Parallel adaptive wavelet collocation method for PDEs
Nejadmalayeri, Alireza; Vezolainen, Alexei; Brown-Dymkoski, Eric; Vasilyev, Oleg V.
2015-10-01
A parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by developing an asynchronous parallel wavelet transform, which allows one to perform parallel wavelet transform and derivative calculations with only one data synchronization at the highest level of resolution. The data are stored using tree-like structure with tree roots starting at a priori defined level of resolution. Both static and dynamic domain partitioning approaches are developed. For the dynamic domain partitioning, trees are considered to be the minimum quanta of data to be migrated between the processes. This allows fully automated and efficient handling of non-simply connected partitioning of a computational domain. Dynamic load balancing is achieved via domain repartitioning during the grid adaptation step and reassigning trees to the appropriate processes to ensure approximately the same number of grid points on each process. The parallel efficiency of the approach is discussed based on parallel adaptive wavelet-based Coherent Vortex Simulations of homogeneous turbulence with linear forcing at effective non-adaptive resolutions up to 2048{sup 3} using as many as 2048 CPU cores.
Parallel adaptive wavelet collocation method for PDEs
NASA Astrophysics Data System (ADS)
Nejadmalayeri, Alireza; Vezolainen, Alexei; Brown-Dymkoski, Eric; Vasilyev, Oleg V.
2015-10-01
A parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by developing an asynchronous parallel wavelet transform, which allows one to perform parallel wavelet transform and derivative calculations with only one data synchronization at the highest level of resolution. The data are stored using tree-like structure with tree roots starting at a priori defined level of resolution. Both static and dynamic domain partitioning approaches are developed. For the dynamic domain partitioning, trees are considered to be the minimum quanta of data to be migrated between the processes. This allows fully automated and efficient handling of non-simply connected partitioning of a computational domain. Dynamic load balancing is achieved via domain repartitioning during the grid adaptation step and reassigning trees to the appropriate processes to ensure approximately the same number of grid points on each process. The parallel efficiency of the approach is discussed based on parallel adaptive wavelet-based Coherent Vortex Simulations of homogeneous turbulence with linear forcing at effective non-adaptive resolutions up to 20483 using as many as 2048 CPU cores.
Efficient Combustion Simulation via the Adaptive Wavelet Collocation Method
NASA Astrophysics Data System (ADS)
Lung, Kevin; Brown-Dymkoski, Eric; Guerrero, Victor; Doran, Eric; Museth, Ken; Balme, Jo; Urberger, Bob; Kessler, Andre; Jones, Stephen; Moses, Billy; Crognale, Anthony
Rocket engine development continues to be driven by the intuition and experience of designers, progressing through extensive trial-and-error test campaigns. Extreme temperatures and pressures frustrate direct observation, while high-fidelity simulation can be impractically expensive owing to the inherent muti-scale, multi-physics nature of the problem. To address this cost, an adaptive multi-resolution PDE solver has been designed which targets the high performance, many-core architecture of GPUs. The adaptive wavelet collocation method is used to maintain a sparse-data representation of the high resolution simulation, greatly reducing the memory footprint while tightly controlling physical fidelity. The tensorial, stencil topology of wavelet-based grids lends itself to highly vectorized algorithms which are necessary to exploit the performance of GPUs. This approach permits efficient implementation of direct finite-rate kinetics, and improved resolution of steep thermodynamic gradients and the smaller mixing scales that drive combustion dynamics. Resolving these scales is crucial for accurate chemical kinetics, which are typically degraded or lost in statistical modeling approaches.
Adaptive-Anisotropic Wavelet Collocation Method on general curvilinear coordinate systems
NASA Astrophysics Data System (ADS)
Brown-Dymkoski, Eric; Vasilyev, Oleg V.
2017-03-01
A new general framework for an Adaptive-Anisotropic Wavelet Collocation Method (A-AWCM) for the solution of partial differential equations is developed. This proposed framework addresses two major shortcomings of existing wavelet-based adaptive numerical methodologies, namely the reliance on a rectangular domain and the "curse of anisotropy", i.e. drastic over-resolution of sheet- and filament-like features arising from the inability of the wavelet refinement mechanism to distinguish highly correlated directional information in the solution. The A-AWCM addresses both of these challenges by incorporating coordinate transforms into the Adaptive Wavelet Collocation Method for the solution of PDEs. The resulting integrated framework leverages the advantages of both the curvilinear anisotropic meshes and wavelet-based adaptive refinement in a complimentary fashion, resulting in greatly reduced cost of resolution for anisotropic features. The proposed Adaptive-Anisotropic Wavelet Collocation Method retains the a priori error control of the solution and fully automated mesh refinement, while offering new abilities through the flexible mesh geometry, including body-fitting. The new A-AWCM is demonstrated for a variety of cases, including parabolic diffusion, acoustic scattering, and unsteady external flow.
Webster, Clayton G; Zhang, Guannan; Gunzburger, Max D
2012-10-01
Accurate predictive simulations of complex real world applications require numerical approximations to first, oppose the curse of dimensionality and second, converge quickly in the presence of steep gradients, sharp transitions, bifurcations or finite discontinuities in high-dimensional parameter spaces. In this paper we present a novel multi-dimensional multi-resolution adaptive (MdMrA) sparse grid stochastic collocation method, that utilizes hierarchical multiscale piecewise Riesz basis functions constructed from interpolating wavelets. The basis for our non-intrusive method forms a stable multiscale splitting and thus, optimal adaptation is achieved. Error estimates and numerical examples will used to compare the efficiency of the method with several other techniques.
Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's
NASA Technical Reports Server (NTRS)
Cai, Wei; Wang, Jian-Zhong
1993-01-01
We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.
NASA Astrophysics Data System (ADS)
Regele, Jonathan D.
Multi-dimensional numerical modeling of detonation initiation is the primary goal of this thesis. The particular scenario under examination is initiating a detonation wave through acoustic timescale thermal power deposition. Physically this would correspond to igniting a reactive mixture with a laser pulse as opposed to a typical electric spark. Numerous spatial and temporal scales are involved, which makes these problems computationally challenging to solve. In order to model these problems, a shock capturing scheme is developed that utilizes the computational efficiency of the Adaptive Wavelet-Collocation Method (AWCM) to properly handle the multiple scales involved. With this technique, previous one-dimensional problems with unphysically small activation energies are revisited and simulated with the AWCM. The results demonstrate a qualitative agreement with previous work that used a uniform grid MacCormack scheme. Both sets of data show the basic sequence of events that are needed in order for a DDT process to occur. Instead of starting with a strong shock-coupled reaction zone as many other studies have done, the initial pulse is weak enough to allow the shock and the reaction zone to decouple. Reflected compression waves generated by the inertially confined reaction zone lead to localized reaction centers, which eventually explode and further accelerate the process. A shock-coupled reaction zone forms an initially overdriven detonation, which relaxes to a steady CJ wave. The one-dimensional problems are extended to two dimensions using a circular heat deposition in a channel. Two-dimensional results demonstrate the same sequence of events, which suggests that the concepts developed in the original one-dimensional work are applicable to multiple dimensions.
Szu, H.; Hsu, C.
1996-12-31
Human sensors systems (HSS) may be approximately described as an adaptive or self-learning version of the Wavelet Transforms (WT) that are capable to learn from several input-output associative pairs of suitable transform mother wavelets. Such an Adaptive WT (AWT) is a redundant combination of mother wavelets to either represent or classify inputs.
NASA Astrophysics Data System (ADS)
Vasilyev, Oleg V.; Gazzola, Mattia; Koumoutsakos, Petros
2009-11-01
In this talk we discuss preliminary results for the use of hybrid wavelet collocation - Brinkman penalization approach for shape and topology optimization of fluid flows. Adaptive wavelet collocation method tackles the problem of efficiently resolving a fluid flow on a dynamically adaptive computational grid in complex geometries (where grid resolution varies both in space and time time), while Brinkman volume penalization allows easy variation of flow geometry without using body-fitted meshes by simply changing the shape of the penalization region. The use of Brinkman volume penalization approach allow seamless transition from shape to topology optimization by combining it with level set approach and increasing the size of the optimization space. The approach is demonstrated for shape optimization of a variety of fluid flows by optimizing single cost function (time averaged Drag coefficient) using covariance matrix adaptation (CMA) evolutionary algorithm.
NASA Astrophysics Data System (ADS)
Vasilyev, Oleg V.; Gazzola, Mattia; Koumoutsakos, Petros
2010-11-01
In this talk we discuss preliminary results for the use of hybrid wavelet collocation - Brinkman penalization approach for shape optimization for drag reduction in flows past linked bodies. This optimization relies on Adaptive Wavelet Collocation Method along with the Brinkman penalization technique and the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Adaptive wavelet collocation method tackles the problem of efficiently resolving a fluid flow on a dynamically adaptive computational grid, while a level set approach is used to describe the body shape and the Brinkman volume penalization allows for an easy variation of flow geometry without requiring body-fitted meshes. We perform 2D simulations of linked bodies in order to investigate whether flat geometries are optimal for drag reduction. In order to accelerate the costly cost function evaluations we exploit the inherent parallelism of ES and we extend the CMA-ES implementation to a multi-host framework. This framework allows for an easy distribution of the cost function evaluations across several parallel architectures and it is not limited to only one computing facility. The resulting optimal shapes are geometrically consistent with the shapes that have been obtained in the pioneering wind tunnel experiments for drag reduction using Evolution Strategies by Ingo Rechenberg.
Adaptive boxcar/wavelet transform
NASA Astrophysics Data System (ADS)
Sezer, Osman G.; Altunbasak, Yucel
2009-01-01
This paper presents a new adaptive Boxcar/Wavelet transform for image compression. Boxcar/Wavelet decomposition emphasizes the idea of average-interpolation representation which uses dyadic averages and their interpolation to explain a special case of biorthogonal wavelet transforms (BWT). This perspective for image compression together with lifting scheme offers the ability to train an optimum 2-D filter set for nonlinear prediction (interpolation) that will adapt to the context around the low-pass wavelet coefficients for reducing energy in the high-pass bands. Moreover, the filters obtained after training is observed to posses directional information with some textural clues that can provide better prediction performance. This work addresses a firrst step towards obtaining this new set of training-based fillters in the context of Boxcar/Wavelet transform. Initial experimental results show better subjective quality performance compared to popular 9/7-tap and 5/3-tap BWTs with comparable results in objective quality.
A Haar wavelet collocation method for coupled nonlinear Schrödinger-KdV equations
NASA Astrophysics Data System (ADS)
Oruç, Ömer; Esen, Alaattin; Bulut, Fatih
2016-04-01
In this paper, to obtain accurate numerical solutions of coupled nonlinear Schrödinger-Korteweg-de Vries (KdV) equations a Haar wavelet collocation method is proposed. An explicit time stepping scheme is used for discretization of time derivatives and nonlinear terms that appeared in the equations are linearized by a linearization technique and space derivatives are discretized by Haar wavelets. In order to test the accuracy and reliability of the proposed method L2, L∞ error norms and conserved quantities are used. Also obtained results are compared with previous ones obtained by finite element method, Crank-Nicolson method and radial basis function meshless methods. Error analysis of Haar wavelets is also given.
Gearbox Fault Diagnosis Using Adaptive Wavelet Filter
NASA Astrophysics Data System (ADS)
LIN, J.; ZUO, M. J.
2003-11-01
Vibration signals from a gearbox are usually noisy. As a result, it is difficult to find early symptoms of a potential failure in a gearbox. Wavelet transform is a powerful tool to disclose transient information in signals. An adaptive wavelet filter based on Morlet wavelet is introduced in this paper. The parameters in the Morlet wavelet function are optimised based on the kurtosis maximisation principle. The wavelet used is adaptive because the parameters are not fixed. The adaptive wavelet filter is found to be very effective in detection of symptoms from vibration signals of a gearbox with early fatigue tooth crack. Two types of discrete wavelet transform (DWT), the decimated with DB4 wavelet and the undecimated with harmonic wavelet, are also used to analyse the same signals for comparison. No periodic impulses appear on any scale in either DWT decomposition.
