, sample dimensions, and crystal orientation. Extracting the parameter of interest involves performing the inverse problem, which typically entails an iterative routine that compares calculated and measured eigenfrequencies. Here, we propose an alternative method based on laser-based resonant ultrasound spectroscopy (LRUS) that uses the eigenmodes. LRUS uses a pulsed laser to thermoelastically excite ultrasound and an interferometer to detect out-of-plane displacement associated with ultrasonic resonances. By raster scanning the probe along the sample surface, an image of the out-ofplane displacement pattern (i.e., eigenmode) is obtained. As an example of this method, we describe a technique to calculate the crystallographic orientation of a single-crystal high-purity copper sample. The crystallographic orientation is computed by comparing theoretical and experimental eigenmodes. The computed angle is shown to be in very good agreement with the angle obtained using electron backscatter diffraction. In addition, a comparison is made using eigenfrequencies and eigenmodes to calculate the crystallographic orientation. It is found for this particular application, the eigenmode method has superior sensitivity to crystal orientation.
On the inverse problem of blade design for centrifugal pumps and fans
NASA Astrophysics Data System (ADS)
Kruyt, N. P.; Westra, R. W.
2014-06-01
The inverse problem of blade design for centrifugal pumps and fans has been studied. The solution to this problem provides the geometry of rotor blades that realize specified performance characteristics, together with the corresponding flow field. Here a three-dimensional solution method is described in which the so-called meridional geometry is fixed and the distribution of the azimuthal angle at the three-dimensional blade surface is determined for blades of infinitesimal thickness. The developed formulation is based on potential-flow theory. Besides the blade impermeability condition at the pressure and suction side of the blades, an additional boundary condition at the blade surface is required in order to fix the unknown blade geometry. For this purpose the mean-swirl distribution is employed. The iterative numerical method is based on a three-dimensional finite element method approach in which the flow equations are solved on the domain determined by the latest estimate of the blade geometry, with the mean-swirl distribution boundary condition at the blade surface being enforced. The blade impermeability boundary condition is then used to find an improved estimate of the blade geometry. The robustness of the method is increased by specific techniques, such as spanwise-coupled solution of the discretized impermeability condition and the use of under-relaxation in adjusting the estimates of the blade geometry. Various examples are shown that demonstrate the effectiveness and robustness of the method in finding a solution for the blade geometry of different types of centrifugal pumps and fans. The influence of the employed mean-swirl distribution on the performance characteristics is also investigated.
NASA Astrophysics Data System (ADS)
Nassar, Mohamed K.; Ginn, Timothy R.
2014-08-01
We investigate the effect of computational error on the inversion of a density-dependent flow and transport model, using SEAWAT and UCODE-2005 in an inverse identification of hydraulic conductivity and dispersivity using head and concentration data from a 2-D laboratory experiment. We investigated inversions using three different solution schemes including variation of number of particles and time step length, in terms of the three aspects: the shape and smoothness of the objective function surface, the consequent impacts to the optimization, and the resulting Pareto analyses. This study demonstrates that the inversion is very sensitive to the choice of the forward model solution scheme. In particular, standard finite difference methods provide the smoothest objective function surface; however, this is obtained at the cost of numerical artifacts that can lead to erroneous warping of the objective function surface. Total variation diminishing (TVD) schemes limit these impacts at the cost of more computation time, while the hybrid method of characteristics (HMOC) approach with increased particle numbers and/or reduced time step gives both smoothed and accurate objective function surface. Use of the most accurate methods (TVD and HMOC) did lead to successful inversion of the two parameters; however, with distinct results for Pareto analyses. These results illuminate the sensitivity of the inversion to a number of aspects of the forward solution of the density-driven flow problem and reveal that parameter values may result that are erroneous but that counteract numerical errors in the solution.
NASA Astrophysics Data System (ADS)
Dolenko, T. A.; Burikov, S. A.; Vervald, E. N.; Efitorov, A. O.; Laptinskiy, K. A.; Sarmanova, O. E.; Dolenko, S. A.
2017-02-01
Elaboration of methods for the control of biochemical reactions with deoxyribonucleic acid (DNA) strands is necessary for the solution of one of the basic problems in the creation of biocomputers—improvement in the reliability of molecular DNA computing. In this paper, the results of the solution of the four-parameter inverse problem of laser Raman spectroscopy—the determination of the type and concentration of each of the DNA nitrogenous bases in multi-component solutions—are presented.
Terekhov, Alexander V; Pesin, Yakov B; Niu, Xun; Latash, Mark L; Zatsiorsky, Vladimir M
2010-09-01
We consider the problem of what is being optimized in human actions with respect to various aspects of human movements and different motor tasks. From the mathematical point of view this problem consists of finding an unknown objective function given the values at which it reaches its minimum. This problem is called the inverse optimization problem. Until now the main approach to this problems has been the cut-and-try method, which consists of introducing an objective function and checking how it reflects the experimental data. Using this approach, different objective functions have been proposed for the same motor action. In the current paper we focus on inverse optimization problems with additive objective functions and linear constraints. Such problems are typical in human movement science. The problem of muscle (or finger) force sharing is an example. For such problems we obtain sufficient conditions for uniqueness and propose a method for determining the objective functions. To illustrate our method we analyze the problem of force sharing among the fingers in a grasping task. We estimate the objective function from the experimental data and show that it can predict the force-sharing pattern for a vast range of external forces and torques applied to the grasped object. The resulting objective function is quadratic with essentially non-zero linear terms.
Pesin, Yakov B.; Niu, Xun; Latash, Mark L.
2010-01-01
We consider the problem of what is being optimized in human actions with respect to various aspects of human movements and different motor tasks. From the mathematical point of view this problem consists of finding an unknown objective function given the values at which it reaches its minimum. This problem is called the inverse optimization problem. Until now the main approach to this problems has been the cut-and-try method, which consists of introducing an objective function and checking how it reflects the experimental data. Using this approach, different objective functions have been proposed for the same motor action. In the current paper we focus on inverse optimization problems with additive objective functions and linear constraints. Such problems are typical in human movement science. The problem of muscle (or finger) force sharing is an example. For such problems we obtain sufficient conditions for uniqueness and propose a method for determining the objective functions. To illustrate our method we analyze the problem of force sharing among the fingers in a grasping task. We estimate the objective function from the experimental data and show that it can predict the force-sharing pattern for a vast range of external forces and torques applied to the grasped object. The resulting objective function is quadratic with essentially non-zero linear terms. PMID:19902213
Magnetic field topology of τ Scorpii. The uniqueness problem of Stokes V ZDI inversions
NASA Astrophysics Data System (ADS)
Kochukhov, O.; Wade, G. A.
2016-02-01
Context. The early B-type star τ Sco exhibits an unusually complex, relatively weak surface magnetic field. Its topology was previously studied with the Zeeman Doppler imaging (ZDI) modelling of high-resolution circular polarisation (Stokes V) observations. Aims: Here we assess the robustness of the Stokes V ZDI reconstruction of the magnetic field geometry of τ Sco and explore the consequences of using different parameterisations of the surface magnetic maps. Methods: This analysis is based on the archival ESPaDOnS high-resolution Stokes V observations and employs an independent ZDI magnetic inversion code. Results: We succeeded in reproducing previously published magnetic field maps of τ Sco using both general harmonic expansion and a direct, pixel-based representation of the magnetic field. These maps suggest that the field topology of τ Sco is comprised of comparable contributions of the poloidal and toroidal magnetic components. At the same time, we also found that available Stokes V observations can be successfully fitted with restricted harmonic expansions, by either neglecting the toroidal field altogether, or linking the radial and horizontal components of the poloidal field as required by the widely used potential field extrapolation technique. These alternative modelling approaches lead to a stronger and topologically more complex surface field structure. The field distributions, which were recovered with different ZDI options, differ significantly and yield indistinguishable Stokes V profiles but different linear polarisation (Stokes Q and U) signatures. Conclusions: Our investigation underscores the well-known problem of non-uniqueness of the Stokes V ZDI inversions. For the magnetic stars with properties similar to τ Sco (relatively complex field, slow rotation) the outcome of magnetic reconstruction strongly depends on the adopted field parameterisation, rendering photospheric magnetic mapping and determination of the extended magnetospheric
Bakhos, Tania; Saibaba, Arvind K.; Kitanidis, Peter K.
2015-10-15
We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in solving these inverse problems using Newton-type methods is the computational cost associated with solving the forward problem and with repeated construction of the Jacobian, which represents the sensitivity of the measurements to the unknown parameters. Forming the Jacobian can be prohibitively expensive because it requires repeated solutions of the forward and adjoint time-dependent parabolic partial differential equations corresponding to multiple sources and receivers. We propose an efficient method based on a Laplace transform-based exponential time integrator combined with a flexible Krylov subspace approach to solve the resulting shifted systems of equations efficiently. Our proposed solver speeds up the computation of the forward and adjoint problems, thus yielding significant speedup in total inversion time. We consider an application from Transient Hydraulic Tomography (THT), which is an imaging technique to estimate hydraulic parameters related to the subsurface from pressure measurements obtained by a series of pumping tests. The algorithms discussed are applied to a synthetic example taken from THT to demonstrate the resulting computational gains of this proposed method.
A Bayesian approach to multiscale inverse problems with on-the-fly scale determination
NASA Astrophysics Data System (ADS)
Ellam, Louis; Zabaras, Nicholas; Girolami, Mark
2016-12-01
A Bayesian computational approach is presented to provide a multi-resolution estimate of an unknown spatially varying parameter from indirect measurement data. In particular, we are interested in spatially varying parameters with multiscale characteristics. In our work, we consider the challenge of not knowing the characteristic length scale(s) of the unknown a priori, and present an algorithm for on-the-fly scale determination. Our approach is based on representing the spatial field with a wavelet expansion. Wavelet basis functions are hierarchically structured, localized in both spatial and frequency domains and tend to provide sparse representations in that a large number of wavelet coefficients are approximately zero. For these reasons, wavelet bases are suitable for representing permeability fields with non-trivial correlation structures. Moreover, the intra-scale correlations between wavelet coefficients form a quadtree, and this structure is exploited to identify additional basis functions to refine the model. Bayesian inference is performed using a sequential Monte Carlo (SMC) sampler with a Markov Chain Monte Carlo (MCMC) transition kernel. The SMC sampler is used to move between posterior densities defined on different scales, thereby providing a computationally efficient method for adaptive refinement of the wavelet representation. We gain insight from the marginal likelihoods, by computing Bayes factors, for model comparison and model selection. The marginal likelihoods provide a termination criterion for our scale determination algorithm. The Bayesian computational approach is rather general and applicable to several inverse problems concerning the estimation of a spatially varying parameter. The approach is demonstrated with permeability estimation for groundwater flow using pressure sensor measurements.
Růzek, Michal; Sedlák, Petr; Seiner, Hanus; Kruisová, Alena; Landa, Michal
2010-12-01
In this paper, linearized approximations of both the forward and the inverse problems of resonant ultrasound spectroscopy for the determination of mechanical properties of thin surface layers are presented. The linear relations between the frequency shifts induced by the deposition of the layer and the in-plane elastic coefficients of the layer are derived and inverted, the applicability range of the obtained linear model is discussed by a comparison with nonlinear models and finite element method (FEM), and an algorithm for the estimation of experimental errors in the inversely determined elastic coefficients is described. In the final part of the paper, the linearized inverse procedure is applied to evaluate elastic coefficients of a 310 nm thick diamond-like carbon layer deposited on a silicon substrate.