Nonuniform spatially adaptive wavelet packets
NASA Astrophysics Data System (ADS)
Carre, Philippe; Fernandez-Maloigne, Christine
2000-12-01
In this paper, we propose a new decomposition scheme for spatially adaptive wavelet packets. Contrary to the double tree algorithm, our method is non-uniform and shift- invariant in the time and frequency domains, and is minimal for an information cost function. We prose some-restrictions to our algorithm to reduce the complexity and permitting us to provide some time-frequency partitions of the signal in agreement with its structure. This new 'totally' non-uniform transform, more adapted than Malvar, Packets or dyadic double-tree decomposition, allows the study of all possible time-frequency partitions with the only restriction that the blocks are rectangular. It permits one to obtain a satisfying Time-Frequency representation, and is applied for the study of EEG signals.
Adaptive probabilistic collocation based Kalman filter for unsaturated flow problem
NASA Astrophysics Data System (ADS)
Man, J.; Li, W.; Zeng, L.; Wu, L.
2015-12-01
The ensemble Kalman filter (EnKF) has gained popularity in hydrological data assimilation problems. As a Monte Carlo based method, a relatively large ensemble size is usually required to guarantee the accuracy. As an alternative approach, the probabilistic collocation based Kalman filter (PCKF) employs the Polynomial Chaos to approximate the original system. In this way, the sampling error can be reduced. However, PCKF suffers from the so called "cure of dimensionality". When the system nonlinearity is strong and number of parameters is large, PCKF is even more computationally expensive than EnKF. Motivated by recent developments in uncertainty quantification, we propose a restart adaptive probabilistic collocation based Kalman filter (RAPCKF) for data assimilation in unsaturated flow problem. During the implementation of RAPCKF, the important parameters are identified and active PCE basis functions are adaptively selected. The "restart" technology is used to alleviate the inconsistency between model parameters and states. The performance of RAPCKF is tested by unsaturated flow numerical cases. It is shown that RAPCKF is more efficient than EnKF with the same computational cost. Compared with the traditional PCKF, the RAPCKF is more applicable in strongly nonlinear and high dimensional problems.
Mathematical theorems of adaptive wavelet transform
NASA Astrophysics Data System (ADS)
Szu, Harold H.; Telfer, Brian A.
1994-03-01
The computational efficiency of the adaptive wavelet transform (AWT) is due both to the compact support closely matching with signal characteristics, and to a larger redundancy factor of the superposition-mother (s(x), or in short super-mother, created adaptively by a linear superposition of other admissible mother wavelets. We prove that the super-mother always forms a complete basis, but usually associated with a higher redundancy number than its constituent C.O.N. bases. Then, in terms of Daubechies frame redundancy, we prove that the robustness of super-mother in suffering less noise contamination (since noise is everywhere, and a redundant sampling by band-passings can suppress the noise and enhance the signal). Since the continuous function of super- mother has been created with least-mean-squares (LMS) off-line using neural nets and is formulated in discrete approximation in terms of high-pass and low-pass filter bank coefficients, then such a digital subband coding via QMF saves the in-situ computational time of AWT. Moreover, the power of such an adaptive wavelet transform is due to the potential of massive parallel real-time implementation by means of artificial neural networks, where each node is a daughter wavelet similar to a radial basis function using dyadic affine scaling.
Adaptive wavelet simulation of global ocean dynamics
NASA Astrophysics Data System (ADS)
Kevlahan, N. K.-R.; Dubos, T.; Aechtner, M.
2015-07-01
In order to easily enforce solid-wall boundary conditions in the presence of complex coastlines, we propose a new mass and energy conserving Brinkman penalization for the rotating shallow water equations. This penalization does not lead to higher wave speeds in the solid region. The error estimates for the penalization are derived analytically and verified numerically for linearized one dimensional equations. The penalization is implemented in a conservative dynamically adaptive wavelet method for the rotating shallow water equations on the sphere with bathymetry and coastline data from NOAA's ETOPO1 database. This code could form the dynamical core for a future global ocean model. The potential of the dynamically adaptive ocean model is illustrated by using it to simulate the 2004 Indonesian tsunami and wind-driven gyres.
A New Adaptive Mother Wavelet for Electromagnetic Transient Analysis
NASA Astrophysics Data System (ADS)
Guillén, Daniel; Idárraga-Ospina, Gina; Cortes, Camilo
2016-01-01
Wavelet Transform (WT) is a powerful technique of signal processing, its applications in power systems have been increasing to evaluate power system conditions, such as faults, switching transients, power quality issues, among others. Electromagnetic transients in power systems are due to changes in the network configuration, producing non-periodic signals, which have to be identified to avoid power outages in normal operation or transient conditions. In this paper a methodology to develop a new adaptive mother wavelet for electromagnetic transient analysis is proposed. Classification is carried out with an innovative technique based on adaptive wavelets, where filter bank coefficients will be adapted until a discriminant criterion is optimized. Then, its corresponding filter coefficients will be used to get the new mother wavelet, named wavelet ET, which allowed to identify and to distinguish the high frequency information produced by different electromagnetic transients.
WAKES: Wavelet Adaptive Kinetic Evolution Solvers
NASA Astrophysics Data System (ADS)
Mardirian, Marine; Afeyan, Bedros; Larson, David
2016-10-01
We are developing a general capability to adaptively solve phase space evolution equations mixing particle and continuum techniques in an adaptive manner. The multi-scale approach is achieved using wavelet decompositions which allow phase space density estimation to occur with scale dependent increased accuracy and variable time stepping. Possible improvements on the SFK method of Larson are discussed, including the use of multiresolution analysis based Richardson-Lucy Iteration, adaptive step size control in explicit vs implicit approaches. Examples will be shown with KEEN waves and KEEPN (Kinetic Electrostatic Electron Positron Nonlinear) waves, which are the pair plasma generalization of the former, and have a much richer span of dynamical behavior. WAKES techniques are well suited for the study of driven and released nonlinear, non-stationary, self-organized structures in phase space which have no fluid, limit nor a linear limit, and yet remain undamped and coherent well past the drive period. The work reported here is based on the Vlasov-Poisson model of plasma dynamics. Work supported by a Grant from the AFOSR.
Identification of Infinite Dimensional Systems via Adaptive Wavelet Neural Networks
1993-01-01
We consider identification of distributed systems via adaptive wavelet neural networks (AWNNs). We take advantage of the multiresolution property of...wavelet systems and the computational structure of neural networks to approximate the unknown plant successively. A systematic approach is developed
Yankov, A.; Downar, T.
2013-07-01
Recent efforts in the application of uncertainty quantification to nuclear systems have utilized methods based on generalized perturbation theory and stochastic sampling. While these methods have proven to be effective they both have major drawbacks that may impede further progress. A relatively new approach based on spectral elements for uncertainty quantification is applied in this paper to several problems in reactor simulation. Spectral methods based on collocation attempt to couple the approximation free nature of stochastic sampling methods with the determinism of generalized perturbation theory. The specific spectral method used in this paper employs both the Smolyak algorithm and adaptivity by using Newton-Cotes collocation points along with linear hat basis functions. Using this approach, a surrogate model for the outputs of a computer code is constructed hierarchically by adaptively refining the collocation grid until the interpolant is converged to a user-defined threshold. The method inherently fits into the framework of parallel computing and allows for the extraction of meaningful statistics and data that are not within reach of stochastic sampling and generalized perturbation theory. This paper aims to demonstrate the advantages of spectral methods-especially when compared to current methods used in reactor physics for uncertainty quantification-and to illustrate their full potential. (authors)
Adaptive Filtering in the Wavelet Transform Domain via Genetic Algorithms
2004-08-06
identification. Figure 1 shows a very basic example of this type of system . x(n) Figure 1. Basic system identification using adaptive filters block diagram...block diagram of adaptive wavelet filtering system . The main objective of the system shown in Figure 2 is to minimize the error signal, e(k), which is...in Table 1. Daub4 wavelets use filter banks (Vaidyanathan 1992) containing exactly four elements. 5 Figure 4. Time-Domain Representation of
Edge-preserving image compression using adaptive lifting wavelet transform
NASA Astrophysics Data System (ADS)
Zhang, Libao; Qiu, Bingchang
2015-07-01
In this paper, a novel 2-D adaptive lifting wavelet transform is presented. The proposed algorithm is designed to further reduce the high-frequency energy of wavelet transform, improve the image compression efficiency and preserve the edge or texture of original images more effectively. In this paper, a new optional direction set, covering the surrounding integer pixels and sub-pixels, is designed. Hence, our algorithm adapts far better to the image orientation features in local image blocks. To obtain the computationally efficient and coding performance, the complete processes of 2-D adaptive lifting wavelet transform is introduced and implemented. Compared with the traditional lifting-based wavelet transform, the adaptive directional lifting and the direction-adaptive discrete wavelet transform, the new structure reduces the high-frequency wavelet coefficients more effectively, and the texture structures of the reconstructed images are more refined and clear than that of the other methods. The peak signal-to-noise ratio and the subjective quality of the reconstructed images are significantly improved.
NASA Astrophysics Data System (ADS)
Man, Jun; Li, Weixuan; Zeng, Lingzao; Wu, Laosheng
2016-06-01
The ensemble Kalman filter (EnKF) has gained popularity in hydrological data assimilation problems. As a Monte Carlo based method, a sufficiently large ensemble size is usually required to guarantee the accuracy. As an alternative approach, the probabilistic collocation based Kalman filter (PCKF) employs the polynomial chaos expansion (PCE) to represent and propagate the uncertainties in parameters and states. However, PCKF suffers from the so-called "curse of dimensionality". Its computational cost increases drastically with the increasing number of parameters and system nonlinearity. Furthermore, PCKF may fail to provide accurate estimations due to the joint updating scheme for strongly nonlinear models. Motivated by recent developments in uncertainty quantification and EnKF, we propose a restart adaptive probabilistic collocation based Kalman filter (RAPCKF) for data assimilation in unsaturated flow problems. During the implementation of RAPCKF, the important parameters are identified and active PCE basis functions are adaptively selected at each assimilation step; the "restart" scheme is utilized to eliminate the inconsistency between updated model parameters and states variables. The performance of RAPCKF is systematically tested with numerical cases of unsaturated flow models. It is shown that the adaptive approach and restart scheme can significantly improve the performance of PCKF. Moreover, RAPCKF has been demonstrated to be more efficient than EnKF with the same computational cost.
Stabilized Conservative Level Set Method with Adaptive Wavelet-based Mesh Refinement
NASA Astrophysics Data System (ADS)
Shervani-Tabar, Navid; Vasilyev, Oleg V.
2016-11-01
This paper addresses one of the main challenges of the conservative level set method, namely the ill-conditioned behavior of the normal vector away from the interface. An alternative formulation for reconstruction of the interface is proposed. Unlike the commonly used methods which rely on the unit normal vector, Stabilized Conservative Level Set (SCLS) uses a modified renormalization vector with diminishing magnitude away from the interface. With the new formulation, in the vicinity of the interface the reinitialization procedure utilizes compressive flux and diffusive terms only in the normal direction to the interface, thus, preserving the conservative level set properties, while away from the interfaces the directional diffusion mechanism automatically switches to homogeneous diffusion. The proposed formulation is robust and general. It is especially well suited for use with adaptive mesh refinement (AMR) approaches due to need for a finer resolution in the vicinity of the interface in comparison with the rest of the domain. All of the results were obtained using the Adaptive Wavelet Collocation Method, a general AMR-type method, which utilizes wavelet decomposition to adapt on steep gradients in the solution while retaining a predetermined order of accuracy.
Man, Jun; Li, Weixuan; Zeng, Lingzao; Wu, Laosheng
2016-06-01
The ensemble Kalman filter (EnKF) has gained popularity in hydrological data assimilation problems. As a Monte Carlo based method, a relatively large ensemble size is usually required to guarantee the accuracy. As an alternative approach, the probabilistic collocation based Kalman filter (PCKF) employs the polynomial chaos to approximate the original system. In this way, the sampling error can be reduced. However, PCKF suffers from the so-called "curse of dimensionality". When the system nonlinearity is strong and number of parameters is large, PCKF could be even more computationally expensive than EnKF. Motivated by most recent developments in uncertainty quantification, we propose a restart adaptive probabilistic collocation based Kalman filter (RAPCKF) for data assimilation in unsaturated flow problems. During the implementation of RAPCKF, the important parameters are identified and active PCE basis functions are adaptively selected. The "restart" technology is used to eliminate the inconsistency between model parameters and states. The performance of RAPCKF is tested with numerical cases of unsaturated flow models. It is shown that RAPCKF is more efficient than EnKF with the same computational cost. Compared with the traditional PCKF, the RAPCKF is more applicable in strongly nonlinear and high dimensional problems.
Adaptive wavelet transform algorithm for lossy image compression
NASA Astrophysics Data System (ADS)
Pogrebnyak, Oleksiy B.; Ramirez, Pablo M.; Acevedo Mosqueda, Marco Antonio
2004-11-01
A new algorithm of locally adaptive wavelet transform based on the modified lifting scheme is presented. It performs an adaptation of the wavelet high-pass filter at the prediction stage to the local image data activity. The proposed algorithm uses the generalized framework for the lifting scheme that permits to obtain easily different wavelet filter coefficients in the case of the (~N, N) lifting. Changing wavelet filter order and different control parameters, one can obtain the desired filter frequency response. It is proposed to perform the hard switching between different wavelet lifting filter outputs according to the local data activity estimate. The proposed adaptive transform possesses a good energy compaction. The designed algorithm was tested on different images. The obtained simulation results show that the visual and quantitative quality of the restored images is high. The distortions are less in the vicinity of high spatial activity details comparing to the non-adaptive transform, which introduces ringing artifacts. The designed algorithm can be used for lossy image compression and in the noise suppression applications.
Adaptive zero-tree structure for curved wavelet image coding
NASA Astrophysics Data System (ADS)
Zhang, Liang; Wang, Demin; Vincent, André
2006-02-01
We investigate the issue of efficient data organization and representation of the curved wavelet coefficients [curved wavelet transform (WT)]. We present an adaptive zero-tree structure that exploits the cross-subband similarity of the curved wavelet transform. In the embedded zero-tree wavelet (EZW) and the set partitioning in hierarchical trees (SPIHT), the parent-child relationship is defined in such a way that a parent has four children, restricted to a square of 2×2 pixels, the parent-child relationship in the adaptive zero-tree structure varies according to the curves along which the curved WT is performed. Five child patterns were determined based on different combinations of curve orientation. A new image coder was then developed based on this adaptive zero-tree structure and the set-partitioning technique. Experimental results using synthetic and natural images showed the effectiveness of the proposed adaptive zero-tree structure for encoding of the curved wavelet coefficients. The coding gain of the proposed coder can be up to 1.2 dB in terms of peak SNR (PSNR) compared to the SPIHT coder. Subjective evaluation shows that the proposed coder preserves lines and edges better than the SPIHT coder.
Motion-compensated wavelet video coding using adaptive mode selection
NASA Astrophysics Data System (ADS)
Zhai, Fan; Pappas, Thrasyvoulos N.
2004-01-01
A motion-compensated wavelet video coder is presented that uses adaptive mode selection (AMS) for each macroblock (MB). The block-based motion estimation is performed in the spatial domain, and an embedded zerotree wavelet coder (EZW) is employed to encode the residue frame. In contrast to other motion-compensated wavelet video coders, where all the MBs are forced to be in INTER mode, we construct the residue frame by combining the prediction residual of the INTER MBs with the coding residual of the INTRA and INTER_ENCODE MBs. Different from INTER MBs that are not coded, the INTRA and INTER_ENCODE MBs are encoded separately by a DCT coder. By adaptively selecting the quantizers of the INTRA and INTER_ENCODE coded MBs, our goal is to equalize the characteristics of the residue frame in order to improve the overall coding efficiency of the wavelet coder. The mode selection is based on the variance of the MB, the variance of the prediction error, and the variance of the neighboring MBs' residual. Simulations show that the proposed motion-compensated wavelet video coder achieves a gain of around 0.7-0.8dB PSNR over MPEG-2 TM5, and a comparable PSNR to other 2D motion-compensated wavelet-based video codecs. It also provides potential visual quality improvement.
NASA Astrophysics Data System (ADS)
Cui, Xiongwei; Yao, Xiongliang; Wang, Zhikai; Liu, Minghao
2017-03-01
A second generation wavelet-based adaptive finite-difference Lattice Boltzmann method (FD-LBM) is developed in this paper. In this approach, the adaptive wavelet collocation method (AWCM) is firstly, to the best of our knowledge, incorporated into the FD-LBM. According to the grid refinement criterion based on the wavelet amplitudes of density distribution functions, an adaptive sparse grid is generated by the omission and addition of collocation points. On the sparse grid, the finite differences are used to approximate the derivatives. To eliminate the special treatments in using the FD-based derivative approximation near boundaries, the immersed boundary method (IBM) is also introduced into FD-LBM. By using the adaptive technique, the adaptive code requires much less grid points as compared to the uniform-mesh code. As a consequence, the computational efficiency can be improved. To justify the proposed method, a series of test cases, including fixed boundary cases and moving boundary cases, are invested. A good agreement between the present results and the data in previous literatures is obtained, which demonstrates the accuracy and effectiveness of the present AWCM-IB-LBM.
A stable interface element scheme for the p-adaptive lifting collocation penalty formulation
NASA Astrophysics Data System (ADS)
Cagnone, J. S.; Nadarajah, S. K.
2012-02-01
This paper presents a procedure for adaptive polynomial refinement in the context of the lifting collocation penalty (LCP) formulation. The LCP scheme is a high-order unstructured discretization method unifying the discontinuous Galerkin, spectral volume, and spectral difference schemes in single differential formulation. Due to the differential nature of the scheme, the treatment of inter-cell fluxes for spatially varying polynomial approximations is not straightforward. Specially designed elements are proposed to tackle non-conforming polynomial approximations. These elements are constructed such that a conforming interface between polynomial approximations of different degrees is recovered. The stability and conservation properties of the scheme are analyzed and various inviscid compressible flow calculations are performed to demonstrate the potential of the proposed approach.
Adaptive wavelet-based recognition of oscillatory patterns on electroencephalograms
NASA Astrophysics Data System (ADS)
Nazimov, Alexey I.; Pavlov, Alexey N.; Hramov, Alexander E.; Grubov, Vadim V.; Koronovskii, Alexey A.; Sitnikova, Evgenija Y.
2013-02-01
The problem of automatic recognition of specific oscillatory patterns on electroencephalograms (EEG) is addressed using the continuous wavelet-transform (CWT). A possibility of improving the quality of recognition by optimizing the choice of CWT parameters is discussed. An adaptive approach is proposed to identify sleep spindles (SS) and spike wave discharges (SWD) that assumes automatic selection of CWT-parameters reflecting the most informative features of the analyzed time-frequency structures. Advantages of the proposed technique over the standard wavelet-based approaches are considered.
Adaptively wavelet-based image denoising algorithm with edge preserving
NASA Astrophysics Data System (ADS)
Tan, Yihua; Tian, Jinwen; Liu, Jian
2006-02-01
A new wavelet-based image denoising algorithm, which exploits the edge information hidden in the corrupted image, is presented. Firstly, a canny-like edge detector identifies the edges in each subband. Secondly, multiplying the wavelet coefficients in neighboring scales is implemented to suppress the noise while magnifying the edge information, and the result is utilized to exclude the fake edges. The isolated edge pixel is also identified as noise. Unlike the thresholding method, after that we use local window filter in the wavelet domain to remove noise in which the variance estimation is elaborated to utilize the edge information. This method is adaptive to local image details, and can achieve better performance than the methods of state of the art.
Adaptive solution of the biharmonic problem with shortly supported cubic spline-wavelets
NASA Astrophysics Data System (ADS)
Černá, Dana; Finěk, Václav
2012-09-01
In our contribution, we design a cubic spline-wavelet basis on the interval. The basis functions have small support and wavelets have vanishing moments. We show that stiffness matrices arising from discretization of the two-dimensional biharmonic problem using a constructed wavelet basis have uniformly bounded condition numbers and these condition numbers are very small. We compare quantitative behavior of adaptive wavelet method with a constructed basis and other cubic spline-wavelet bases, and show the superiority of our construction.
Wavelet-Based Speech Enhancement Using Time-Frequency Adaptation
NASA Astrophysics Data System (ADS)
Wang, Kun-Ching
2003-12-01
Wavelet denoising is commonly used for speech enhancement because of the simplicity of its implementation. However, the conventional methods generate the presence of musical residual noise while thresholding the background noise. The unvoiced components of speech are often eliminated from this method. In this paper, a novel algorithm of wavelet coefficient threshold (WCT) based on time-frequency adaptation is proposed. In addition, an unvoiced speech enhancement algorithm is also integrated into the system to improve the intelligibility of speech. The wavelet coefficient threshold (WCT) of each subband is first temporally adjusted according to the value of a posterior signal-to-noise ratio (SNR). To prevent the degradation of unvoiced sounds during noise, the algorithm utilizes a simple speech/noise detector (SND) and further divides speech signal into unvoiced and voiced sounds. Then, we apply appropriate wavelet thresholding according to voiced/unvoiced (V/U) decision. Based on the masking properties of human auditory system, a perceptual gain factor is adopted into wavelet thresholding for suppressing musical residual noise. Simulation results show that the proposed method is capable of reducing noise with little speech degradation and the overall performance is superior to several competitive methods.
Adaptive wavelet transform algorithm for image compression applications
NASA Astrophysics Data System (ADS)
Pogrebnyak, Oleksiy B.; Manrique Ramirez, Pablo
2003-11-01
A new algorithm of locally adaptive wavelet transform is presented. The algorithm implements the integer-to-integer lifting scheme. It performs an adaptation of the wavelet function at the prediction stage to the local image data activity. The proposed algorithm is based on the generalized framework for the lifting scheme that permits to obtain easily different wavelet coefficients in the case of the (N~,N) lifting. It is proposed to perform the hard switching between (2, 4) and (4, 4) lifting filter outputs according to an estimate of the local data activity. When the data activity is high, i.e., in the vicinity of edges, the (4, 4) lifting is performed. Otherwise, in the plain areas, the (2,4) decomposition coefficients are calculated. The calculations are rather simples that permit the implementation of the designed algorithm in fixed point DSP processors. The proposed adaptive transform possesses the perfect restoration of the processed data and possesses good energy compactation. The designed algorithm was tested on different images. The proposed adaptive transform algorithm can be used for image/signal lossless compression.
Multi-Scale SSA or Data-Adaptive Wavelets
NASA Astrophysics Data System (ADS)
Yiou, P.; Sornette, D.; Sornette, D.; Sornette, D.; Ghil, M.; Ghil, M.
2001-05-01
Using multi-scale ideas from wavelet analysis, the singular-spectrum analysis (SSA) is extended to the study of nonstationary time series, including the case where their variance diverges. The wavelet transform is similar to a local Fourier transform within a finite moving window whose width W, proportional to the major period of interest, is varied to explore a broad range of such periods. SSA, on the other hand, relies on the construction of the lag-correlation matrix C on M lagged copies of the time series over a fixed window width W proportional to M to detect the regular part of the variability in that window in terms of the minimal number of oscillatory components. The proposed multi-scale SSA is a local SSA analysis within a moving window of width M<= W <= N, where N is the length of the time series. Multi-scale SSA varies W, while keeping a fixed W/M ratio, and uses the eigenvectors of the corresponding lag-correlation matrix C(M) as data-adaptive wavelets; successive eigenvectors of C(M) correspond approximately to successive derivatives of the first mother wavelet in standard wavelet analysis. Multi-scale SSA thus solves objectively the delicate problem of optimizing the analyzing wavelet in the time-frequency domain, by a suitable localization of the signal's correlation matrix. We present several examples of application to synthetic signals with fractal or power-law behavior which mimic selected features of certain climatic or geophysical time series. The method is applied to the monthly values of the Southern Oscillation index (SOI) which captures major features of the El Niño/Southern Oscillation in the Tropical Pacific. Our methodology highlights an abrupt periodicity shift in the SOI near 1960. This abrupt shift between 5 and 3 years supports the Devil's staircase scenario for the El Niño/Southern Oscillation phenomenon.
Wavelet domain image restoration with adaptive edge-preserving regularization.
Belge, M; Kilmer, M E; Miller, E L
2000-01-01
In this paper, we consider a wavelet based edge-preserving regularization scheme for use in linear image restoration problems. Our efforts build on a collection of mathematical results indicating that wavelets are especially useful for representing functions that contain discontinuities (i.e., edges in two dimensions or jumps in one dimension). We interpret the resulting theory in a statistical signal processing framework and obtain a highly flexible framework for adapting the degree of regularization to the local structure of the underlying image. In particular, we are able to adapt quite easily to scale-varying and orientation-varying features in the image while simultaneously retaining the edge preservation properties of the regularizer. We demonstrate a half-quadratic algorithm for obtaining the restorations from observed data.
Adaptive directional lifting-based wavelet transform for image coding.