Albocher, U; Barbone, P E; Richards, M S; Oberai, A A; Harari, I
2014-01-01
We apply the adjoint weighted equation method (AWE) to the direct solution of inverse problems of incompressible plane strain elasticity. We show that based on untreated noisy displacements, the reconstruction of the shear modulus can be very poor. We link this poor performance to loss of coercivity of the weak form when treating problems with discontinuous coefficients. We demonstrate that by smoothing the displacements and appending a regularization term to the AWE formulation, a dramatic improvement in the reconstruction can be achieved. With these improvements, the advantages of the AWE method as a direct solution approach can be extended to a wider range of problems.
Albocher, U.; Barbone, P.E.; Richards, M.S.; Oberai, A.A.; Harari, I.
2014-01-01
We apply the adjoint weighted equation method (AWE) to the direct solution of inverse problems of incompressible plane strain elasticity. We show that based on untreated noisy displacements, the reconstruction of the shear modulus can be very poor. We link this poor performance to loss of coercivity of the weak form when treating problems with discontinuous coefficients. We demonstrate that by smoothing the displacements and appending a regularization term to the AWE formulation, a dramatic improvement in the reconstruction can be achieved. With these improvements, the advantages of the AWE method as a direct solution approach can be extended to a wider range of problems. PMID:25383085
NASA Technical Reports Server (NTRS)
Sidi, Avram; Pennline, James A.
1999-01-01
In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + definite integral of g(x, t)F(t,y(t))dt with limits between 0 and 1,0 less than or equal to x les than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integral equations arise, e.g., when one applied Green's function techniques to nonlinear two-point boundary value problems of the form y "(x) =f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and y(l) = y(sub l), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trepezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal rule, thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.
NASA Technical Reports Server (NTRS)
Sidi, Avram; Pennline, James A.
1999-01-01
In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + integral(0 to 1) g(x,t) F(t, y(t)) dt, 0 less than or equal to x less than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integrals equations arise, e.g., when one applies Green's function techniques to nonlinear two-point boundary value problems of the form U''(x) = f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and g(l) = y(sub 1), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trapezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.
NASA Astrophysics Data System (ADS)
Jia, Junxiong; Peng, Jigen; Yang, Jiaqing
2017-04-01
In this paper, we focus on a space-time fractional diffusion equation with the generalized Caputo's fractional derivative operator and a general space nonlocal operator (with the fractional Laplace operator as a special case). A weak Harnack's inequality has been established by using a special test function and some properties of the space nonlocal operator. Based on the weak Harnack's inequality, a strong maximum principle has been obtained which is an important characterization of fractional parabolic equations. With these tools, we establish a uniqueness result of an inverse source problem on the determination of the temporal component of the inhomogeneous term, which seems to be the first theoretical result of the inverse problem for such a general fractional diffusion model.
Piskozub, J.
1994-12-31
The multifrequency lidar inverse problem discussed consists of calculating the size distribution of sol particles from backscattered lidar data. Sea-water (marine) aerosol is particularly well suited for this kind of study as its scattering characteristics can be accurately represented by Mie theory as its particles are almost spherical and their complex index of refraction is well known. Here, a solution of the inverse problem concerning finding aerosol size distribution for a multifrequency lidar system working on a small number of wavelengths is proposed. The solution involves a best-fit method of finding parameters in a pre-set formula of particle size distribution. A comparison of results calculated with the algorithm from experimental lidar profiles with PMS data collected in Baltic Sea coastal zone is given.
NASA Astrophysics Data System (ADS)
Vedelago, J.; Quiroga, A.; Valente, M.
2014-10-01
Diffusion of ferric ions in ferrous sulfate (Fricke) gels represents one of the main drawbacks of some radiation detectors, such as Fricke gel dosimeters. In practice, this disadvantage can be overcome by prompt dosimeter analysis, and constraining strongly the time between irradiation and analysis, implementing special dedicated protocols aimed at minimizing signal blurring due to diffusion effects. This work presents a novel analytic modeling and numerical calculation approach of diffusion coefficients in Fricke gel radiation sensitive materials. Samples are optically analyzed by means of visible light transmission measurements by capturing images with a charge-coupled device camera provided with a monochromatic filter corresponding to the XO-infused Fricke solution absorbance peak. Dose distributions in Fricke gels are suitably delivered by assessing specific initial conditions further studied by periodical sample image acquisitions. Diffusion coefficient calculations were performed using a set of computational algorithms based on inverse problem formulation. Although 1D approaches to the diffusion equation might provide estimations of the diffusion coefficient, it should be calculated in the 2D framework due to the intrinsic bi-dimensional characteristics of Fricke gel layers here considered as radiation dosimeters. Thus a suitable 2D diffusion model capable of determining diffusion coefficients was developed by fitting the obtained algorithm numerical solutions with the corresponding experimental data. Comparisons were performed by introducing an appropriate functional in order to analyze both experimental and numerical values. Solutions to the second-order diffusion equation are calculated in the framework of a dedicated method that incorporates finite element method. Moreover, optimized solutions can be attained by gradient-type minimization algorithms. Knowledge about diffusion coefficient for a Fricke gel radiation detector is helpful in accounting for
NASA Astrophysics Data System (ADS)
Fujimoto, Ken'ichi; Tanaka, Yoshihiro; Abou Al-Ola, Omar M.; Yoshinaga, Tetsuya
2014-06-01
We propose a novel approach for solving box-constrained inverse problems in intensity-modulated radiation therapy (IMRT) treatment planning based on the idea of continuous dynamical methods and split-feasibility algorithms. Our method can compute a feasible solution without the second derivative of an objective function, which is required for gradient-based optimization algorithms. We prove theoretically that a double Kullback-Leibler divergence can be used as the Lyapunov function for the IMRT planning system.
NASA Astrophysics Data System (ADS)
Cui, Tiangang; Marzouk, Youssef; Willcox, Karen
2016-06-01
Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or noisy data, the state variation and parameter dependence of the forward model, and correlations in the prior collectively provide useful structure that can be exploited for dimension reduction in this setting-both in the parameter space of the inverse problem and in the state space of the forward model. To this end, we show how to jointly construct low-dimensional subspaces of the parameter space and the state space in order to accelerate the Bayesian solution of the inverse problem. As a byproduct of state dimension reduction, we also show how to identify low-dimensional subspaces of the data in problems with high-dimensional observations. These subspaces enable approximation of the posterior as a product of two factors: (i) a projection of the posterior onto a low-dimensional parameter subspace, wherein the original likelihood is replaced by an approximation involving a reduced model; and (ii) the marginal prior distribution on the high-dimensional complement of the parameter subspace. We present and compare several strategies for constructing these subspaces using only a limited number of forward and adjoint model simulations. The resulting posterior approximations can rapidly be characterized using standard sampling techniques, e.g., Markov chain Monte Carlo. Two numerical examples demonstrate the accuracy and efficiency of our approach: inversion of an integral equation in atmospheric remote sensing, where the data dimension is very high; and the inference of a heterogeneous transmissivity field in a groundwater system, which involves a partial differential equation forward model with high dimensional state and parameters.
NASA Astrophysics Data System (ADS)
Dorn, O.; Lesselier, D.
2010-07-01
Inverse problems in electromagnetics have a long history and have stimulated exciting research over many decades. New applications and solution methods are still emerging, providing a rich source of challenging topics for further investigation. The purpose of this special issue is to combine descriptions of several such developments that are expected to have the potential to fundamentally fuel new research, and to provide an overview of novel methods and applications for electromagnetic inverse problems. There have been several special sections published in Inverse Problems over the last decade addressing fully, or partly, electromagnetic inverse problems. Examples are: Electromagnetic imaging and inversion of the Earth's subsurface (Guest Editors: D Lesselier and T Habashy) October 2000 Testing inversion algorithms against experimental data (Guest Editors: K Belkebir and M Saillard) December 2001 Electromagnetic and ultrasonic nondestructive evaluation (Guest Editors: D Lesselier and J Bowler) December 2002 Electromagnetic characterization of buried obstacles (Guest Editors: D Lesselier and W C Chew) December 2004 Testing inversion algorithms against experimental data: inhomogeneous targets (Guest Editors: K Belkebir and M Saillard) December 2005 Testing inversion algorithms against experimental data: 3D targets (Guest Editors: A Litman and L Crocco) February 2009 In a certain sense, the current issue can be understood as a continuation of this series of special sections on electromagnetic inverse problems. On the other hand, its focus is intended to be more general than previous ones. Instead of trying to cover a well-defined, somewhat specialized research topic as completely as possible, this issue aims to show the broad range of techniques and applications that are relevant to electromagnetic imaging nowadays, which may serve as a source of inspiration and encouragement for all those entering this active and rapidly developing research area. Also, the
NASA Astrophysics Data System (ADS)
Urmanov, A. M.; Gribok, A. V.; Bozdogan, H.; Hines, J. W.; Uhrig, R. E.
2002-04-01
We propose an information complexity-based regularization parameter selection method for solution of ill conditioned inverse problems. The regularization parameter is selected to be the minimizer of the Kullback-Leibler (KL) distance between the unknown data-generating distribution and the fitted distribution. The KL distance is approximated by an information complexity criterion developed by Bozdogan. The method is not limited to the white Gaussian noise case. It can be extended to correlated and non-Gaussian noise. It can also account for possible model misspecification. We demonstrate the performance of the proposed method on a test problem from Hansen's regularization tools.
Inverse Problems and a Unified Approach to Integrability in 1, 1+1 and 2+1 Dimensions,
1986-01-01
PROBLEMS IN 2+1 w-, Let us consider the Davey-Stewartson equation (a two dimensional ana- logue of the nonlinear Schr ~ dinger equation ) . J. 1 2 2 2Q 2... depends on appropriate inverse data T(zR,zlfm 2 ..... Mn), zRc]Rn, zi]R,. m C R. T satisfies --hf==._T .Using this equation and introducing Born variables...Schro- p dinger equation one can reconstruct the potential in closed form, here one can only reduce the general problem to one for 2 x 2 matrices in
Numerical inversion of the Laplace transform in some problems of granular media dynamics
NASA Astrophysics Data System (ADS)
Yavich, Nikolay B.
2004-04-01
Approximated value for the vertical displacement of a surface bounding a half space and a layer laying on rigid foundation filled with granular medium caused by a vertical symmetric load is received here. The results obtained for Kandaurov standard linear medium model are used. This model takes in account an internal friction. The Papoulis method of numerical inversion of the Laplace transform is applied.
On parameterization of the inverse problem for estimating aquifer properties using tracer data
NASA Astrophysics Data System (ADS)
Kowalsky, M. B.; Finsterle, S.; Williams, K. H.; Murray, C.; Commer, M.; Newcomer, D.; Englert, A.; Steefel, C. I.; Hubbard, S. S.