Ding, Wenpeng; Wu, Feng; Wu, Xiaolin; Li, Shipeng; Li, Houqiang
2007-02-01
We present a novel 2-D wavelet transform scheme of adaptive directional lifting (ADL) in image coding. Instead of alternately applying horizontal and vertical lifting, as in present practice, ADL performs lifting-based prediction in local windows in the direction of high pixel correlation. Hence, it adapts far better to the image orientation features in local windows. The ADL transform is achieved by existing 1-D wavelets and is seamlessly integrated into the global wavelet transform. The predicting and updating signals of ADL can be derived even at the fractional pixel precision level to achieve high directional resolution, while still maintaining perfect reconstruction. To enhance the ADL performance, a rate-distortion optimized directional segmentation scheme is also proposed to form and code a hierarchical image partition adapting to local features. Experimental results show that the proposed ADL-based image coding technique outperforms JPEG 2000 in both PSNR and visual quality, with the improvement up to 2.0 dB on images with rich orientation features.
NASA Astrophysics Data System (ADS)
Liao, Qinzhuo; Zhang, Dongxiao; Tchelepi, Hamdi
2017-02-01
A new computational method is proposed for efficient uncertainty quantification of multiphase flow in porous media with stochastic permeability. For pressure estimation, it combines the dimension-adaptive stochastic collocation method on Smolyak sparse grids and the Kronrod-Patterson-Hermite nested quadrature formulas. For saturation estimation, an additional stage is developed, in which the pressure and velocity samples are first generated by the sparse grid interpolation and then substituted into the transport equation to solve for the saturation samples, to address the low regularity problem of the saturation. Numerical examples are presented for multiphase flow with stochastic permeability fields to demonstrate accuracy and efficiency of the proposed two-stage adaptive stochastic collocation method on nested sparse grids.
Radecki, Peter P; Farinholt, Kevin M; Park, Gyuhae; Bement, Matthew T
2008-01-01
The machining process is very important in many engineering applications. In high precision machining, surface finish is strongly correlated with vibrations and the dynamic interactions between the part and the cutting tool. Parameters affecting these vibrations and dynamic interactions, such as spindle speed, cut depth, feed rate, and the part's material properties can vary in real-time, resulting in unexpected or undesirable effects on the surface finish of the machining product. The focus of this research is the development of an improved machining process through the use of active vibration damping. The tool holder employs a high bandwidth piezoelectric actuator with an adaptive positive position feedback control algorithm for vibration and chatter suppression. In addition, instead of using external sensors, the proposed approach investigates the use of a collocated piezoelectric sensor for measuring the dynamic responses from machining processes. The performance of this method is evaluated by comparing the surface finishes obtained with active vibration control versus baseline uncontrolled cuts. Considerable improvement in surface finish (up to 50%) was observed for applications in modern day machining.
Mathematics of adaptive wavelet transforms: relating continuous with discrete transforms
NASA Astrophysics Data System (ADS)
Szu, Harold H.; Telfer, Brian A.
1994-07-01
We prove several theorems and construct explicitly the bridge between the continuous and discrete adaptive wavelet transform (AWT). The computational efficiency of the AWT is a result of its compact support closely matching linearly the signal's time-frequency characteristics, and is also a result of a larger redundancy factor of the superposition-mother s(x) (super-mother), created adaptively by a linear superposition of other admissible mother wavelets. The super-mother always forms a complete basis, but is usually associated with a higher redundancy number than its constituent complete orthonormal bases. The robustness of super-mother suffers less noise contamination (since noise is everywhere, and a redundant sampling by bandpassings can suppress the noise and enhance the signal). Since the continuous super-mother has been created off-line by AWT (using least-mean- squares neural nets), we wish to accomplish fast AWT on line. Thus, we formulate AWT in discrete high-pass (H) and low-pass (L) filter bank coefficients via the quadrature mirror filter, (QMF), a digital subband lossless coding. A linear combination of two special cases of complete biorthogonal normalized (Cbi-ON) QMF [L(z), H(z), L+(z), H+(z)], called (alpha) -bank and (Beta) -bank, becomes a hybrid a(alpha) + b(Beta) -bank (for any real positive constants a and b) that is still admissible, meaning Cbi-ON and lossless. Finally, the power of AWT is the implementation by means of wavelet chips and neurochips, in which each node is a daughter wavelet similar to a radial basis function using dyadic affine scaling.
Application of adaptive wavelet transforms via lifting in image data compression
NASA Astrophysics Data System (ADS)
Ye, Shujiang; Zhang, Ye; Liu, Baisen
2008-10-01
The adaptive wavelet transforms via lifting is proposed. In the transform, update filter is selected by the signal's character. Perfect reconstruction is possible without any overhead cost. To make sure the system's stability, in the lifting scheme of adaptive wavelet, update step is placed before prediction step. The Adaptive wavelet transforms via lifting is benefit for the image compression, because of the high stability, the small coefficients of high frequency parts, and the perfect reconstruction. With the adaptive wavelet transforms via lifting and the SPIHT, the image compression is realized in this paper, and the result is pleasant.
Wavelet-Based Adaptive Denoising of Phonocardiographic Records
2007-11-02
the approximated signal, and d the signal details at the given scale; h and g are biorthogonal filters, corresponding to the selected mother wavelet ...dyadic scale can be written as: where is the orthogonal mother wavelet , and: The discrete version of the dyadic wavelet transform can be based on... wavelet with 4 moments equal to zero (Coiflet-2) as the mother wavelet . The two channels were wavelet decomposed up to the 9th order (i = 0, 1 ... 8
Johnson, Richard Wayne
2003-05-01
The application of collocation methods using spline basis functions to solve differential model equations has been in use for a few decades. However, the application of spline collocation to the solution of the nonlinear, coupled, partial differential equations (in primitive variables) that define the motion of fluids has only recently received much attention. The issues that affect the effectiveness and accuracy of B-spline collocation for solving differential equations include which points to use for collocation, what degree B-spline to use and what level of continuity to maintain. Success using higher degree B-spline curves having higher continuity at the knots, as opposed to more traditional approaches using orthogonal collocation, have recently been investigated along with collocation at the Greville points for linear (1D) and rectangular (2D) geometries. The development of automatic knot insertion techniques to provide sufficient accuracy for B-spline collocation has been underway. The present article reviews recent progress for the application of B-spline collocation to fluid motion equations as well as new work in developing a novel adaptive knot insertion algorithm for a 1D convection-diffusion model equation.
Wavelet methods in multi-conjugate adaptive optics
NASA Astrophysics Data System (ADS)
Helin, T.; Yudytskiy, M.
2013-08-01
The next generation ground-based telescopes rely heavily on adaptive optics for overcoming the limitation of atmospheric turbulence. In the future adaptive optics modalities, like multi-conjugate adaptive optics (MCAO), atmospheric tomography is the major mathematical and computational challenge. In this severely ill-posed problem, a fast and stable reconstruction algorithm is needed that can take into account many real-life phenomena of telescope imaging. We introduce a novel reconstruction method for the atmospheric tomography problem and demonstrate its performance and flexibility in the context of MCAO. Our method is based on using locality properties of compactly supported wavelets, both in the spatial and frequency domains. The reconstruction in the atmospheric tomography problem is obtained by solving the Bayesian MAP estimator with a conjugate-gradient-based algorithm. An accelerated algorithm with preconditioning is also introduced. Numerical performance is demonstrated on the official end-to-end simulation tool OCTOPUS of European Southern Observatory.
Adaptive lifting scheme of wavelet transforms for image compression
NASA Astrophysics Data System (ADS)
Wu, Yu; Wang, Guoyin; Nie, Neng
2001-03-01
Aiming at the demand of adaptive wavelet transforms via lifting, a three-stage lifting scheme (predict-update-adapt) is proposed according to common two-stage lifting scheme (predict-update) in this paper. The second stage is updating stage. The third is adaptive predicting stage. Our scheme is an update-then-predict scheme that can detect jumps in image from the updated data and it needs not any more additional information. The first stage is the key in our scheme. It is the interim of updating. Its coefficient can be adjusted to adapt to data to achieve a better result. In the adaptive predicting stage, we use symmetric prediction filters in the smooth area of image, while asymmetric prediction filters at the edge of jumps to reduce predicting errors. We design these filters using spatial method directly. The inherent relationships between the coefficients of the first stage and the other stages are found and presented by equations. Thus, the design result is a class of filters with coefficient that are no longer invariant. Simulation result of image coding with our scheme is good.
NASA Technical Reports Server (NTRS)
Momoh, James A.; Wang, Yanchun; Dolce, James L.
1997-01-01
This paper describes the application of neural network adaptive wavelets for fault diagnosis of space station power system. The method combines wavelet transform with neural network by incorporating daughter wavelets into weights. Therefore, the wavelet transform and neural network training procedure become one stage, which avoids the complex computation of wavelet parameters and makes the procedure more straightforward. The simulation results show that the proposed method is very efficient for the identification of fault locations.
NASA Astrophysics Data System (ADS)
Nazimov, A. I.; Pavlov, A. N.; Lychagov, V. V.; Semyachkina-Glushkovskaya, O. V.
2013-10-01
A method of adaptive wavelet analysis permitting one to set parameters of the wavelet transform based on principles of the optimization theory is proposed. Applying the method to optical coherent tomography data processing is considered. The efficiency of the proposed method for diagnosing functional disorders in the dynamics of cerebral vessels is illustrated.
Wavelet-Based Adaptive Solvers on Multi-core Architectures for the Simulation of Complex Systems
NASA Astrophysics Data System (ADS)
Rossinelli, Diego; Bergdorf, Michael; Hejazialhosseini, Babak; Koumoutsakos, Petros
We build wavelet-based adaptive numerical methods for the simulation of advection dominated flows that develop multiple spatial scales, with an emphasis on fluid mechanics problems. Wavelet based adaptivity is inherently sequential and in this work we demonstrate that these numerical methods can be implemented in software that is capable of harnessing the capabilities of multi-core architectures while maintaining their computational efficiency. Recent designs in frameworks for multi-core software development allow us to rethink parallelism as task-based, where parallel tasks are specified and automatically mapped into physical threads. This way of exposing parallelism enables the parallelization of algorithms that were considered inherently sequential, such as wavelet-based adaptive simulations. In this paper we present a framework that combines wavelet-based adaptivity with the task-based parallelism. We demonstrate good scaling performance obtained by simulating diverse physical systems on different multi-core and SMP architectures using up to 16 cores.
Reversible wavelet filter banks with side informationless spatially adaptive low-pass filters
NASA Astrophysics Data System (ADS)
Abhayaratne, Charith
2011-07-01
Wavelet transforms that have an adaptive low-pass filter are useful in applications that require the signal singularities, sharp transitions, and image edges to be left intact in the low-pass signal. In scalable image coding, the spatial resolution scalability is achieved by reconstructing the low-pass signal subband, which corresponds to the desired resolution level, and discarding other high-frequency wavelet subbands. In such applications, it is vital to have low-pass subbands that are not affected by smoothing artifacts associated with low-pass filtering. We present the mathematical framework for achieving 1-D wavelet transforms that have a spatially adaptive low-pass filter (SALP) using the prediction-first lifting scheme. The adaptivity decisions are computed using the wavelet coefficients, and no bookkeeping is required for the perfect reconstruction. Then, 2-D wavelet transforms that have a spatially adaptive low-pass filter are designed by extending the 1-D SALP framework. Because the 2-D polyphase decompositions are used in this case, the 2-D adaptivity decisions are made nonseparable as opposed to the separable 2-D realization using 1-D transforms. We present examples using the 2-D 5/3 wavelet transform and their lossless image coding and scalable decoding performances in terms of quality and resolution scalability. The proposed 2-D-SALP scheme results in better performance compared to the existing adaptive update lifting schemes.
Lossless image compression with projection-based and adaptive reversible integer wavelet transforms.
Deever, Aaron T; Hemami, Sheila S
2003-01-01
Reversible integer wavelet transforms are increasingly popular in lossless image compression, as evidenced by their use in the recently developed JPEG2000 image coding standard. In this paper, a projection-based technique is presented for decreasing the first-order entropy of transform coefficients and improving the lossless compression performance of reversible integer wavelet transforms. The projection technique is developed and used to predict a wavelet transform coefficient as a linear combination of other wavelet transform coefficients. It yields optimal fixed prediction steps for lifting-based wavelet transforms and unifies many wavelet-based lossless image compression results found in the literature. Additionally, the projection technique is used in an adaptive prediction scheme that varies the final prediction step of the lifting-based transform based on a modeling context. Compared to current fixed and adaptive lifting-based transforms, the projection technique produces improved reversible integer wavelet transforms with superior lossless compression performance. It also provides a generalized framework that explains and unifies many previous results in wavelet-based lossless image compression.