2012-06-01
In developing a reliable approach for inferring hydrological properties through inverse modeling of tracer data, decisions made on how to parameterize heterogeneity (i.e., how to represent a heterogeneous distribution using a limited number of parameters that are amenable to estimation) are of paramount importance, as errors in the model structure are partly compensated for by estimating biased property values during the inversion. These biased estimates, while potentially providing an improved fit to the calibration data, may lead to wrong interpretations and conclusions and reduce the ability of the model to make reliable predictions. We consider the estimation of spatial variations in permeability and several other parameters through inverse modeling of tracer data, specifically synthetic and actual field data associated with the 2007 Winchester experiment from the Department of Energy Rifle site. Characterization is challenging due to the real-world complexities associated with field experiments in such a dynamic groundwater system. Our aim is to highlight and quantify the impact on inversion results of various decisions related to parameterization, such as the positioning of pilot points in a geostatistical parameterization; the handling of up-gradient regions; the inclusion of zonal information derived from geophysical data or core logs; extension from 2-D to 3-D; assumptions regarding the gradient direction, porosity, and the semivariogram function; and deteriorating experimental conditions. This work adds to the relatively limited number of studies that offer guidance on the use of pilot points in complex real-world experiments involving tracer data (as opposed to hydraulic head data).
Ogawa, Takahiro; Haseyama, Miki
2016-10-10
This paper presents adaptive subspace-based inverse projections via division into multiple sub-problems (ASIP-DIMS) for missing image data restoration. In the proposed method, a target problem for estimating missing image data is divided into multiple sub-problems, and each sub-problem is iteratively solved with constraints of other known image data. By projection into a subspace model of image patches, the solution of each subproblem is calculated, where we call this procedure "subspacebased inverse projection" for simplicity. The proposed method can use higher-dimensional subspaces for finding unique solutions in each sub-problem, and successful restoration becomes feasible since a high level of image representation performance can be preserved. This is the biggest contribution of this paper. Furthermore, the proposed method generates several subspaces from known training examples and enables derivation of a new criterion in the above framework to adaptively select the optimal subspace for each target patch. In this way, the proposed method realizes missing image data restoration using ASIP-DIMS. Since our method can estimate any kind of missing image data, its potential in two image restoration tasks, image inpainting and super-resolution, based on several methods for multivariate analysis is also shown in this paper.
Local sensitivity analysis for inverse problems solved by singular value decomposition
Hill, M.C.; Nolan, B.T.
2010-01-01
Local sensitivity analysis provides computationally frugal ways to evaluate models commonly used for resource management, risk assessment, and so on. This includes diagnosing inverse model convergence problems caused by parameter insensitivity and(or) parameter interdependence (correlation), understanding what aspects of the model and data contribute to measures of uncertainty, and identifying new data likely to reduce model uncertainty. Here, we consider sensitivity statistics relevant to models in which the process model parameters are transformed using singular value decomposition (SVD) to create SVD parameters for model calibration. The statistics considered include the PEST identifiability statistic, and combined use of the process-model parameter statistics composite scaled sensitivities and parameter correlation coefficients (CSS and PCC). The statistics are complimentary in that the identifiability statistic integrates the effects of parameter sensitivity and interdependence, while CSS and PCC provide individual measures of sensitivity and interdependence. PCC quantifies correlations between pairs or larger sets of parameters; when a set of parameters is intercorrelated, the absolute value of PCC is close to 1.00 for all pairs in the set. The number of singular vectors to include in the calculation of the identifiability statistic is somewhat subjective and influences the statistic. To demonstrate the statistics, we use the USDA’s Root Zone Water Quality Model to simulate nitrogen fate and transport in the unsaturated zone of the Merced River Basin, CA. There are 16 log-transformed process-model parameters, including water content at field capacity (WFC) and bulk density (BD) for each of five soil layers. Calibration data consisted of 1,670 observations comprising soil moisture, soil water tension, aqueous nitrate and bromide concentrations, soil nitrate concentration, and organic matter content. All 16 of the SVD parameters could be estimated by
NASA Technical Reports Server (NTRS)
Devasia, Santosh; Bayo, Eduardo
1993-01-01
This paper addresses the problem of inverse dynamics for articulated flexible structures with both lumped and distributed actuators. This problem arises, for example, in the combined vibration minimization and trajectory control of space robots and structures. A new inverse dynamics scheme for computing the nominal lumped and distributed inputs for tracking a prescribed trajectory is given.
NASA Astrophysics Data System (ADS)
Devasia, Santosh; Bayo, Eduardo
1993-02-01
This paper addresses the problem of inverse dynamics for articulated flexible structures with both lumped and distributed actuators. This problem arises, for example, in the combined vibration minimization and trajectory control of space robots and structures. A new inverse dynamics scheme for computing the nominal lumped and distributed inputs for tracking a prescribed trajectory is given.
Scott, I; Phelps, G; Dalton, S
2014-12-01
Healthcare in Australia faces significant challenges. Variations in care, suboptimal safety and reliability, fragmentation of care and unsustainable cost increases are compounded by substantial overuse and underuse of clinical interventions. These problems arise not from intentional actions of individual clinicians, but from deficiencies in the design, operations and governance of systems of care. Physicians play an important role in optimising systems of care and, in doing so, must rely on enhanced skills in a range of domains. These include: how to evaluate and improve quality and safety of clinical processes; analyse and interpret clinical and administrative data in ways that can be used to enhance care delivery; build and lead cohesive multidisciplinary teams capable of solving operational defects and inefficient workarounds; and implement new and effective innovations in clinical service delivery. While clinical skills are essential in individual patient care, skills that improve systems of care targeting whole patient populations will become increasingly desirable and recognised as core skills.
[Optimization approach to inverse problems in near-infrared optical tomography].
Li, Weitao; Wang, Huinan; Qian, Zhiyu
2008-04-01
In this paper, we introduce an optimization approach to the inverse model of near-infrared optical tomography (NIR OT), which can reconstruct the optical properties, namely the absorption and scattering coefficients of thick tissue such as brain and breast tissues. A modeling and simulation tool, named Femlab and based on finite element methods, has been tested wherein the forward models are based on the diffusion equation. Then the inverse model is soved; this is regarded as an optimization approach, including the tests on difference between the measured data and the predicted data, and the optimization methods of optical properties. The algorithms used for optimization are multi-species Genetic Algorithms based on multi-encoding. At last, the whole strategy for the Femlab and optimization approach is given. The strategy is proved to be sufficient by the simulation results.
Inverse backscattering problem for the generalized nonlinear Schrödinger operator in two dimensions
NASA Astrophysics Data System (ADS)
Serov, V.; Sandhu, J.
2010-08-01
The inverse Born approximation is studied for the generalized nonlinear two-dimensional Schrödinger equation - \\Delta u + \\sum _ {l = 0} ^ m \\alpha _ l |u| ^ l u = k ^ 2 u, where the real-valued unknown potentials αl belong to L ^ {p} _ {\\mathrm{comp}} (\\mathbb {R} ^ 2) for some 2 <= p <= ∞ and their Fourier transforms belong to the space L ^ {s} (\\mathbb {R} ^ 2) for some 1 < s < 2. We prove that the leading-order singularities of the sum of the unknown potentials can be recovered from the inverse Born approximation. We also prove that the approximation is equal to the true function up to sum of two functions: one of them from the Sobolev space Ht while the other being a continuous function.
NASA Technical Reports Server (NTRS)
Fymat, A. L.; Lenoble, J.
1979-01-01
The paper considers three complementary inverse multiple scattering problems relating to a uniquely defined atmospheric scattering model. Consideration is given to the appropriateness, for data inversion purposes, of intensities observed in diffuse reflection under a variety of experimental conditions; the uniqueness of the inverse solution is investigated. It is found that light curves representing monotonic variations, such as limb darkening curves and phase curves for a planetary (e.g., Venus) disk center are unsuitable for inferring atmospheric and scattering parameters.
A statistical approach for isolating fossil fuel emissions in atmospheric inverse problems
Yadav, Vineet; Michalak, Anna M.; Ray, Jaideep; Shiga, Yoichi P.
2016-10-27
We study independent verification and quantification of fossil fuel (FF) emissions that constitutes a considerable scientific challenge. By coupling atmospheric observations of CO_{2} with models of atmospheric transport, inverse models offer the possibility of overcoming this challenge. However, disaggregating the biospheric and FF flux components of terrestrial fluxes from CO_{2} concentration measurements has proven to be difficult, due to observational and modeling limitations. In this study, we propose a statistical inverse modeling scheme for disaggregating winter time fluxes on the basis of their unique error covariances and covariates, where these covariances and covariates are representative of the underlying processes affecting FF and biospheric fluxes. The application of the method is demonstrated with one synthetic and two real data prototypical inversions by using in situ CO_{2} measurements over North America. Also, inversions are performed only for the month of January, as predominance of biospheric CO_{2} signal relative to FF CO_{2} signal and observational limitations preclude disaggregation of the fluxes in other months. The quality of disaggregation is assessed primarily through examination of a posteriori covariance between disaggregated FF and biospheric fluxes at regional scales. Findings indicate that the proposed method is able to robustly disaggregate fluxes regionally at monthly temporal resolution with a posteriori cross covariance lower than 0.15 µmol m^{-2} s^{-1} between FF and biospheric fluxes. Error covariance models and covariates based on temporally varying FF inventory data provide a more robust disaggregation over static proxies (e.g., nightlight intensity and population density). However, the synthetic data case study shows that disaggregation is possible even in absence of detailed temporally varying FF inventory data.
A statistical approach for isolating fossil fuel emissions in atmospheric inverse problems
Yadav, Vineet; Michalak, Anna M.; Ray, Jaideep; ...
2016-10-27
We study independent verification and quantification of fossil fuel (FF) emissions that constitutes a considerable scientific challenge. By coupling atmospheric observations of CO2 with models of atmospheric transport, inverse models offer the possibility of overcoming this challenge. However, disaggregating the biospheric and FF flux components of terrestrial fluxes from CO2 concentration measurements has proven to be difficult, due to observational and modeling limitations. In this study, we propose a statistical inverse modeling scheme for disaggregating winter time fluxes on the basis of their unique error covariances and covariates, where these covariances and covariates are representative of the underlying processes affectingmore » FF and biospheric fluxes. The application of the method is demonstrated with one synthetic and two real data prototypical inversions by using in situ CO2 measurements over North America. Also, inversions are performed only for the month of January, as predominance of biospheric CO2 signal relative to FF CO2 signal and observational limitations preclude disaggregation of the fluxes in other months. The quality of disaggregation is assessed primarily through examination of a posteriori covariance between disaggregated FF and biospheric fluxes at regional scales. Findings indicate that the proposed method is able to robustly disaggregate fluxes regionally at monthly temporal resolution with a posteriori cross covariance lower than 0.15 µmol m-2 s-1 between FF and biospheric fluxes. Error covariance models and covariates based on temporally varying FF inventory data provide a more robust disaggregation over static proxies (e.g., nightlight intensity and population density). However, the synthetic data case study shows that disaggregation is possible even in absence of detailed temporally varying FF inventory data.« less
A statistical approach for isolating fossil fuel emissions in atmospheric inverse problems
NASA Astrophysics Data System (ADS)
Yadav, Vineet; Michalak, Anna M.; Ray, Jaideep; Shiga, Yoichi P.
2016-10-01
Independent verification and quantification of fossil fuel (FF) emissions constitutes a considerable scientific challenge. By coupling atmospheric observations of CO2 with models of atmospheric transport, inverse models offer the possibility of overcoming this challenge. However, disaggregating the biospheric and FF flux components of terrestrial fluxes from CO2 concentration measurements has proven to be difficult, due to observational and modeling limitations. In this study, we propose a statistical inverse modeling scheme for disaggregating winter time fluxes on the basis of their unique error covariances and covariates, where these covariances and covariates are representative of the underlying processes affecting FF and biospheric fluxes. The application of the method is demonstrated with one synthetic and two real data prototypical inversions by using in situ CO2 measurements over North America. Inversions are performed only for the month of January, as predominance of biospheric CO2 signal relative to FF CO2 signal and observational limitations preclude disaggregation of the fluxes in other months. The quality of disaggregation is assessed primarily through examination of a posteriori covariance between disaggregated FF and biospheric fluxes at regional scales. Findings indicate that the proposed method is able to robustly disaggregate fluxes regionally at monthly temporal resolution with a posteriori cross covariance lower than 0.15 µmol m-2 s-1 between FF and biospheric fluxes. Error covariance models and covariates based on temporally varying FF inventory data provide a more robust disaggregation over static proxies (e.g., nightlight intensity and population density). However, the synthetic data case study shows that disaggregation is possible even in absence of detailed temporally varying FF inventory data.
Information-theory-based solution of the inverse problem in classical statistical mechanics.
D'Alessandro, Marco; Cilloco, Francesco
2010-08-01
We present a procedure for the determination of the interaction potential from the knowledge of the radial pair distribution function. The method, realized inside an inverse Monte Carlo simulation scheme, is based on the application of the maximum entropy principle of information theory and the interaction potential emerges as the asymptotic expression of the transition probability. Results obtained for high density monoatomic fluids are very satisfactory and provide an accurate extraction of the potential, despite a modest computational effort.
Modeling direct and inverse problems in ferritic heat-exchanger tubes
NASA Astrophysics Data System (ADS)
Sabbagh, Harold A.; Aldrin, John C.; Murphy, R. Kim; Sabbagh, Elias H.
2012-05-01
We develop forward and inverse models, together with laboratory data, to characterize a SEACURE tube, with and without a drilled hole and/or tube-support plate (TSP). The measured data are impedances obtained using the HP4192A impedance analyzer, and model calculations are carred out using VIC-3D{copyright, serif}. We demonstrate conditions that are peculiar to ferritic tubes, and give insight into the optimum methods for characterizing the tubes and flaws within them.
Problems with the TiO Hypothesis for Thermal Inversions in Hot Jupiter Atmospheres
NASA Astrophysics Data System (ADS)
Spiegel, David S.; Silverio, K.; Burrows, A.
2009-12-01
Infrared observations indicate that several transiting extrasolar giant planets have thermal inversions in their upper atmospheres. Above a relative minimum, the temperature appears to increase with altitude. We examine the hypothesis that absorption of optical irradiation by TiO in the upper atmosphere is responsible for the inferred inversions. We find that two processes are likely to drain the upper atmospheres of any TiO that might originally have been there. First, molecular diffusion in a gravitational field will lead heavy molecules, such as TiO, to settle. Furthermore, many planets with thermal inversions are likely to have regions lower in their atmospheres that are cold enough that titanium would condense and rain out, creating a titanium cold-trap. For TiO to persist above the cold trap requires extremely vigorous macroscopic mixing. Parameterizing the macroscopic mixing as a turbulent diffusivity Kzz, we find that maintaining TiO in the upper atmosphere requires Kzz values of 107 - 1011 cm2/s, values that might not be realized in a stably stratified atmosphere.
PREFACE: 6th International Conference on Inverse Problems in Engineering: Theory and Practice
NASA Astrophysics Data System (ADS)
Bonnet, Marc
2008-07-01
The 6th International Conference on Inverse Problems in Engineering: Theory and Practice (ICIPE 2008) belongs to a successful series of conferences held up to now following a three-year cycle. Previous conferences took place in Palm Coast, Florida, USA (1993), Le Croisic, France (1996), Port Ludlow, Washington, USA (1999), Angra dos Reis, Brazil (2002), and Cambridge, UK (2005). The conference has its roots on the informal seminars organized by Professor J V Beck at Michigan State University, which were initiated in 1987. The organization of this Conference, which took place in Dourdan (Paris) France, 15-19 June 2008, was made possible through a joint effort by four research departments from four different universities: LEMTA (Laboratoire de Mécanique Théorique et Appliquée, Nancy-Université) LMS (Laboratoire de Mécanique des Solides, Ecole Polytechnique, Paris) LMAC (Laboratoire de Mathématiques Appliquées, UTC Compiègne) LTN (Laboratoire de Thermocinétique, Université de Nantes) It received support from three organizations: SFT (Société Française de Thermique: French Heat Transfer Association) ACSM (Association Calcul de Structures et Simulation : Computational Structural Mechanics Association) GdR Ondes - CNRS (`Waves' Network, French National Center for Scientific Research) The objective of the conference was to provide the opportunity for interaction and cross-fertilization between designers of inverse methods and practitioners. The delegates came from very different fields, such as applied mathematics, heat transfer, solid mechanics, tomography.... Consequently the sessions were organised along mostly methodological topics in order to facilitate interaction among participants who might not meet otherwise. The present proceedings, published in the Journal of Physics: Conference Series, gathers the four plenary invited lectures and the full-length versions of 103 presentations. The latter have been reviewed by the scientific committee (see
Akcelik, Volkan; Flath, Pearl; Ghattas, Omar; Hill, Judith C; Van Bloemen Waanders, Bart; Wilcox, Lucas
2011-01-01
We consider the problem of estimating the uncertainty in large-scale linear statistical inverse problems with high-dimensional parameter spaces within the framework of Bayesian inference. When the noise and prior probability densities are Gaussian, the solution to the inverse problem is also Gaussian, and is thus characterized by the mean and covariance matrix of the posterior probability density. Unfortunately, explicitly computing the posterior covariance matrix requires as many forward solutions as there are parameters, and is thus prohibitive when the forward problem is expensive and the parameter dimension is large. However, for many ill-posed inverse problems, the Hessian matrix of the data misfit term has a spectrum that collapses rapidly to zero. We present a fast method for computation of an approximation to the posterior covariance that exploits the lowrank structure of the preconditioned (by the prior covariance) Hessian of the data misfit. Analysis of an infinite-dimensional model convection-diffusion problem, and numerical experiments on large-scale 3D convection-diffusion inverse problems with up to 1.5 million parameters, demonstrate that the number of forward PDE solves required for an accurate low-rank approximation is independent of the problem dimension. This permits scalable estimation of the uncertainty in large-scale ill-posed linear inverse problems at a small multiple (independent of the problem dimension) of the cost of solving the forward problem.
Not Just Hats Anymore: Binomial Inversion and the Problem of Multiple Coincidences
ERIC Educational Resources Information Center
Hathout, Leith
2007-01-01
The well-known "hats" problem, in which a number of people enter a restaurant and check their hats, and then receive them back at random, is often used to illustrate the concept of derangements, that is, permutations with no fixed points. In this paper, the problem is extended to multiple items of clothing, and a general solution to the problem of…
Inverse problems of determining the shape of incompressible bodies under finite strains
NASA Astrophysics Data System (ADS)
Zhukov, B. A.
2014-05-01
Transformations preserving the volume under finite strains are given for some classes of two-dimensional problems. Several settings of nonlinear elasticity problems meant for determining the shape of mechanical rubber objects from a given configuration in a strained state are proposed on the basis of these transformations. Two axisymmetric problems are solved as an example. In the first problem, we determine the shape of a rubber bushing in a combined rubber-metal joint which has a prescribed configuration in the assembled state. In the second problem, we determine the shape of the rubber element of a cylindrical compression damper in working state.
Liao, Ke; Zhu, Min; Ding, Lei
2013-08-01
The present study investigated the use of transform sparseness of cortical current density on human brain surface to improve electroencephalography/magnetoencephalography (EEG/MEG) inverse solutions. Transform sparseness was assessed by evaluating compressibility of cortical current densities in transform domains. To do that, a structure compression method from computer graphics was first adopted to compress cortical surface structure, either regular or irregular, into hierarchical multi-resolution meshes. Then, a new face-based wavelet method based on generated multi-resolution meshes was proposed to compress current density functions defined on cortical surfaces. Twelve cortical surface models were built by three EEG/MEG softwares and their structural compressibility was evaluated and compared by the proposed method. Monte Carlo simulations were implemented to evaluate the performance of the proposed wavelet method in compressing various cortical current density distributions as compared to other two available vertex-based wavelet methods. The present results indicate that the face-based wavelet method can achieve higher transform sparseness than vertex-based wavelet methods. Furthermore, basis functions from the face-based wavelet method have lower coherence against typical EEG and MEG measurement systems than vertex-based wavelet methods. Both high transform sparseness and low coherent measurements suggest that the proposed face-based wavelet method can improve the performance of L1-norm regularized EEG/MEG inverse solutions, which was further demonstrated in simulations and experimental setups using MEG data. Thus, this new transform on complicated cortical structure is promising to significantly advance EEG/MEG inverse source imaging technologies.
NASA Astrophysics Data System (ADS)
Grayver, Alexander V.; Kuvshinov, Alexey V.
2016-05-01
This paper presents a methodology to sample equivalence domain (ED) in nonlinear partial differential equation (PDE)-constrained inverse problems. For this purpose, we first applied state-of-the-art stochastic optimization algorithm called Covariance Matrix Adaptation Evolution Strategy (CMAES) to identify low-misfit regions of the model space. These regions were then randomly sampled to create an ensemble of equivalent models and quantify uncertainty. CMAES is aimed at exploring model space globally and is robust on very ill-conditioned problems. We show that the number of iterations required to converge grows at a moderate rate with respect to number of unknowns and the algorithm is embarrassingly parallel. We formulated the problem by using the generalized Gaussian distribution. This enabled us to seamlessly use arbitrary norms for residual and regularization terms. We show that various regularization norms facilitate studying different classes of equivalent solutions. We further show how performance of the standard Metropolis-Hastings Markov chain Monte Carlo algorithm can be substantially improved by using information CMAES provides. This methodology was tested by using individual and joint inversions of magneotelluric, controlled-source electromagnetic (EM) and global EM induction data.
Molokanov, A; Chojnacki, E; Blanchardon, E
2010-01-01
The individual monitoring of internal exposure of workers comprises two steps: measurement and measurement interpretation. The latter consists in reconstructing the intake of a radionuclide from the activity measurement and calculating the dose using a biokinetic model of the radionuclide behavior in the human body. Mathematically, reconstructing the intake is solving an inverse problem described by a measurement-model equation. The aim of this paper is to propose a solution to this inverse problem when the measurement-model parameters are considered as uncertain. For that, an analysis of the uncertainty on the intake calculation is performed taking into account the dispersion of the measured quantity and the uncertainties of the measurement-model parameters. It is shown that both frequentist and Bayesian approaches can be used to solve the problem according to the measurement-model formulation. A common calculation algorithm is proposed to support both approaches and applied to the examples of tritiated water intake and plutonium inhalation by a worker.