Efficient architecture for adaptive directional lifting-based wavelet transform
NASA Astrophysics Data System (ADS)
Yin, Zan; Zhang, Li; Shi, Guangming
2010-07-01
Adaptive direction lifting-based wavelet transform (ADL) has better performance than conventional lifting both in image compression and de-noising. However, no architecture has been proposed to hardware implement it because of its high computational complexity and huge internal memory requirements. In this paper, we propose a four-stage pipelined architecture for 2 Dimensional (2D) ADL with fast computation and high data throughput. The proposed architecture comprises column direction estimation, column lifting, row direction estimation and row lifting which are performed in parallel in a pipeline mode. Since the column processed data is transposed, the row processor can reuse the column processor which can decrease the design complexity. In the lifting step, predict and update are also performed in parallel. For an 8×8 image sub-block, the proposed architecture can finish the ADL forward transform within 78 clock cycles. The architecture is implemented on Xilinx Virtex5 device on which the frequency can achieve 367 MHz. The processed time is 212.5 ns, which can meet the request of real-time system.
Wavelet-Based Speech Enhancement Using Time-Adapted Noise Estimation
NASA Astrophysics Data System (ADS)
Lei, Sheau-Fang; Tung, Ying-Kai
Spectral subtraction is commonly used for speech enhancement in a single channel system because of the simplicity of its implementation. However, this algorithm introduces perceptually musical noise while suppressing the background noise. We propose a wavelet-based approach in this paper for suppressing the background noise for speech enhancement in a single channel system. The wavelet packet transform, which emulates the human auditory system, is used to decompose the noisy signal into critical bands. Wavelet thresholding is then temporally adjusted with the noise power by time-adapted noise estimation. The proposed algorithm can efficiently suppress the noise while reducing speech distortion. Experimental results, including several objective measurements, show that the proposed wavelet-based algorithm outperforms spectral subtraction and other wavelet-based denoising approaches for speech enhancement for nonstationary noise environments.
NASA Astrophysics Data System (ADS)
DeVore, Ronald A.; Lucier, Bradley J.
The subject of `wavelets' is expanding at such a tremendous rate that it is impossible to give, within these few pages, a complete introduction to all aspects of its theory. We hope, however, to allow the reader to become sufficiently acquainted with the subject to understand, in part, the enthusiasm of its proponents toward its potential application to various numerical problems. Furthermore, we hope that our exposition can guide the reader who wishes to make more serious excursions into the subject. Our viewpoint is biased by our experience in approximation theory and data compression; we warn the reader that there are other viewpoints that are either not represented here or discussed only briefly. For example, orthogonal wavelets were developed primarily in the context of signal processing, an application upon which we touch only indirectly. However, there are several good expositions (e.g. Daubechies (1990) and Rioul and Vetterli (1991)) of this application. A discussion of wavelet decompositions in the context of Littlewood-Paley theory can be found in the monograph of Frazier et al. (1991). We shall also not attempt to give a complete discussion of the history of wavelets. Historical accounts can be found in the book of Meyer (1990) and the introduction of the article of Daubechies (1990). We shall try to give sufficient historical commentary in the course of our presentation to provide some feeling for the subject's development.
NASA Astrophysics Data System (ADS)
Zhang, Yan; Tang, Baoping; Liu, Ziran; Chen, Rengxiang
2016-02-01
Fault diagnosis of rolling element bearings is important for improving mechanical system reliability and performance. Vibration signals contain a wealth of complex information useful for state monitoring and fault diagnosis. However, any fault-related impulses in the original signal are often severely tainted by various noises and the interfering vibrations caused by other machine elements. Narrow-band amplitude demodulation has been an effective technique to detect bearing faults by identifying bearing fault characteristic frequencies. To achieve this, the key step is to remove the corrupting noise and interference, and to enhance the weak signatures of the bearing fault. In this paper, a new method based on adaptive wavelet filtering and spectral subtraction is proposed for fault diagnosis in bearings. First, to eliminate the frequency associated with interfering vibrations, the vibration signal is bandpass filtered with a Morlet wavelet filter whose parameters (i.e. center frequency and bandwidth) are selected in separate steps. An alternative and efficient method of determining the center frequency is proposed that utilizes the statistical information contained in the production functions (PFs). The bandwidth parameter is optimized using a local ‘greedy’ scheme along with Shannon wavelet entropy criterion. Then, to further reduce the residual in-band noise in the filtered signal, a spectral subtraction procedure is elaborated after wavelet filtering. Instead of resorting to a reference signal as in the majority of papers in the literature, the new method estimates the power spectral density of the in-band noise from the associated PF. The effectiveness of the proposed method is validated using simulated data, test rig data, and vibration data recorded from the transmission system of a helicopter. The experimental results and comparisons with other methods indicate that the proposed method is an effective approach to detecting the fault-related impulses
Shape-adaptive discrete wavelet transform for coding arbitrarily shaped texture
NASA Astrophysics Data System (ADS)
Li, Shipeng; Li, Weiping
1997-01-01
This paper presents a shape adaptive discrete wavelet transform (SA-DWT) scheme for coding arbitrarily shaped texture. The proposed SA-DWT can be used for object-oriented image coding. The number of coefficients after SA-DWT is identical to the number of pels contained in the arbitrarily shaped image objects. The locality property of wavelet transform and self-similarity among subbands are well preserved throughout this process.For a rectangular region, the SA-DWT is identical to a standard wavelet transform. With SA-DWT, conventional wavelet based coding schemes can be readily extended to the coding of arbitrarily shaped objects. The proposed shape adaptive wavelet transform is not unitary but the small energy increase is restricted at the boundary of objects in subbands. Two approaches of using the SA-DWT algorithm for object-oriented image and video coding are presented. One is to combine scalar SA-DWT with embedded zerotree wavelet (EZW) coding technique, the other is an extension of the normal vector wavelet coding (VWC) technique to arbitrarily shaped objects. Results of applying SA-VWC to real arbitrarily shaped texture coding are also given at the end of this paper.
Adaptive Bayesian-based speck-reduction in SAR images using complex wavelet transform
NASA Astrophysics Data System (ADS)
Ma, Ning; Yan, Wei; Zhang, Peng
2005-10-01
In this paper, an improved adaptive speckle reduction method is presented based on dual tree complex wavelet transform (CWT). It combines the characteristics of additive noise reduction of soft thresholding with the CWT's directional selectivity, being its main contribution to adapt the effective threshold to preserve the edge detail. A Bayesian estimator is applied to the decomposed data also to estimate the best value for the noise-free complex wavelet coefficients. This estimation is based on alpha-stable and Gaussian distribution hypotheses for complex wavelet coefficients of the signal and noise, respectively. Experimental results show that the denoising performance is among the state-of-the-art techniques based on real discrete wavelet transform (DWT).
NASA Technical Reports Server (NTRS)
Jawerth, Bjoern; Sweldens, Wim
1993-01-01
We present ideas on how to use wavelets in the solution of boundary value ordinary differential equations. Rather than using classical wavelets, we adapt their construction so that they become (bi)orthogonal with respect to the inner product defined by the operator. The stiffness matrix in a Galerkin method then becomes diagonal and can thus be trivially inverted. We show how one can construct an O(N) algorithm for various constant and variable coefficient operators.
Wavelet detection of weak far-magnetic signal based on adaptive ARMA model threshold
NASA Astrophysics Data System (ADS)
Zhang, Ning; Lin, Chun-sheng; Fang, Shi
2009-10-01
Based on Mallat algorithm, a de-noising algorithm of adaptive wavelet threshold is applied for weak magnetic signal detection of far moving target in complex magnetic environment. The choice of threshold is the key problem. With the spectrum analysis of the magnetic field target, a threshold algorithm on the basis of adaptive ARMA model filter is brought forward to improve the wavelet filtering performance. The simulation of this algorithm on measured data is carried out. Compared to Donoho threshold algorithm, it shows that adaptive ARMA model threshold algorithm significantly improved the capability of weak magnetic signal detection in complex magnetic environment.
Spatially adaptive bases in wavelet-based coding of semi-regular meshes
NASA Astrophysics Data System (ADS)
Denis, Leon; Florea, Ruxandra; Munteanu, Adrian; Schelkens, Peter
2010-05-01
In this paper we present a wavelet-based coding approach for semi-regular meshes, which spatially adapts the employed wavelet basis in the wavelet transformation of the mesh. The spatially-adaptive nature of the transform requires additional information to be stored in the bit-stream in order to allow the reconstruction of the transformed mesh at the decoder side. In order to limit this overhead, the mesh is first segmented into regions of approximately equal size. For each spatial region, a predictor is selected in a rate-distortion optimal manner by using a Lagrangian rate-distortion optimization technique. When compared against the classical wavelet transform employing the butterfly subdivision filter, experiments reveal that the proposed spatially-adaptive wavelet transform significantly decreases the energy of the wavelet coefficients for all subbands. Preliminary results show also that employing the proposed transform for the lowest-resolution subband systematically yields improved compression performance at low-to-medium bit-rates. For the Venus and Rabbit test models the compression improvements add up to 1.47 dB and 0.95 dB, respectively.
A wavelet approach to binary blackholes with asynchronous multitasking
NASA Astrophysics Data System (ADS)
Lim, Hyun; Hirschmann, Eric; Neilsen, David; Anderson, Matthew; Debuhr, Jackson; Zhang, Bo
2016-03-01
Highly accurate simulations of binary black holes and neutron stars are needed to address a variety of interesting problems in relativistic astrophysics. We present a new method for the solving the Einstein equations (BSSN formulation) using iterated interpolating wavelets. Wavelet coefficients provide a direct measure of the local approximation error for the solution and place collocation points that naturally adapt to features of the solution. Further, they exhibit exponential convergence on unevenly spaced collection points. The parallel implementation of the wavelet simulation framework presented here deviates from conventional practice in combining multi-threading with a form of message-driven computation sometimes referred to as asynchronous multitasking.
An adaptive wavelet neural network for spatio-temporal system identification.
Wei, H L; Billings, S A; Zhao, Y F; Guo, L Z
2010-12-01
Starting from the basic concept of coupled map lattices, a new family of adaptive wavelet neural networks (AWNN) is introduced for spatio-temporal system identification, by combining an efficient wavelet representation with a coupled map lattice model. A new orthogonal projection pursuit (OPP) method, coupled with a particle swarm optimization (PSO) algorithm, is proposed for augmenting the proposed network. A novel two-stage hybrid training scheme is developed for constructing a parsimonious network model. In the first stage, by applying the orthogonal projection pursuit algorithm, significant wavelet neurons are adaptively and successively recruited into the network, where adjustable parameters of the associated wavelet neurons are optimized using a particle swarm optimizer. The resultant network model, obtained in the first stage, may however be redundant. In the second stage, an orthogonal least squares algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet neurons from the network. The proposed two-stage hybrid training procedure can generally produce a parsimonious network model, where a ranked list of wavelet neurons, according to the capability of each neuron to represent the total variance in the system output signal is produced. Two spatio-temporal system identification examples are presented to demonstrate the performance of the proposed new modelling framework.
Yang, Zijing; Cai, Ligang; Gao, Lixin; Wang, Huaqing
2012-01-01
A least square method based on data fitting is proposed to construct a new lifting wavelet, together with the nonlinear idea and redundant algorithm, the adaptive redundant lifting transform based on fitting is firstly stated in this paper. By variable combination selections of basis function, sample number and dimension of basis function, a total of nine wavelets with different characteristics are constructed, which are respectively adopted to perform redundant lifting wavelet transforms on low-frequency approximate signals at each layer. Then the normalized lP norms of the new node-signal obtained through decomposition are calculated to adaptively determine the optimal wavelet for the decomposed approximate signal. Next, the original signal is taken for subsection power spectrum analysis to choose the node-signal for single branch reconstruction and demodulation. Experiment signals and engineering signals are respectively used to verify the above method and the results show that bearing faults can be diagnosed more effectively by the method presented here than by both spectrum analysis and demodulation analysis. Meanwhile, compared with the symmetrical wavelets constructed with Lagrange interpolation algorithm, the asymmetrical wavelets constructed based on data fitting are more suitable in feature extraction of fault signal of roller bearings. PMID:22666035
Coherent structure extraction in turbulent channel flow using boundary adapted wavelets
NASA Astrophysics Data System (ADS)
Sakurai, Teluo; Yoshimatsu, Katsunori; Schneider, Kai; Farge, Marie; Morishita, Koji; Ishihara, Takashi
2017-04-01
We present a construction of isotropic boundary adapted wavelets, which are orthogonal and yield a multi-resolution analysis. We analyze direct numerical simulation data of turbulent channel flow computed at a friction Reynolds number of 395, and investigate the role of coherent vorticity. Thresholding of the vorticity wavelet coefficients allows to split the flow into two parts, coherent and incoherent vorticity. The coherent vorticity is reconstructed from their few intense wavelet coefficients. The statistics of the coherent part, i.e., energy and enstrophy spectra, are close to the statistics of the total flow, and moreover, the nonlinear energy budgets are very well preserved. The remaining incoherent part, represented by the large majority of the weak wavelet coefficients, corresponds to a structureless, i.e., noise-like, background flow whose energy is equidistributed.