Chemyakin, Eduard; Burton, Sharon; Kolgotin, Alexei; Müller, Detlef; Hostetler, Chris; Ferrare, Richard
2016-03-20
We present an investigation of some important mathematical and numerical features related to the retrieval of microphysical parameters [complex refractive index, single-scattering albedo, effective radius, total number, surface area, and volume concentrations] of ambient aerosol particles using multiwavelength Raman or high-spectral-resolution lidar. Using simple examples, we prove the non-uniqueness of an inverse solution to be the major source of the retrieval difficulties. Some theoretically possible ways of partially compensating for these difficulties are offered. For instance, an increase in the variety of input data via combination of lidar and certain passive remote sensing instruments will be helpful to reduce the error of estimation of the complex refractive index. We also demonstrate a significant interference between Aitken and accumulation aerosol modes in our inversion algorithm, and confirm that the solutions can be better constrained by limiting the particle radii. Applying a combination of an analytical approach and numerical simulations, we explain the statistical behavior of the microphysical size parameters. We reveal and clarify why the total surface area concentration is consistent even in the presence of non-unique solution sets and is on average the most stable parameter to be estimated, as long as at least one extinction optical coefficient is employed. We find that for selected particle size distributions, the total surface area and volume concentrations can be quickly retrieved with fair precision using only single extinction coefficients in a simple arithmetical relationship.
NASA Astrophysics Data System (ADS)
Wyatt, Philip
2009-03-01
The electromagnetic inverse scattering problem suggests that if a homogeneous and non-absorbing object be illuminated with a monochromatic light source and if the far field scattered light intensity is known at sufficient scattering angles, then, in principle, one could derive the dielectric structure of the scattering object. In general, this is an ill-posed problem and methods must be developed to regularize the search for unique solutions. An iterative procedure often begins with a model of the scattering object, solves the forward scattering problem using this model, and then compares these calculated results with the measured values. Key to any such solution is instrumentation capable of providing adequate data. To this end, the development of the first laser based absolute light scattering photometers is described together with their continuing evolution and some of the remarkable discoveries made with them. For particles much smaller than the wavelength of the incident light (e.g. macromolecules), the inverse scattering problems are easily solved. Among the many solutions derived with this instrumentation are the in situ structure of bacterial cells, new drug delivery mechanisms, the development of new vaccines and other biologicals, characterization of wines, the possibility of custom chemotherapy, development of new polymeric materials, identification of protein crystallization conditions, and a variety discoveries concerning protein interactions. A new form of the problem is described to address bioterrorist threats. Over the many years of development and refinement, one element stands out as essential for the successes that followed: the R and D teams were always directed and executed by physics trained theorists and experimentalists. 14 Ph. D. physicists each made his/her unique contribution to the development of these evolving instruments and the interpretation of their results.
NASA Astrophysics Data System (ADS)
Chelnokov, Yu. N.
2013-01-01
The problem of reducing the body-attached coordinate system to the reference (programmed) coordinate system moving relative to the fixed coordinate system with a given instantaneous velocity screw along a given trajectory is considered in the kinematic statement. The biquaternion kinematic equations of motion of a rigid body in normalized and unnormalized finite displacement biquaternions are used as the mathematical model of motion, and the dual orthogonal projections of the instantaneous velocity screw of the body motion onto the body coordinate axes are used as the control. Various types of correction (stabilization), which are biquaternion analogs of position and integral corrections, are proposed. It is shown that the linear (obtained without linearization) and stationary biquaternion error equations that are invariant under any chosen programmed motion of the reference coordinate system can be obtained for the proposed types of correction and the use of unnormalized finite displacement biquaternions and four-dimensional dual controls allows one to construct globally regular control laws. The general solution of the error equation is constructed, and conditions for asymptotic stability of the programmed motion are obtained. The constructed theory of kinematic control of motion is used to solve inverse problems of robot-manipulator kinematics. The control problem under study is a generalization of the kinematic problem [1, 2] of reducing the body-attached coordinate system to the reference coordinate system rotating at a given (programmed) absolute angular velocity, and the presentedmethod for solving inverse problems of robotmanipulator kinematics is a development of the method proposed in [3-5].
Retrieving the Balanced Winds on the Globe as a Generalized Inverse Problem
NASA Technical Reports Server (NTRS)
Lu, Huei-Iin; Robertson, Franklin R.; Arnold, James E. (Technical Monitor)
2000-01-01
A generalized inverse technique is applied to retrieve two types of balanced winds that characterize the large-scale dynamics of the atmosphere: rotational winds based upon the linear balance equation, and divergent winds based upon the vorticity budget equation. Both balance equations are singular at or near the equator. The balance equations are transformed in spherical harmonic function space to an under-determined system, for which the scale-weighed least-squares solution consists of a sum of principal and singular components. The principal components represent the response to the source function for the regular eigenmodes, while the singular components are determined by the projection of an independent measurement on the singular eigenmodes. The method was tested with the NCEP/NCAR reanalysis data in which a quasi-balance condition exists. A realistic balanced wind field is retrievable when the singular components are computed based upon the reanalyzed wind data.
NASA Astrophysics Data System (ADS)
Bertagna, Luca; Veneziani, Alessandro
2014-05-01
Scientific computing has progressively become an important tool for research in cardiovascular diseases. The role of quantitative analyses based on numerical simulations has moved from ‘proofs of concept’ to patient-specific investigations, thanks to a strong integration between imaging and computational tools. However, beyond individual geometries, numerical models require the knowledge of parameters that are barely retrieved from measurements, especially in vivo. For this reason, recently cardiovascular mathematics considered data assimilation procedures for extracting the knowledge of patient-specific parameters from measures and images. In this paper, we consider specifically the quantification of vascular compliance, i.e. the parameter quantifying the tendency of arterial walls to deform under blood stress. Following up a previous paper, where a variational data assimilation procedure was proposed, based on solving an inverse fluid-structure interaction problem, here we consider model reduction techniques based on a proper orthogonal decomposition approach to accomplish the solution of the inverse problem in a computationally efficient way.
Inversion of Heavy Current Electroheat Problems on a Graphics Processing Unit (GPU)
2013-11-10
Genetic and Gradient-based Optimization Algorithms for Solving Electromagnetics Problem,” IEEE Trans. Magnetics, Vol. 31 (3), pp. 1932-1935, 1995...and the optimization, we use the GPU to perform the electroheat optimization by the genetic algorithm to achieve computational efficiencies better...part problem and the optimization, we use the GPU to perform the electroheat optimization by the genetic algorithm to achieve computational
Inexact trajectory planning and inverse problems in the Hamilton–Pontryagin framework
Burnett, Christopher L.; Holm, Darryl D.; Meier, David M.
2013-01-01
We study a trajectory-planning problem whose solution path evolves by means of a Lie group action and passes near a designated set of target positions at particular times. This is a higher-order variational problem in optimal control, motivated by potential applications in computational anatomy and quantum control. Reduction by symmetry in such problems naturally summons methods from Lie group theory and Riemannian geometry. A geometrically illuminating form of the Euler–Lagrange equations is obtained from a higher-order Hamilton–Pontryagin variational formulation. In this context, the previously known node equations are recovered with a new interpretation as Legendre–Ostrogradsky momenta possessing certain conservation properties. Three example applications are discussed as well as a numerical integration scheme that follows naturally from the Hamilton–Pontryagin principle and preserves the geometric properties of the continuous-time solution. PMID:24353467
NASA Astrophysics Data System (ADS)
Cordier, G.; Choi, J.; Raguin, L. G.
2008-11-01
Skin microcirculation plays an important role in diseases such as chronic venous insufficiency and diabetes. Magnetic resonance imaging (MRI) can provide quantitative information with a better penetration depth than other noninvasive methods, such as laser Doppler flowmetry or optical coherence tomography. Moreover, successful MRI skin studies have recently been reported. In this article, we investigate three potential inverse models to quantify skin microcirculation using diffusion-weighted MRI (DWI), also known as q-space MRI. The model parameters are estimated based on nonlinear least-squares (NLS). For each of the three models, an optimal DWI sampling scheme is proposed based on D-optimality in order to minimize the size of the confidence region of the NLS estimates and thus the effect of the experimental noise inherent to DWI. The resulting covariance matrices of the NLS estimates are predicted by asymptotic normality and compared to the ones computed by Monte-Carlo simulations. Our numerical results demonstrate the effectiveness of the proposed models and corresponding DWI sampling schemes as compared to conventional approaches.
A theoretical discussion on Vening Meinesz-Moritz inverse problem of isostasy
NASA Astrophysics Data System (ADS)
Eshagh, Mehdi
2016-12-01
The Moho surface can be determined according to isostatic theories, and among them, the recent Vening Meinesz-Moritz (VMM) theory of isostasy has been successfully applied for this purpose. In this paper, this method is studied from a theoretical prospective and its connection to the Airy-Heiskanen (AH) and Vening Meinesz original theories are presented. Jeffrey's inverse solution to isostasy is developed according to the recent developments of the VMM method and both are compared in similar situations. It is shown that they are generalizations of the AH model in a global and continuous domain. In the VMM spherical harmonic solution for Moho depth, the mean Moho depth contributes only to the zero-degree term of the series, while in Jeffrey's solution it contributes to all frequencies. In addition, the VMM spherical harmonic series is improved further so that the mean Moho can contribute to all frequencies of the solution. This modification makes the VMM global solution superior to the Jeffrey one, but in a global scale, the difference between both solutions is less than 3 km. Both solutions are asymptotically convergent and we present two methods to obtain smooth solutions for Moho from them.
Adaptive finite element methods for the solution of inverse problems in optical tomography
NASA Astrophysics Data System (ADS)
Bangerth, Wolfgang; Joshi, Amit
2008-06-01
Optical tomography attempts to determine a spatially variable coefficient in the interior of a body from measurements of light fluxes at the boundary. Like in many other applications in biomedical imaging, computing solutions in optical tomography is complicated by the fact that one wants to identify an unknown number of relatively small irregularities in this coefficient at unknown locations, for example corresponding to the presence of tumors. To recover them at the resolution needed in clinical practice, one has to use meshes that, if uniformly fine, would lead to intractably large problems with hundreds of millions of unknowns. Adaptive meshes are therefore an indispensable tool. In this paper, we will describe a framework for the adaptive finite element solution of optical tomography problems. It takes into account all steps starting from the formulation of the problem including constraints on the coefficient, outer Newton-type nonlinear and inner linear iterations, regularization, and in particular the interplay of these algorithms with discretizing the problem on a sequence of adaptively refined meshes. We will demonstrate the efficiency and accuracy of these algorithms on a set of numerical examples of clinical relevance related to locating lymph nodes in tumor diagnosis.
NASA Astrophysics Data System (ADS)
Power, Joan F.
1997-02-01
The expectation minimum (EM) principle is a new method of inverse problem theory that can be used to obtain stable solutions to first-kind Fredholm integrals. The EM principle uses the addition of noise to a basis of model vectors that are related to the experimental data by a multilinear discrete model. The experimental data are projected onto this randomized basis set and solution vectors for individual data projections are recovered by any one of a number of standard algorithms. The solutions are averaged arithmetically to obtain a stable estimate of the minimum error solution by expectation. It is shown from theory that the presence of noise in the model basis provides a method of regularization of the problem. Examples applicable to the problem of source localization in inverse heat conduction are examined. When factorization methods are used to recover the solution vectors corresponding to each data projection, the solutions recovered by the EM principle are shown to quantitatively converge to the zero-order uniform Tikhonov regularized solutions. When a stepwise projection method is used in lieu of factorizations, the recovered solutions agree nearly quantitatively with the solutions recovered using the autocorrelation method of linear filtering derived via a modified form of the Yule-Walker equations. The resolution and robustness of the EM solutions in this second case are greatly superior to those obtained by the autocorrelation method. The ultimate accuracy and resolution of the EM solutions in this latter case is limited by the noise in the model basis. Through appropriate sampling methods, the noise in the model basis may be set as low as three orders of magnitude below the noise on the experimental data. This gives an enormous improvement in performance over the previous methods of solution using regularization.
Semenov, Alexander; Zaikin, Oleg
2016-01-01
In this paper we propose an approach for constructing partitionings of hard variants of the Boolean satisfiability problem (SAT). Such partitionings can be used for solving corresponding SAT instances in parallel. For the same SAT instance one can construct different partitionings, each of them is a set of simplified versions of the original SAT instance. The effectiveness of an arbitrary partitioning is determined by the total time of solving of all SAT instances from it. We suggest the approach, based on the Monte Carlo method, for estimating time of processing of an arbitrary partitioning. With each partitioning we associate a point in the special finite search space. The estimation of effectiveness of the particular partitioning is the value of predictive function in the corresponding point of this space. The problem of search for an effective partitioning can be formulated as a problem of optimization of the predictive function. We use metaheuristic algorithms (simulated annealing and tabu search) to move from point to point in the search space. In our computational experiments we found partitionings for SAT instances encoding problems of inversion of some cryptographic functions. Several of these SAT instances with realistic predicted solving time were successfully solved on a computing cluster and in the volunteer computing project SAT@home. The solving time agrees well with estimations obtained by the proposed method.
NASA Astrophysics Data System (ADS)
Hunziker, J.; Thorbecke, J.; Slob, E. C.
2014-12-01
Commonly, electromagnetic measurements for exploring and monitoring hydrocarbon reservoirs are inverted for the subsurface conductivity distribution by minimizing the difference between the actual data and a forward modeled dataset. The convergence of the inversion process to the correct solution strongly depends on the shape of the solution space. Since this is a non-linear problem, there exist a multitude of minima of which only the global one provides the correct conductivity values. To easily find the global minimum we desire it to have a broad cone of attraction, while it should also feature a very narrow bottom in order to obtain the subsurface conductivity with high resolution. In this study, we aim to determine which combination of input data corresponds to a favorable shape of the solution space. Since the solution space is N-dimensional, with N being the number of unknown subsurface parameters, plotting it is out of the question. In our approach, we use a genetic algorithm (Goldberg, 1989) to probe the solution space. Such algorithms have the advantage that every run of the same problem will end up at a different solution. Most of these solutions are expected to lie close to the global minimum. A situation where only few runs end up in the global minimum indicates that the solution space consists of a lot of local minima or that the cone of attraction of the global minimum is small. If a lot of runs end up with a similar data-misfit but with a large spread of the subsurface medium parameters in one or more direction, it can be concluded that the chosen data-input is not sensitive with respect to that direction. Compared to the study of Hunziker et al. 2014, we allow also to invert for subsurface boundaries and include more combinations of input datasets. The results so far suggest that it is essential to include the magnetic field in the inversion process in order to find the anisotropic conductivity values. ReferencesGoldberg, D. E., 1989. Genetic
Stability results for the parameter identification inverse problem in cardiac electrophysiology
NASA Astrophysics Data System (ADS)
Lassoued, Jamila; Mahjoub, Moncef; Zemzemi, Néjib
2016-11-01
In this paper we prove a stability estimate of the parameter identification problem in cardiac electrophysiology modeling. We use the monodomain model which is a reaction diffusion parabolic equation where the reaction term is obtained by solving an ordinary differential equation (ODE). We are interested in proving the stability of the identification of the parameter {τ }{in}, which is the parameter that multiplies the cubic term in the reaction term. The proof of the result is based on a new Carleman-type estimate for both partial differential equation (PDE) and ODE problems. As a consequence of the stability result we prove the uniqueness of the parameter {τ }{in} giving some observations of both state variables at a given time t 0 in the whole domain and in the PDE variable in a non empty open subset w 0 of the domain.
Approximation methods for inverse problems involving the vibration of beams with tip bodies
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1984-01-01
Two cubic spline based approximation schemes for the estimation of structural parameters associated with the transverse vibration of flexible beams with tip appendages are outlined. The identification problem is formulated as a least squares fit to data subject to the system dynamics which are given by a hybrid system of coupled ordinary and partial differential equations. The first approximation scheme is based upon an abstract semigroup formulation of the state equation while a weak/variational form is the basis for the second. Cubic spline based subspaces together with a Rayleigh-Ritz-Galerkin approach were used to construct sequences of easily solved finite dimensional approximating identification problems. Convergence results are briefly discussed and a numerical example demonstrating the feasibility of the schemes and exhibiting their relative performance for purposes of comparison is provided.
The three-body problem with an inverse square law potential
NASA Astrophysics Data System (ADS)
Jiménez-Lara, Lidia; Piña, Eduardo
2003-09-01
We study the motion of three masses in a plane interacting with a central potential proportional to 1/r2 using the coordinates introduced recently by Piña. We show that this problem with four degrees of freedom (three angles and a distance related to the inertia moment of the system in these coordinates) is partially separable, and can be reduced to a problem with two degrees of freedom (two angles) with a new constant of motion. We find a symmetry of reflection (an involution) for this system and we use the symmetry lines to find periodic orbits in the angular coordinates. These orbits will not be periodic in general on the whole phase space because the coordinate of distance type grows as t when t→∞ and it is unbounded. However, if the inertia moment of the system remains constant, they will be periodic on the whole phase space.
Fundamental Mechanisms of NeuroInformation Processing: Inverse Problems and Spike Processing
2016-08-04
identifying a single dendritic stimulus processor (DSP) is mathematically dual to decoding of stimuli encoded by a population of neurons with a bank of...established that identifying a single dendritic stimulus processor is mathematically dual to decoding of stimuli encoded by a population of neurons with a...channel identification problem becomes mathematically tractable. Furthermore, we demonstrated that the choice of the input signal space profoundly e↵ects
NASA Astrophysics Data System (ADS)
Yao, Zhewei; Hu, Zixi; Li, Jinglai
2016-07-01
Many scientific and engineering problems require to perform Bayesian inferences in function spaces, where the unknowns are of infinite dimension. In such problems, choosing an appropriate prior distribution is an important task. In particular, when the function to infer is subject to sharp jumps, the commonly used Gaussian measures become unsuitable. On the other hand, the so-called total variation (TV) prior can only be defined in a finite-dimensional setting, and does not lead to a well-defined posterior measure in function spaces. In this work we present a TV-Gaussian (TG) prior to address such problems, where the TV term is used to detect sharp jumps of the function, and the Gaussian distribution is used as a reference measure so that it results in a well-defined posterior measure in the function space. We also present an efficient Markov Chain Monte Carlo (MCMC) algorithm to draw samples from the posterior distribution of the TG prior. With numerical examples we demonstrate the performance of the TG prior and the efficiency of the proposed MCMC algorithm.
FELIX: advances in modeling forward and inverse ice-sheet problems
NASA Astrophysics Data System (ADS)
Gunzburger, Max; Hoffman, Mattew; Leng, Wei; Perego, Mauro; Price, Stephen; Salinger, Andrew; Stadler, Georg; Ju, Lili
2013-04-01
Several models of different complexity and accuracy have been proposed for describing ice-sheet dynamics. We introduce a parallel, finite element framework for implementing these models, which range from the "shallow ice approximation" up through nonlinear Stokes flow. These models make up the land ice dynamical core of FELIX, which is being developed under the Community Ice Sheet Model. We present results from large-scale simulations of the Greenland ice-sheet, compare models of differing complexity and accuracy, and explore different solution methods for the resulting linear and nonlinear systems. We also address the problem of finding an optimal initial state for Greenland ice-sheet via estimating the spatially varying linear-friction coefficient at the ice-bedrock interface. The problem, which consists of minimizing the mismatch between a specified and computed surface mass balance and/or the mismatch between observed and modeled surface velocities, is solved as an optimal control problem constrained by the governing model equations.
DEM analysis for AIA/SDO EUV channels using a probabilistic approach to the spectral inverse problem
NASA Astrophysics Data System (ADS)
Goryaev, Farid; Parenti, Susanna; Hochedez, Jean-François; Urnov, Alexander
The Atmospheric Imaging Assembly (AIA) for the Solar Dynamics Observatory (SDO) mis-sion is designed to observe the Sun from the photosphere to the flaring corona. These data have to improve our understanding of processes in the solar atmosphere. The differential emis-sion measure (DEM) analysis is one of the main methods to derive information about coronal optically thin plasma characteristics from EUV and SXR emission. In this work we analyze AIA/SDO EUV channels to estimate their ability to reconstruct DEM(T) distributions. We use an iterative method (called Bayesian iterative method, BIM) within the framework of a probabilistic approach to the spectral inverse problem for determining the thermal structures of the emitting plasma sources (Goryaev et al., submitted to AA). The BIM is an iterative procedure based on Bayes' theorem and used for the reconstruction of DEM profiles. Using the BIM algorithm we performed various numerical tests and model simulations demonstrating abilities of our inversion approach for DEM analysis with AIA/SDO EUV channels.
NASA Astrophysics Data System (ADS)
di Volo, Matteo; Burioni, Raffaella; Casartelli, Mario; Livi, Roberto; Vezzani, Alessandro
2016-01-01
We study the dynamics of networks with inhibitory and excitatory leak-integrate-and-fire neurons with short-term synaptic plasticity in the presence of depressive and facilitating mechanisms. The dynamics is analyzed by a heterogeneous mean-field approximation, which allows us to keep track of the effects of structural disorder in the network. We describe the complex behavior of different classes of excitatory and inhibitory components, which give rise to a rich dynamical phase diagram as a function of the fraction of inhibitory neurons. Using the same mean-field approach, we study and solve a global inverse problem: reconstructing the degree probability distributions of the inhibitory and excitatory components and the fraction of inhibitory neurons from the knowledge of the average synaptic activity field. This approach unveils new perspectives on the numerical study of neural network dynamics and the possibility of using these models as a test bed for the analysis of experimental data.
NASA Technical Reports Server (NTRS)
Mutterperl, William
1944-01-01
A method of conformal transformation is developed that maps an airfoil into a straight line, the line being chosen as the extended chord line of the airfoil. The mapping is accomplished by operating directly with the airfoil ordinates. The absence of any preliminary transformation is found to shorten the work substantially over that of previous methods. Use is made of the superposition of solutions to obtain a rigorous counterpart of the approximate methods of thin-airfoils theory. The method is applied to the solution of the direct and inverse problems for arbitrary airfoils and pressure distributions. Numerical examples are given. Applications to more general types of regions, in particular to biplanes and to cascades of airfoils, are indicated. (author)
Alcocer-Sosa, Mauricio; Gutiérrez, David
2016-06-25
We present a forward modeling solution in the form of an array response kernel for magnetoencephalography. We consider the case when the brain's anatomy is approximated by an ellipsoid and an equivalent current dipole model is used to approximate brain sources. The proposed solution includes the contributions up to the third-order ellipsoidal harmonic terms; hence, we compare this new approximation against the previously available one that only considered up to second-order harmonics. We evaluated the proposed solution when used in the inverse problem of estimating physiologically feasible visual evoked responses from magnetoencephalography data. Our results showed that the contribution of the third-order harmonic terms provides a more realistic representation of the magnetic fields (closer to those generated with a numerical approximation based on the boundary element method) and, subsecuently, the estimated equivalent current dipoles are a better fit to those observed in practice (e.g., in visual evoked potentials). Copyright © 2016 John Wiley & Sons, Ltd.