Optimal rejection of multiplicative noise via adaptive shrinkage of undecimated wavelet coefficients
NASA Astrophysics Data System (ADS)
Alparone, Luciano; Anghele, Nicola; Argenti, Fabrizio
2001-12-01
In this paper speckle reduction is approached as a Wiener-like filtering performed in the wavelet domain by means of an adaptive shrinkage of the detail coefficients of an undecimated decomposition. The amplitude of each coefficient is divided by the variance ratio of the noisy coefficient to the noise-free one. All the above quantities are analytically calculated from the speckled image, the speckle variance, and the wavelet filters. On the test image Lenna corrupted by synthetic speckle, the proposed method outperforms Kuan's LLMMSE filtering by almost 3 dB SNR. Experiments carried out on true and synthetic speckled images demonstrate that the visual quality of the results is excellent in terms of both background smoothing and preservation of edge sharpness and textures. The absence of decimation in the wavelet decomposition avoids the typical ringing impairments produced by critically-subsampled wavelet-based denoising.
Serial identification of EEG patterns using adaptive wavelet-based analysis
NASA Astrophysics Data System (ADS)
Nazimov, A. I.; Pavlov, A. N.; Nazimova, A. A.; Grubov, V. V.; Koronovskii, A. A.; Sitnikova, E.; Hramov, A. E.
2013-10-01
A problem of recognition specific oscillatory patterns in the electroencephalograms with the continuous wavelet-transform is discussed. Aiming to improve abilities of the wavelet-based tools we propose a serial adaptive method for sequential identification of EEG patterns such as sleep spindles and spike-wave discharges. This method provides an optimal selection of parameters based on objective functions and enables to extract the most informative features of the recognized structures. Different ways of increasing the quality of patterns recognition within the proposed serial adaptive technique are considered.
Zhang, Guannan; Webster, Clayton G; Gunzburger, Max D
2012-09-01
Although Bayesian analysis has become vital to the quantification of prediction uncertainty in groundwater modeling, its application has been hindered due to the computational cost associated with numerous model executions needed for exploring the posterior probability density function (PPDF) of model parameters. This is particularly the case when the PPDF is estimated using Markov Chain Monte Carlo (MCMC) sampling. In this study, we develop a new approach that improves computational efficiency of Bayesian inference by constructing a surrogate system based on an adaptive sparse-grid high-order stochastic collocation (aSG-hSC) method. Unlike previous works using first-order hierarchical basis, we utilize a compactly supported higher-order hierar- chical basis to construct the surrogate system, resulting in a significant reduction in the number of computational simulations required. In addition, we use hierarchical surplus as an error indi- cator to determine adaptive sparse grids. This allows local refinement in the uncertain domain and/or anisotropic detection with respect to the random model parameters, which further improves computational efficiency. Finally, we incorporate a global optimization technique and propose an iterative algorithm for building the surrogate system for the PPDF with multiple significant modes. Once the surrogate system is determined, the PPDF can be evaluated by sampling the surrogate system directly with very little computational cost. The developed method is evaluated first using a simple analytical density function with multiple modes and then using two synthetic groundwater reactive transport models. The groundwater models represent different levels of complexity; the first example involves coupled linear reactions and the second example simulates nonlinear ura- nium surface complexation. The results show that the aSG-hSC is an effective and efficient tool for Bayesian inference in groundwater modeling in comparison with conventional
Optical image compression based on adaptive directional prediction discrete wavelet transform
NASA Astrophysics Data System (ADS)
Zhang, Libao; Qiu, Bingchang
2013-11-01
The traditional lifting wavelet transform cannot effectively reconstruct the nonhorizontal and nonvertical high-frequency information of an image. In this paper, we present a new image compression method based on adaptive directional prediction discrete wavelet transform (ADP-DWT). We first design a directional prediction model to obtain the optimal transform direction of the lifting wavelet. Then, we execute the directional lifting transform along the optimal transform direction. The edge and texture energy can be reduced in the nonhorizontal and nonvertical directions of the high-frequency sub-bands. Finally, the wavelet coefficients are coded with the set partitioning in hierarchical trees (SPIHT) algorithm. The new method holds the advantages of both adaptive directional lifting (ADL) and direction-adaptive discrete wavelet transform (DA-DWT), and the computational complexity is far lower than that in these methods. For the images containing regular and fine textures or edges, the coding preformance of ADP-DWT is better than that of ADL and DA-DWT.
NASA Technical Reports Server (NTRS)
Sjoegreen, B.; Yee, H. C.
2001-01-01
The recently developed essentially fourth-order or higher low dissipative shock-capturing scheme of Yee, Sandham and Djomehri (1999) aimed at minimizing nu- merical dissipations for high speed compressible viscous flows containing shocks, shears and turbulence. To detect non smooth behavior and control the amount of numerical dissipation to be added, Yee et al. employed an artificial compression method (ACM) of Harten (1978) but utilize it in an entirely different context than Harten originally intended. The ACM sensor consists of two tuning parameters and is highly physical problem dependent. To minimize the tuning of parameters and physical problem dependence, new sensors with improved detection properties are proposed. The new sensors are derived from utilizing appropriate non-orthogonal wavelet basis functions and they can be used to completely switch to the extra numerical dissipation outside shock layers. The non-dissipative spatial base scheme of arbitrarily high order of accuracy can be maintained without compromising its stability at all parts of the domain where the solution is smooth. Two types of redundant non-orthogonal wavelet basis functions are considered. One is the B-spline wavelet (Mallat & Zhong 1992) used by Gerritsen and Olsson (1996) in an adaptive mesh refinement method, to determine regions where re nement should be done. The other is the modification of the multiresolution method of Harten (1995) by converting it to a new, redundant, non-orthogonal wavelet. The wavelet sensor is then obtained by computing the estimated Lipschitz exponent of a chosen physical quantity (or vector) to be sensed on a chosen wavelet basis function. Both wavelet sensors can be viewed as dual purpose adaptive methods leading to dynamic numerical dissipation control and improved grid adaptation indicators. Consequently, they are useful not only for shock-turbulence computations but also for computational aeroacoustics and numerical combustion. In addition, these
Mouse EEG spike detection based on the adapted continuous wavelet transform
NASA Astrophysics Data System (ADS)
Tieng, Quang M.; Kharatishvili, Irina; Chen, Min; Reutens, David C.
2016-04-01
Objective. Electroencephalography (EEG) is an important tool in the diagnosis of epilepsy. Interictal spikes on EEG are used to monitor the development of epilepsy and the effects of drug therapy. EEG recordings are generally long and the data voluminous. Thus developing a sensitive and reliable automated algorithm for analyzing EEG data is necessary. Approach. A new algorithm for detecting and classifying interictal spikes in mouse EEG recordings is proposed, based on the adapted continuous wavelet transform (CWT). The construction of the adapted mother wavelet is founded on a template obtained from a sample comprising the first few minutes of an EEG data set. Main Result. The algorithm was tested with EEG data from a mouse model of epilepsy and experimental results showed that the algorithm could distinguish EEG spikes from other transient waveforms with a high degree of sensitivity and specificity. Significance. Differing from existing approaches, the proposed approach combines wavelet denoising, to isolate transient signals, with adapted CWT-based template matching, to detect true interictal spikes. Using the adapted wavelet constructed from a predefined template, the adapted CWT is calculated on small EEG segments to fit dynamical changes in the EEG recording.
Adaptive 2-D wavelet transform based on the lifting scheme with preserved vanishing moments.
Vrankic, Miroslav; Sersic, Damir; Sucic, Victor
2010-08-01
In this paper, we propose novel adaptive wavelet filter bank structures based on the lifting scheme. The filter banks are nonseparable, based on quincunx sampling, with their properties being pixel-wise adapted according to the local image features. Despite being adaptive, the filter banks retain a desirable number of primal and dual vanishing moments. The adaptation is introduced in the predict stage of the filter bank with an adaptation region chosen independently for each pixel, based on the intersection of confidence intervals (ICI) rule. The image denoising results are presented for both synthetic and real-world images. It is shown that the obtained wavelet decompositions perform well, especially for synthetic images that contain periodic patterns, for which the proposed method outperforms the state of the art in image denoising.
Non-parametric transient classification using adaptive wavelets
NASA Astrophysics Data System (ADS)
Varughese, Melvin M.; von Sachs, Rainer; Stephanou, Michael; Bassett, Bruce A.
2015-11-01
Classifying transients based on multiband light curves is a challenging but crucial problem in the era of GAIA and Large Synoptic Sky Telescope since the sheer volume of transients will make spectroscopic classification unfeasible. We present a non-parametric classifier that predicts the transient's class given training data. It implements two novel components: the use of the BAGIDIS wavelet methodology - a characterization of functional data using hierarchical wavelet coefficients - as well as the introduction of a ranked probability classifier on the wavelet coefficients that handles both the heteroscedasticity of the data in addition to the potential non-representativity of the training set. The classifier is simple to implement while a major advantage of the BAGIDIS wavelets is that they are translation invariant. Hence, BAGIDIS does not need the light curves to be aligned to extract features. Further, BAGIDIS is non-parametric so it can be used effectively in blind searches for new objects. We demonstrate the effectiveness of our classifier against the Supernova Photometric Classification Challenge to correctly classify supernova light curves as Type Ia or non-Ia. We train our classifier on the spectroscopically confirmed subsample (which is not representative) and show that it works well for supernova with observed light-curve time spans greater than 100 d (roughly 55 per cent of the data set). For such data, we obtain a Ia efficiency of 80.5 per cent and a purity of 82.4 per cent, yielding a highly competitive challenge score of 0.49. This indicates that our `model-blind' approach may be particularly suitable for the general classification of astronomical transients in the era of large synoptic sky surveys.
Gap Measurement of Point Machine Using Adaptive Wavelet Threshold and Mathematical Morphology
Xu, Tianhua; Wang, Guang; Wang, Haifeng; Yuan, Tangming; Zhong, Zhiwang
2016-01-01
A point machine’s gap is an important indication of its healthy status. An edge detection algorithm is proposed to measure and calculate a point machine’s gap from the gap image captured by CCD plane arrays. This algorithm integrates adaptive wavelet-based image denoising, locally adaptive image binarization, and mathematical morphology technologies. The adaptive wavelet-based image denoising obtains not only an optimal denoising threshold, but also unblurred edges. Locally adaptive image binarization has the advantage of overcoming the local intensity variation in gap images. Mathematical morphology may suppress speckle spots caused by reflective metal surfaces in point machines. The subjective and objective evaluations of the proposed method are presented by using point machine gap images from a railway corporation in China. The performance between the proposed method and conventional edge detection methods has also been compared, and the result shows that the former outperforms the latter. PMID:27898042
Hyperspectral image compression: adapting SPIHT and EZW to anisotropic 3-D wavelet coding.
Christophe, Emmanuel; Mailhes, Corinne; Duhamel, Pierre
2008-12-01
Hyperspectral images present some specific characteristics that should be used by an efficient compression system. In compression, wavelets have shown a good adaptability to a wide range of data, while being of reasonable complexity. Some wavelet-based compression algorithms have been successfully used for some hyperspectral space missions. This paper focuses on the optimization of a full wavelet compression system for hyperspectral images. Each step of the compression algorithm is studied and optimized. First, an algorithm to find the optimal 3-D wavelet decomposition in a rate-distortion sense is defined. Then, it is shown that a specific fixed decomposition has almost the same performance, while being more useful in terms of complexity issues. It is shown that this decomposition significantly improves the classical isotropic decomposition. One of the most useful properties of this fixed decomposition is that it allows the use of zero tree algorithms. Various tree structures, creating a relationship between coefficients, are compared. Two efficient compression methods based on zerotree coding (EZW and SPIHT) are adapted on this near-optimal decomposition with the best tree structure found. Performances are compared with the adaptation of JPEG 2000 for hyperspectral images on six different areas presenting different statistical properties.