NASA Astrophysics Data System (ADS)
Giudici, Mauro; Casabianca, Davide; Comunian, Alessandro
2015-04-01
The basic classical inverse problem of groundwater hydrology aims at determining aquifer transmissivity (T ) from measurements of hydraulic head (h), estimates or measures of source terms and with the least possible knowledge on hydraulic transmissivity. The theory of inverse problems shows that this is an example of ill-posed problem, for which non-uniqueness and instability (or at least ill-conditioning) might preclude the computation of a physically acceptable solution. One of the methods to reduce the problems with non-uniqueness, ill-conditioning and instability is a tomographic approach, i.e., the use of data corresponding to independent flow situations. The latter might correspond to different hydraulic stimulations of the aquifer, i.e., to different pumping schedules and flux rates. Three inverse methods have been analyzed and tested to profit from the use of multiple sets of data: the Differential System Method (DSM), the Comparison Model Method (CMM) and the Double Constraint Method (DCM). DSM and CMM need h all over the domain and thus the first step for their application is the interpolation of measurements of h at sparse points. Moreover, they also need the knowledge of the source terms (aquifer recharge, well pumping rates) all over the aquifer. DSM is intrinsically based on the use of multiple data sets, which permit to write a first-order partial differential equation for T , whereas CMM and DCM were originally proposed to invert a single data set and have been extended to work with multiple data sets in this work. CMM and DCM are based on Darcy's law, which is used to update an initial guess of the T field with formulas based on a comparison of different hydraulic gradients. In particular, the CMM algorithm corrects the T estimate with ratio of the observed hydraulic gradient and that obtained with a comparison model which shares the same boundary conditions and source terms as the model to be calibrated, but a tentative T field. On the other hand
Inverse eigenvalue problems in vibration absorption: Passive modification and active control
NASA Astrophysics Data System (ADS)
Mottershead, John E.; Ram, Yitshak M.
2006-01-01
The abiding problem of vibration absorption has occupied engineering scientists for over a century and there remain abundant examples of the need for vibration suppression in many industries. For example, in the automotive industry the resolution of noise, vibration and harshness (NVH) problems is of extreme importance to customer satisfaction. In rotorcraft it is vital to avoid resonance close to the blade passing speed and its harmonics. An objective of the greatest importance, and extremely difficult to achieve, is the isolation of the pilot's seat in a helicopter. It is presently impossible to achieve the objectives of vibration absorption in these industries at the design stage because of limitations inherent in finite element models. Therefore, it is necessary to develop techniques whereby the dynamic of the system (possibly a car or a helicopter) can be adjusted after it has been built. There are two main approaches: structural modification by passive elements and active control. The state of art of the mathematical theory of vibration absorption is presented and illustrated for the benefit of the reader with numerous simple examples.
Blakeslee, Barbara; McCourt, Mark E.
2015-01-01
Research in lightness perception centers on understanding the prior assumptions and processing strategies the visual system uses to parse the retinal intensity distribution (the proximal stimulus) into the surface reflectance and illumination components of the scene (the distal stimulus—ground truth). It is agreed that the visual system must compare different regions of the visual image to solve this inverse problem; however, the nature of the comparisons and the mechanisms underlying them are topics of intense debate. Perceptual illusions are of value because they reveal important information about these visual processing mechanisms. We propose a framework for lightness research that resolves confusions and paradoxes in the literature, and provides insight into the mechanisms the visual system employs to tackle the inverse problem. The main idea is that much of the debate and confusion in the literature stems from the fact that lightness, defined as apparent reflectance, is underspecified and refers to three different types of judgments that are not comparable. Under stimulus conditions containing a visible illumination component, such as a shadow boundary, observers can distinguish and match three independent dimensions of achromatic experience: apparent intensity (brightness), apparent local intensity ratio (brightness-contrast), and apparent reflectance (lightness). In the absence of a visible illumination boundary, however, achromatic vision reduces to two dimensions and, depending on stimulus conditions and observer instructions, judgments of lightness are identical to judgments of brightness or brightness-contrast. Furthermore, because lightness judgments are based on different information under different conditions, they can differ greatly in their degree of difficulty and in their accuracy. This may, in part, explain the large variability in lightness constancy across studies. PMID:25954181
Pant, Sanjay; Corsini, Chiara; Baker, Catriona; Hsia, Tain-Yen; Pennati, Giancarlo; Vignon-Clementel, Irene E
2017-01-01
Inverse problems in cardiovascular modelling have become increasingly important to assess each patient individually. These problems entail estimation of patient-specific model parameters from uncertain measurements acquired in the clinic. In recent years, the method of data assimilation, especially the unscented Kalman filter, has gained popularity to address computational efficiency and uncertainty consideration in such problems. This work highlights and presents solutions to several challenges of this method pertinent to models of cardiovascular haemodynamics. These include methods to (i) avoid ill-conditioning of the covariance matrix, (ii) handle a variety of measurement types, (iii) include a variety of prior knowledge in the method, and (iv) incorporate measurements acquired at different heart rates, a common situation in the clinic where the patient state differs according to the clinical situation. Results are presented for two patient-specific cases of congenital heart disease. To illustrate and validate data assimilation with measurements at different heart rates, the results are presented on a synthetic dataset and on a patient-specific case with heart valve regurgitation. It is shown that the new method significantly improves the agreement between model predictions and measurements. The developed methods can be readily applied to other pathophysiologies and extended to dynamical systems which exhibit different responses under different sets of known parameters or different sets of inputs (such as forcing/excitation frequencies).
NASA Astrophysics Data System (ADS)
Ahn, Chi Young; Jeon, Kiwan; Park, Won-Kwang
2015-06-01
This study analyzes the well-known MUltiple SIgnal Classification (MUSIC) algorithm to identify unknown support of thin penetrable electromagnetic inhomogeneity from scattered field data collected within the so-called multi-static response matrix in limited-view inverse scattering problems. The mathematical theories of MUSIC are partially discovered, e.g., in the full-view problem, for an unknown target of dielectric contrast or a perfectly conducting crack with the Dirichlet boundary condition (Transverse Magnetic-TM polarization) and so on. Hence, we perform further research to analyze the MUSIC-type imaging functional and to certify some well-known but theoretically unexplained phenomena. For this purpose, we establish a relationship between the MUSIC imaging functional and an infinite series of Bessel functions of integer order of the first kind. This relationship is based on the rigorous asymptotic expansion formula in the existence of a thin inhomogeneity with a smooth supporting curve. Various results of numerical simulation are presented in order to support the identified structure of MUSIC. Although a priori information of the target is needed, we suggest a least condition of range of incident and observation directions to apply MUSIC in the limited-view problem.
Reconstruction from blind experimental data for an inverse problem for a hyperbolic equation
NASA Astrophysics Data System (ADS)
Beilina, Larisa; Thành, Nguyen Trung; Klibanov, Michael V.; Fiddy, Michael A.
2014-02-01
We consider the problem of the reconstruction of dielectrics from blind backscattered experimental data. The reconstruction is done from time domain data, as opposed to a more conventional case of frequency domain data. Experimental data were collected using a microwave scattering facility which was built at the University of North Carolina at Charlotte. This system sends electromagnetic pulses into the medium and collects the time-resolved backscattered data on a part of a plane. The spatially distributed dielectric constant \\varepsilon _{r}( \\mathbf {x}) ,\\mathbf {x}\\in {R}^{3} is the unknown coefficient of a wave-like PDE. This coefficient is reconstructed from those data in blind cases. To do this, a globally convergent numerical method is used.
Systematic regularization of linear inverse solutions of the EEG source localization problem.
Phillips, Christophe; Rugg, Michael D; Fristont, Karl J
2002-09-01
Distributed linear solutions of the EEG source localization problem are used routinely. Here we describe an approach based on the weighted minimum norm method that imposes constraints using anatomical and physiological information derived from other imaging modalities to regularize the solution. In this approach the hyperparameters controlling the degree of regularization are estimated using restricted maximum likelihood (ReML). EEG data are always contaminated by noise, e.g., exogenous noise and background brain activity. The conditional expectation of the source distribution, given the data, is attained by carefully balancing the minimization of the residuals induced by noise and the improbability of the estimates as determined by their priors. This balance is specified by hyperparameters that control the relative importance of fitting and conforming to prior constraints. Here we introduce a systematic approach to this regularization problem, in the context of a linear observation model we have described previously. In this model, basis functions are extracted to reduce the solution space a priori in the spatial and temporal domains. The basis sets are motivated by knowledge of the evoked EEG response and information theory. In this paper we focus on an iterative "expectation-maximization" procedure to jointly estimate the conditional expectation of the source distribution and the ReML hyperparameters on which this solution rests. We used simulated data mixed with real EEG noise to explore the behavior of the approach with various source locations, priors, and noise levels. The results enabled us to conclude: (i) Solutions in the space of informed basis functions have a high face and construct validity, in relation to conventional analyses. (ii) The hyperparameters controlling the degree of regularization vary largely with source geometry and noise. The second conclusion speaks to the usefulness of using adaptative ReML hyperparameter estimates.
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
NASA Astrophysics Data System (ADS)
Zakharova, Natalia; Piskovatsky, Nicolay; Gusev, Anatoly
2014-05-01
Development of Informational-Computational Systems (ICS) for data assimilation procedures is one of multidisciplinary problems. To study and solve these problems one needs to apply modern results from different disciplines and recent developments in: mathematical modeling; theory of adjoint equations and optimal control; inverse problems; numerical methods theory; numerical algebra and scientific computing. The above problems are studied in the Institute of Numerical Mathematics of the Russian Academy of Science (INM RAS) in ICS for personal computers. In this work the results on the Special data base development for ICS "INM RAS - Black Sea" are presented. In the presentation the input information for ICS is discussed, some special data processing procedures are described. In this work the results of forecast using ICS "INM RAS - Black Sea" with operational observation data assimilation are presented. This study was supported by the Russian Foundation for Basic Research (project No 13-01-00753) and by Presidium Program of Russian Academy of Sciences (project P-23 "Black sea as an imitational ocean model"). References 1. V.I. Agoshkov, M.V. Assovskii, S.A. Lebedev, Numerical simulation of Black Sea hydrothermodynamics taking into account tide-forming forces. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, pp. 5-31. 2. E.I. Parmuzin, V.I. Agoshkov, Numerical solution of the variational assimilation problem for sea surface temperature in the model of the Black Sea dynamics. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, pp. 69-94. 3. V.B. Zalesny, N.A. Diansky, V.V. Fomin, S.N. Moshonkin, S.G. Demyshev, Numerical model of the circulation of Black Sea and Sea of Azov. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, pp. 95-111. 4. Agoshkov V.I.,Assovsky M.B., Giniatulin S. V., Zakharova N.B., Kuimov G.V., Parmuzin E.I., Fomin V.V. Informational Computational system of variational assimilation of observation data "INM RAS - Black sea"// Ecological
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
A full-Bayesian approach to the inverse problem for steady-state groundwater flow and heat transport
NASA Astrophysics Data System (ADS)
Jiang, Yefang; Woodbury, Allan D.
2006-12-01
The full (hierarchal) Bayesian approach proposed by Woodbury & Ulrych and Jiang et al. is extended to the inverse problem for 2-D steady-state groundwater flow and heat transport. A stochastic conceptual framework for the heat flow and groundwater flow is adopted. A perturbation of both the groundwater flow and the advection-conduction heat transport equations leads to a linear formulation between heads, temperature and logarithm transmissivity [denoted as ln (T)]. A Bayesian updating procedure similar to that of Woodbury & Ulrych can then be performed. This new algorithm is examined against a generic example through simulations. The prior mean, variance and integral scales of ln (T) (hyperparameters) are treated as random variables and their pdfs are determined from maximum entropy considerations. It is also assumed that the statistical properties of the noise in the hydraulic head and temperature measurements are also uncertain. Uncertainties in all pertinent hyperparameters are removed by marginalization. It is found that the use of temperature measurements is showed to further improve the ln (T) estimates for the test case in comparison to the updated ln (T) field conditioned on ln (T) and head data; the addition of temperature data without hydraulic head data to the update also aids refinement of the ln (T) field compared to simply interpolating ln (T) data alone these results suggest that temperature measurements are a promising data source for site characterization for heterogeneous aquifer, which can be accomplished through the full-Bayesian methodology.
NASA Astrophysics Data System (ADS)
Mair, H. D.; Ciorau, P.; Owen, D.; Hazelton, T.; Dunning, G.
2000-05-01
Two ultrasonic simulation packages: Imagine 3D and SIMSCAN have specifically been developed to solve the inverse problem for blade root and rotor steeple of low-pressure turbine. The software was integrated with the 3D drawing of the inspected parts, and with the dimensions of linear phased-array probes. SIMSCAN simulates the inspection scenario in both optional conditions: defect location and probe movement/refracted angle range. The results are displayed into Imagine 3-D, with a variety of options: rendering, display 1:1, grid, generated UT beam. The results are very useful for procedure developer, training and to optimize the phased-array probe inspection sequence. A spreadsheet is generated to correlate the defect coordinates with UT data (probe position, skew and refracted angle, UT path, and probe movement). The simulation models were validated during experimental work with phased-array systems. The accuracy in probe position is ±1 mm, and the refracted/skew angle is within ±0.5°. Representative examples of phased array focal laws/probe movement for a specific defect location, are also included.
Dixneuf, Sophie; Rachet, Florent; Chrysos, Michael
2015-02-28
Owing in part to the p orbitals of its filled L shell, neon has repeatedly come on stage for its peculiar properties. In the context of collision-induced Raman spectroscopy, in particular, we have shown, in a brief report published a few years ago [M. Chrysos et al., Phys. Rev. A 80, 054701 (2009)], that the room-temperature anisotropic Raman lineshape of Ne–Ne exhibits, in the far wing of the spectrum, a peculiar structure with an aspect other than a smooth wing (on a logarithmic plot) which contrasts with any of the existing studies, and whose explanation lies in the distinct way in which overlap and exchange interactions interfere with the classical electrostatic ones in making the polarizability anisotropy, α{sub ∥} − α{sub ⊥}. Here, we delve deeper into that study by reporting data for that spectrum up to 450 cm{sup −1} and for even- and odd-order spectral moments up to M{sub 6}, as well as quantum lineshapes, generated from SCF, CCSD, and CCSD(T) models for α{sub ∥} − α{sub ⊥}, which are critically compared with the experiment. On account of the knowledge of the spectrum over the augmented frequency domain, we show how the inverse scattering problem can be tackled both effectively and economically, and we report an analytic function for the anisotropy whose quantum lineshape faithfully reproduces our observations.
Shimoda, Masami; Hoshikawa, Kaori; Shiramizu, Hideki; Oda, Shinri; Matsumae, Mitsunori
2010-01-01
The diagnostic efficacy of fluid-attenuated inversion recovery (FLAIR) magnetic resonance imaging and computed tomography (CT) for acute subarachnoid hemorrhage (SAH) were compared and the problems with diagnosis were investigated in 81 patients with aneurysmal SAH within 24 hours after onset who underwent FLAIR imaging and CT on admission. The number of hematomas in the cisterns and ventricles were evaluated by clot scores. In addition, the frequency of undetected hematomas was calculated for the cisterns and ventricles. Clot scores were significantly higher for FLAIR imaging than for CT in the lateral sylvian, quadrigeminal, and convexity cisterns. On the other hand, clot scores were significantly higher for CT than for FLAIR imaging in the interhemispheric and medial sylvian cisterns. The overall frequency of undetected SAH was 2% for FLAIR imaging and 14% for CT. With the exception of the interhemispheric and medial sylvian cisterns, the frequency of undetected SAH was higher for CT than for FLAIR imaging. In this study, FLAIR imaging was more sensitive than CT for the detection of acute SAH within 24 hours after onset. However, the diagnostic efficacy of FLAIR imaging was reduced in comparatively tight cisterns.
Meschiari, Stefano; Laughlin, Gregory P.
2010-07-20
Transit timing variations (TTVs)-deviations from strict periodicity between successive passages of a transiting planet-can be used to probe the structure and dynamics of multiple-planet systems. In this paper, we examine prospects for numerically solving the so-called inverse problem, the determination of the orbital elements of a perturbing body from the TTVs it induces. We assume that the planetary systems under examination have a limited number of Doppler velocity measurements and show that a more extensive radial velocity (RV) characterization with precision comparable to the semi-amplitude of the perturber may remove degeneracies in the solution. We examine several configurations of interest, including (1) a prototypical non-resonant system, modeled after HD 40307 b and c, which contains multiple super-Earth-mass planets, (2) a hypothetical system containing a transiting giant planet with a terrestrial-mass companion trapped in low-order mean motion resonance, and (3) the HAT-P-13 system, in which forced precession by an outer perturbing body that is well characterized by Doppler RV measurements can give insight into the interior structure of a perturbing planet, and for which the determination of mutual inclination between the transiting planet and its perturber is a key issue.
NASA Technical Reports Server (NTRS)
Kozdoba, L. A.; Krivoshei, F. A.
1985-01-01
The solution of the inverse problem of nonsteady heat conduction is discussed, based on finding the coefficient of the heat conduction and the coefficient of specific volumetric heat capacity. These findings are included in the equation used for the electrical model of this phenomenon.
Paracentric inversions do not normally generate monocentric recombinant chromosomes
Sutherland, G.R.; Callen, D.F.; Gardner, R.J.M.
1995-11-20
Dr. Pettenati et al. recently reported a review of paracentric inversions in humans in which they concluded that carriers of these have a 3.8% risk of viable offspring with recombinant chromosomes. We are of the view that there are serious problems with this estimate which should be much closer to zero. The only recombinant chromosomes which can be generated by a paracentric inversion undergoing a normal meiotic division are dicentrics and acentric fragments. Only two such cases were found by Pettenati et al. Several of the alleged monocentric recombinants were originally reported as arising from parental insertions (3-break rearrangements) and it is not legitimate to include them in any analysis of paracentric inversions. Any monocentric recombinant chromosome can only arise from a paracentric inversion by some abnormal process which must involve chromatid breakage and reunion. 4 refs.
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
Volkov, Yu. O. Kozhevnikov, I. V.; Roshchin, B. S.; Filatova, E. O.; Asadchikov, V. E.
2013-01-15
The key features of the inverse problem of X-ray reflectometry (i.e., the reconstruction of the depth profile of the dielectric constant using an experimental angular dependence of reflectivity) are discussed and essential factors leading to the ambiguity of its solution are analyzed. A simple approach to studying the internal structure of HfO{sub 2} films, which is based on the application of a physically reasonable model, is considered. The principles for constructing a film model and the criteria for choosing a minimal number of fitting parameters are discussed. It is shown that the ambiguity of the solution to the inverse problem is retained even for the simplest single-film models. Approaches allowing one to pick out the most realistic solution from several variants are discussed.
Liu, Tian; Spincemaille, Pascal; de Rochefort, Ludovic; Kressler, Bryan; Wang, Yi
2009-01-01
Magnetic susceptibility differs among tissues based on their contents of iron, calcium, contrast agent, and other molecular compositions. Susceptibility modifies the magnetic field detected in the MR signal phase. The determination of an arbitrary susceptibility distribution from the induced field shifts is a challenging, ill-posed inverse problem. A method called "calculation of susceptibility through multiple orientation sampling" (COSMOS) is proposed to stabilize this inverse problem. The field created by the susceptibility distribution is sampled at multiple orientations with respect to the polarization field, B(0), and the susceptibility map is reconstructed by weighted linear least squares to account for field noise and the signal void region. Numerical simulations and phantom and in vitro imaging validations demonstrated that COSMOS is a stable and precise approach to quantify a susceptibility distribution using MRI.
NASA Astrophysics Data System (ADS)
Borsic, A.; Adler, A.
2012-09-01
Maximum a posteriori estimates in inverse problems are often based on quadratic formulations, corresponding to a least-squares fitting of the data and to the use of the L2 norm on the regularization term. While the implementation of this estimation is straightforward and usually based on the Gauss-Newton method, resulting estimates are sensitive to outliers and result in spatial distributions of the estimates that are smooth. As an alternative, the use of the L1 norm on the data term renders the estimation robust to outliers, and the use of the L1 norm on the regularization term allows the reconstruction of sharp spatial profiles. The ability therefore to use the L1 norm either on the data term, on the regularization term, or on both is desirable, though the use of this norm results in non-smooth objective functions which require more sophisticated implementations compared to quadratic algorithms. Methods for L1-norm minimization have been studied in a number of contexts, including in the recently popular total variation regularization. Different approaches have been used and methods based on primal-dual interior-point methods (PD-IPMs) have been shown to be particularly efficient. In this paper we derive a PD-IPM framework for using the L1 norm indifferently on the two terms of an inverse problem. We use electrical impedance tomography as an example inverse problem to demonstrate the implementation of the algorithms we derive, and the effect of choosing the L2 or the L1 norm on the two terms of the inverse problem. Pseudo-codes for the algorithms and a public domain implementation are provided.
NASA Technical Reports Server (NTRS)
Voorhies, Coerte V.
1993-01-01
The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation (SV) indicated by models of the observed geomagnetic field is examined in the source-free mantle/frozen-flux core (SFI/VFFC) approximation. This inverse problem is non-linear because solutions of the forward problem are deterministically chaotic. The SFM/FFC approximation is inexact, and neither the models nor the observations they represent are either complete or perfect. A method is developed for solving the non-linear inverse motional induction problem posed by the hypothesis of (piecewise, statistically) steady core surface flow and the supposition of a complete initial geomagnetic condition. The method features iterative solution of the weighted, linearized least-squares problem and admits optional biases favoring surficially geostrophic flow and/or spatially simple flow. Two types of weights are advanced radial field weights for fitting the evolution of the broad-scale portion of the radial field component near Earth's surface implied by the models, and generalized weights for fitting the evolution of the broad-scale portion of the scalar potential specified by the models.
Yang, Yu-Ching; Lee, Haw-Long; Chang, Win-Jin; Chen, Wen-Lih
2017-03-01
The aim of this study is to solve an inverse heat conduction problem to estimate the unknown time-dependent laser irradiance and thermal damage in laser-irradiated biological tissue from the temperature measurements taken within the tissue. The dual-phase-lag model is considered in the formulation of heat conduction equation. The inverse algorithm used in the study is based on the conjugate gradient method and the discrepancy principle. The effect of measurement errors and measurement locations on the estimation accuracy is also investigated. Two different examples of laser irradiance are discussed. Results show that the unknown laser irradiance and thermal damage can be predicted precisely by using the present approach for the test cases considered in this study.