Isotropic boundary adapted wavelets for coherent vorticity extraction in turbulent channel flows
NASA Astrophysics Data System (ADS)
Farge, Marie; Sakurai, Teluo; Yoshimatsu, Katsunori; Schneider, Kai; Morishita, Koji; Ishihara, Takashi
2015-11-01
We present a construction of isotropic boundary adapted wavelets, which are orthogonal and yield a multi-resolution analysis. We analyze DNS data of turbulent channel flow computed at a friction-velocity based Reynolds number of 395 and investigate the role of coherent vorticity. Thresholding of the wavelet coefficients allows to split the flow into two parts, coherent and incoherent vorticity. The statistics of the former, i.e., energy and enstrophy spectra, are close to the ones of the total flow, and moreover the nonlinear energy budgets are well preserved. The remaining incoherent part, represented by the large majority of the weak wavelet coefficients, corresponds to a structureless, i.e., noise-like, background flow and exhibits an almost equi-distribution of energy.
Adaptive wavelet packet-based de-speckling of ultrasound images with bilateral filter.
Esakkirajan, Sankaralingam; Vimalraj, Chinna Thambi; Muhammed, Rashad; Subramanian, Ganapathi
2013-12-01
A new adaptive wavelet packet-based approach to minimize speckle noise in ultrasound images is proposed. This method combines wavelet packet thresholding with a bilateral filter. Here, the best bases after wavelet packet decomposition are selected by comparing the first singular value of all sub-bands, and the noisy coefficients are thresholded using a modified NeighShrink technique. The algorithm is tested with various ultrasound images, and the results, in terms of peak signal-to-noise ratio and mean structural similarity values, are compared with those for some well-known de-speckling techniques. The simulation results indicate that the proposed method has better potential to minimize speckle noise and retain fine details of the ultrasound image.
A study of interceptor attitude control based on adaptive wavelet neural networks
NASA Astrophysics Data System (ADS)
Li, Da; Wang, Qing-chao
2005-12-01
This paper engages to study the 3-DOF attitude control problem of the kinetic interceptor. When the kinetic interceptor enters into terminal guidance it has to maneuver with large angles. The characteristic of interceptor attitude system is nonlinearity, strong-coupling and MIMO. A kind of inverse control approach based on adaptive wavelet neural networks was proposed in this paper. Instead of using one complex neural network as the controller, the nonlinear dynamics of the interceptor can be approximated by three independent subsystems applying exact feedback-linearization firstly, and then controllers for each subsystem are designed using adaptive wavelet neural networks respectively. This method avoids computing a large amount of the weights and bias in one massive neural network and the control parameters can be adaptive changed online. Simulation results betray that the proposed controller performs remarkably well.
Multi-focus image fusion algorithm based on adaptive PCNN and wavelet transform
NASA Astrophysics Data System (ADS)
Wu, Zhi-guo; Wang, Ming-jia; Han, Guang-liang
2011-08-01
Being an efficient method of information fusion, image fusion has been used in many fields such as machine vision, medical diagnosis, military applications and remote sensing. In this paper, Pulse Coupled Neural Network (PCNN) is introduced in this research field for its interesting properties in image processing, including segmentation, target recognition et al. and a novel algorithm based on PCNN and Wavelet Transform for Multi-focus image fusion is proposed. First, the two original images are decomposed by wavelet transform. Then, based on the PCNN, a fusion rule in the Wavelet domain is given. This algorithm uses the wavelet coefficient in each frequency domain as the linking strength, so that its value can be chosen adaptively. Wavelet coefficients map to the range of image gray-scale. The output threshold function attenuates to minimum gray over time. Then all pixels of image get the ignition. So, the output of PCNN in each iteration time is ignition wavelet coefficients of threshold strength in different time. At this moment, the sequences of ignition of wavelet coefficients represent ignition timing of each neuron. The ignition timing of PCNN in each neuron is mapped to corresponding image gray-scale range, which is a picture of ignition timing mapping. Then it can judge the targets in the neuron are obvious features or not obvious. The fusion coefficients are decided by the compare-selection operator with the firing time gradient maps and the fusion image is reconstructed by wavelet inverse transform. Furthermore, by this algorithm, the threshold adjusting constant is estimated by appointed iteration number. Furthermore, In order to sufficient reflect order of the firing time, the threshold adjusting constant αΘ is estimated by appointed iteration number. So after the iteration achieved, each of the wavelet coefficient is activated. In order to verify the effectiveness of proposed rules, the experiments upon Multi-focus image are done. Moreover
Refinement trajectory and determination of eigenstates by a wavelet based adaptive method
Pipek, Janos; Nagy, Szilvia
2006-11-07
The detail structure of the wave function is analyzed at various refinement levels using the methods of wavelet analysis. The eigenvalue problem of a model system is solved in granular Hilbert spaces, and the trajectory of the eigenstates is traced in terms of the resolution. An adaptive method is developed for identifying the fine structure localization regions, where further refinement of the wave function is necessary.
NASA Astrophysics Data System (ADS)
Palaniswamy, Sumithra; Duraisamy, Prakash; Alam, Mohammad Showkat; Yuan, Xiaohui
2012-04-01
Automatic speech processing systems are widely used in everyday life such as mobile communication, speech and speaker recognition, and for assisting the hearing impaired. In speech communication systems, the quality and intelligibility of speech is of utmost importance for ease and accuracy of information exchange. To obtain an intelligible speech signal and one that is more pleasant to listen, noise reduction is essential. In this paper a new Time Adaptive Discrete Bionic Wavelet Thresholding (TADBWT) scheme is proposed. The proposed technique uses Daubechies mother wavelet to achieve better enhancement of speech from additive non- stationary noises which occur in real life such as street noise and factory noise. Due to the integration of human auditory system model into the wavelet transform, bionic wavelet transform (BWT) has great potential for speech enhancement which may lead to a new path in speech processing. In the proposed technique, at first, discrete BWT is applied to noisy speech to derive TADBWT coefficients. Then the adaptive nature of the BWT is captured by introducing a time varying linear factor which updates the coefficients at each scale over time. This approach has shown better performance than the existing algorithms at lower input SNR due to modified soft level dependent thresholding on time adaptive coefficients. The objective and subjective test results confirmed the competency of the TADBWT technique. The effectiveness of the proposed technique is also evaluated for speaker recognition task under noisy environment. The recognition results show that the TADWT technique yields better performance when compared to alternate methods specifically at lower input SNR.
NASA Astrophysics Data System (ADS)
Wang, Dong; Singh, Vijay P.; Shang, Xiaosan; Ding, Hao; Wu, Jichun; Wang, Lachun; Zou, Xinqing; Chen, Yuanfang; Chen, Xi; Wang, Shicheng; Wang, Zhenlong
2014-07-01
De-noising meteorologic and hydrologic time series is important to improve the accuracy and reliability of extraction, analysis, simulation, and forecasting. A hybrid approach, combining sample entropy and wavelet de-noising method, is developed to separate noise from original series and is named as AWDA-SE (adaptive wavelet de-noising approach using sample entropy). The AWDA-SE approach adaptively determines the threshold for wavelet analysis. Two kinds of meteorologic and hydrologic data sets, synthetic data set and 3 representative field measured data sets (one is the annual rainfall data of Jinan station and the other two are annual streamflow series from two typical stations in China, Yingluoxia station on the Heihe River, which is little affected by human activities, and Lijin station on the Yellow River, which is greatly affected by human activities), are used to illustrate the approach. The AWDA-SE approach is compared with three conventional de-noising methods, including fixed-form threshold algorithm, Stein unbiased risk estimation algorithm, and minimax algorithm. Results show that the AWDA-SE approach separates effectively the signal and noise of the data sets and is found to be better than the conventional methods. Measures of assessment standards show that the developed approach can be employed to investigate noisy and short time series and can also be applied to other areas.
Continuous digital ECG analysis over accurate R-peak detection using adaptive wavelet technique.
Gopalakrishnan Nair, T R; Geetha, A P; Asharani, M
2013-10-01
Worldwide, health care segment is under a severe challenge to achieve more accurate and intelligent biomedical systems in order to assist healthcare professionals with more accurate and consistent data as well as reliability. The role of ECG in healthcare is one of the paramount importances and it has got a multitude of abnormal relations and anomalies which characterizes intricate cardiovascular performance image. Until the recent past, ECG instruments and analysis played the role of providing the PQRST signal as raw observational output either on paper or on a console or in a file having many diagnostic clues embedded in the signal left to the expert cardiologist to look out for characteristic intervals and to detect the cardiovascular abnormality. Methods and practises are required more and more, to automate this process of cardiac expertise using knowledge engineering and an intelligent systems approach. This paper presents one of the challenging R-peak detections to classify diagnosis and estimate cardio disorders in a fully automated signal processing sequence. This study used an adaptive wavelet approach to generate an appropriate wavelet for R-signal identification under noise, baseband wandering and temporal variations of R-positions. This study designed an adaptive wavelet and successfully detected R- peak variations under various ECG signal conditions. The result and analysis of this method and the ways to use it for further purposes are presented here.
Effective wavelet-based compression method with adaptive quantization threshold and zerotree coding
NASA Astrophysics Data System (ADS)
Przelaskowski, Artur; Kazubek, Marian; Jamrogiewicz, Tomasz
1997-10-01
Efficient image compression technique especially for medical applications is presented. Dyadic wavelet decomposition by use of Antonini and Villasenor bank filters is followed by adaptive space-frequency quantization and zerotree-based entropy coding of wavelet coefficients. Threshold selection and uniform quantization is made on a base of spatial variance estimate built on the lowest frequency subband data set. Threshold value for each coefficient is evaluated as linear function of 9-order binary context. After quantization zerotree construction, pruning and arithmetic coding is applied for efficient lossless data coding. Presented compression method is less complex than the most effective EZW-based techniques but allows to achieve comparable compression efficiency. Specifically our method has similar to SPIHT efficiency in MR image compression, slightly better for CT image and significantly better in US image compression. Thus the compression efficiency of presented method is competitive with the best published algorithms in the literature across diverse classes of medical images.
Yoo, Sung Jin; Park, Jin Bae; Choi, Yoon Ho
2006-12-01
A new method for the robust control of flexible-joint (FJ) robots with model uncertainties in both robot dynamics and actuator dynamics is proposed. The proposed control system is a combination of the adaptive dynamic surface control (DSC) technique and the self-recurrent wavelet neural network (SRWNN). The adaptive DSC technique provides the ability to overcome the "explosion of complexity" problem in backstepping controllers. The SRWNNs are used to observe the arbitrary model uncertainties of FJ robots, and all their weights are trained online. From the Lyapunov stability analysis, their adaptation laws are induced, and the uniformly ultimately boundedness of all signals in a closed-loop adaptive system is proved. Finally, simulation results for a three-link FJ robot are utilized to validate the good position tracking performance and robustness against payload uncertainties and external disturbances of the proposed control system.
Adaptive three-dimensional motion-compensated wavelet transform for image sequence coding
NASA Astrophysics Data System (ADS)
Leduc, Jean-Pierre
1994-09-01
This paper describes a 3D spatio-temporal coding algorithm for the bit-rate compression of digital-image sequences. The coding scheme is based on different specificities namely, a motion representation with a four-parameter affine model, a motion-adapted temporal wavelet decomposition along the motion trajectories and a signal-adapted spatial wavelet transform. The motion estimation is performed on the basis of four-parameter affine transformation models also called similitude. This transformation takes into account translations, rotations and scalings. The temporal wavelet filter bank exploits bi-orthogonal linear-phase dyadic decompositions. The 2D spatial decomposition is based on dyadic signal-adaptive filter banks with either para-unitary or bi-orthogonal bases. The adaptive filtering is carried out according to a performance criterion to be optimized under constraints in order to eventually maximize the compression ratio at the expense of graceful degradations of the subjective image quality. The major principles of the present technique is, in the analysis process, to extract and to separate the motion contained in the sequences from the spatio-temporal redundancy and, in the compression process, to take into account of the rate-distortion function on the basis of the spatio-temporal psycho-visual properties to achieve the most graceful degradations. To complete this description of the coding scheme, the compression procedure is therefore composed of scalar quantizers which exploit the spatio-temporal 3D psycho-visual properties of the Human Visual System and of entropy coders which finalize the bit rate compression.
Data-adaptive wavelets and multi-scale singular-spectrum analysis
NASA Astrophysics Data System (ADS)
Yiou, Pascal; Sornette, Didier; Ghil, Michael
2000-08-01
Using multi-scale ideas from wavelet analysis, we extend singular-spectrum analysis (SSA) to the study of nonstationary time series, including the case where intermittency gives rise to the divergence of their variance. The wavelet transform resembles a local Fourier transform within a finite moving window whose width W, proportional to the major period of interest, is varied to explore a broad range of such periods. SSA, on the other hand, relies on the construction of the lag-correlation matrix C on M lagged copies of the time series over a fixed window width W to detect the regular part of the variability in that window in terms of the minimal number of oscillatory components; here W= MΔ t with Δ t as the time step. The proposed multi-scale SSA is a local SSA analysis within a moving window of width M≤ W≤ N, where N is the length of the time series. Multi-scale SSA varies W, while keeping a fixed W/ M ratio, and uses the eigenvectors of the corresponding lag-correlation matrix C(M) as data-adaptive wavelets; successive eigenvectors of C(M) correspond approximately to successive derivatives of the first mother wavelet in standard wavelet analysis. Multi-scale SSA thus solves objectively the delicate problem of optimizing the analyzing wavelet in the time-frequency domain by a suitable localization of the signal’s correlation matrix. We present several examples of application to synthetic signals with fractal or power-law behavior which mimic selected features of certain climatic or geophysical time series. The method is applied next to the monthly values of the Southern Oscillation Index (SOI) for 1933-1996; the SOI time series is widely believed to capture major features of the El Niño/Southern Oscillation (ENSO) in the Tropical Pacific. Our methodology highlights an abrupt periodicity shift in the SOI near 1960. This abrupt shift between 5 and 3 years supports the Devil’s staircase scenario for the ENSO phenomenon (preliminary results of this study
Lemeshewsky, G.P.; Rahman, Z.-U.; Schowengerdt, R.A.; Reichenbach, S.E.
2002-01-01
Enhanced false color images from mid-IR, near-IR (NIR), and visible bands of the Landsat thematic mapper (TM) are commonly used for visually interpreting land cover type. Described here is a technique for sharpening or fusion of NIR with higher resolution panchromatic (Pan) that uses a shift-invariant implementation of the discrete wavelet transform (SIDWT) and a reported pixel-based selection rule to combine coefficients. There can be contrast reversals (e.g., at soil-vegetation boundaries between NIR and visible band images) and consequently degraded sharpening and edge artifacts. To improve performance for these conditions, I used a local area-based correlation technique originally reported for comparing image-pyramid-derived edges for the adaptive processing of wavelet-derived edge data. Also, using the redundant data of the SIDWT improves edge data generation. There is additional improvement because sharpened subband imagery is used with the edge-correlation process. A reported technique for sharpening three-band spectral imagery used forward and inverse intensity, hue, and saturation transforms and wavelet-based sharpening of intensity. This technique had limitations with opposite contrast data, and in this study sharpening was applied to single-band multispectral-Pan image pairs. Sharpening used simulated 30-m NIR imagery produced by degrading the spatial resolution of a higher resolution reference. Performance, evaluated by comparison between sharpened and reference image, was improved when sharpened subband data were used with the edge correlation.
A wavelet-optimized, very high order adaptive grid and order numerical method
NASA Technical Reports Server (NTRS)
Jameson, Leland
1996-01-01
Differencing operators of arbitrarily high order can be constructed by interpolating a polynomial through a set of data followed by differentiation of this polynomial and finally evaluation of the polynomial at the point where a derivative approximation is desired. Furthermore, the interpolating polynomial can be constructed from algebraic, trigonometric, or, perhaps exponential polynomials. This paper begins with a comparison of such differencing operator construction. Next, the issue of proper grids for high order polynomials is addressed. Finally, an adaptive numerical method is introduced which adapts the numerical grid and the order of the differencing operator depending on the data. The numerical grid adaptation is performed on a Chebyshev grid. That is, at each level of refinement the grid is a Chebvshev grid and this grid is refined locally based on wavelet analysis.
Adaptive Wavelet Galerkin Methods on Distorted Domains: Setup of the Algebraic System
2000-01-01
let T, and T• be the largest integers such that O E W7!,’°(!2) andj E wTf’,-(Q), respectively. Then, we set R:= min{Ro, Tý - II & II , Th - 11[111. We...the first time. Moreover, for computing the right-hand side, two Adaptive Wavelet Galerkin Methods 71 AI = Ij = jo, AI= jo, = jo + 1 AI= ii = Jo + 1 4J...during the preparation of this paper. The first author is extremely grateful to the Dipartimento di Matematica of the Politecnico di Torino for using its
NASA Astrophysics Data System (ADS)
Xie, Hua; Bosshard, John C.; Hill, Jason E.; Wright, Steven M.; Mitra, Sunanda
2016-03-01
Magnetic Resonance Imaging (MRI) offers noninvasive high resolution, high contrast cross-sectional anatomic images through the body. The data of the conventional MRI is collected in spatial frequency (Fourier) domain, also known as kspace. Because there is still a great need to improve temporal resolution of MRI, Compressed Sensing (CS) in MR imaging is proposed to exploit the sparsity of MR images showing great potential to reduce the scan time significantly, however, it poses its own unique problems. This paper revisits wavelet-encoded MR imaging which replaces phase encoding in conventional MRI data acquisition with wavelet encoding by applying wavelet-shaped spatially selective radiofrequency (RF) excitation, and keeps the readout direction as frequency encoding. The practicality of wavelet encoded MRI by itself is limited due to the SNR penalties and poor time resolution compared to conventional Fourier-based MRI. To compensate for those disadvantages, this paper first introduces an undersampling scheme named significance map for sparse wavelet-encoded k-space to speed up data acquisition as well as allowing for various adaptive imaging strategies. The proposed adaptive wavelet-encoded undersampling scheme does not require prior knowledge of the subject to be scanned. Multiband (MB) parallel imaging is also incorporated with wavelet-encoded MRI by exciting multiple regions simultaneously for further reduction in scan time desirable for medical applications. The simulation and experimental results are presented showing the feasibility of the proposed approach in further reduction of the redundancy of the wavelet k-space data while maintaining relatively high quality.
A Parallel Adaptive Wavelet Method for the Simulation of Compressible Reacting Flows
NASA Astrophysics Data System (ADS)
Zikoski, Zachary; Paolucci, Samuel
2011-11-01
The Wavelet Adaptive Multiresolution Representation (WAMR) method provides a robust method for controlling spatial grid adaption--fine grid spacing in regions of a solution requiring high resolution (i.e. near steep gradients, singularities, or near- singularities) and using much coarser grid spacing where the solution is slowly varying. The sparse grids produced using the WAMR method exhibit very high compression ratios compared to uniform grids of equivalent resolution. Subsequently, a wide range of spatial scales often occurring in continuum physics models can be captured efficiently. Furthermore, the wavelet transform provides a direct measure of local error at each grid point, effectively producing automatically verified solutions. The algorithm is parallelized using an MPI-based domain decomposition approach suitable for a wide range of distributed-memory parallel architectures. The method is applied to the solution of the compressible, reactive Navier-Stokes equations and includes multi-component diffusive transport and chemical kinetics models. Results for the method's parallel performance are reported, and its effectiveness on several challenging compressible reacting flow problems is highlighted.
Adaptive wavelet simulation of global ocean dynamics using a new Brinkman volume penalization
NASA Astrophysics Data System (ADS)
Kevlahan, N. K.-R.; Dubos, T.; Aechtner, M.
2015-12-01
In order to easily enforce solid-wall boundary conditions in the presence of complex coastlines, we propose a new mass and energy conserving Brinkman penalization for the rotating shallow water equations. This penalization does not lead to higher wave speeds in the solid region. The error estimates for the penalization are derived analytically and verified numerically for linearized one-dimensional equations. The penalization is implemented in a conservative dynamically adaptive wavelet method for the rotating shallow water equations on the sphere with bathymetry and coastline data from NOAA's ETOPO1 database. This code could form the dynamical core for a future global ocean model. The potential of the dynamically adaptive ocean model is illustrated by using it to simulate the 2004 Indonesian tsunami and wind-driven gyres.
Zhu, Xiaojun; Lei, Guangtsai; Pan, Guangwen
1997-04-01
In this paper, the continuous operator is discretized into matrix forms by Galerkin`s procedure, using periodic Battle-Lemarie wavelets as basis/testing functions. The polynomial decomposition of wavelets is applied to the evaluation of matrix elements, which makes the computational effort of the matrix elements no more expensive than that of method of moments (MoM) with conventional piecewise basis/testing functions. A new algorithm is developed employing the fast wavelet transform (FWT). Owing to localization, cancellation, and orthogonal properties of wavelets, very sparse matrices have been obtained, which are then solved by the LSQR iterative method. This algorithm is also adaptive in that one can add at will finer wavelet bases in the regions where fields vary rapidly, without any damage to the system orthogonality of the wavelet basis functions. To demonstrate the effectiveness of the new algorithm, we applied it to the evaluation of frequency-dependent resistance and inductance matrices of multiple lossy transmission lines. Numerical results agree with previously published data and laboratory measurements. The valid frequency range of the boundary integral equation results has been extended two to three decades in comparison with the traditional MoM approach. The new algorithm has been integrated into the computer aided design tool, MagiCAD, which is used for the design and simulation of high-speed digital systems and multichip modules Pan et al. 29 refs., 7 figs., 6 tabs.
De-striping hyperspectral imagery using wavelet transform and adaptive frequency domain filtering
NASA Astrophysics Data System (ADS)
Pande-Chhetri, Roshan; Abd-Elrahman, Amr
2011-09-01
Hyperspectral imagers are built line-by-line similar to images acquired by pushbroom sensors. They can experience striping artifacts due to variations in detector response to incident imagery. In this research, a method for hyperspectral image de-striping based on wavelet analysis and adaptive Fourier zero-frequency amplitude normalization has been developed. The algorithm was tested against three other de-striping algorithms. Hyperspectral image bands of different scenes with significant striping and random noise, as well as an image with simulated noise, were used in the testing. The results were assessed visually and quantitatively using frequency domain Signal-to-Noise Ratio (SNR), Root Mean Square Error (RMSE) and/or Peak Signal-to-Ratio (PSNR). The results demonstrated the superiority of our proposed algorithm in de-striping hyperspectral images without introducing unwanted artifacts, yet preserving image details. In the noise-induced image results, the proposed method reduced RMSE error and improved PSNR by 3.5 dB which is better than other tested methods. A Combined method, integrating the proposed algorithm with a generic wavelet-based de-noising algorithm, showed significant random noise suppression in addition to stripe reduction with a PSNR value of 4.3 dB. These findings make the algorithm a candidate for practical implementation on remote sensing images including high resolution hyperspectral images contaminated with stripe and random noise.
Goffin, Mark A.; Buchan, Andrew G.; Dargaville, Steven; Pain, Christopher C.; Smith, Paul N.; Smedley-Stevenson, Richard P.
2015-01-15
A method for applying goal-based adaptive methods to the angular resolution of the neutral particle transport equation is presented. The methods are applied to an octahedral wavelet discretisation of the spherical angular domain which allows for anisotropic resolution. The angular resolution is adapted across both the spatial and energy dimensions. The spatial domain is discretised using an inner-element sub-grid scale finite element method. The goal-based adaptive methods optimise the angular discretisation to minimise the error in a specific functional of the solution. The goal-based error estimators require the solution of an adjoint system to determine the importance to the specified functional. The error estimators and the novel methods to calculate them are described. Several examples are presented to demonstrate the effectiveness of the methods. It is shown that the methods can significantly reduce the number of unknowns and computational time required to obtain a given error. The novelty of the work is the use of goal-based adaptive methods to obtain anisotropic resolution in the angular domain for solving the transport equation. -- Highlights: •Wavelet angular discretisation used to solve transport equation. •Adaptive method developed for the wavelet discretisation. •Anisotropic angular resolution demonstrated through the adaptive method. •Adaptive method provides improvements in computational efficiency.
Singh, Omkar; Sunkaria, Ramesh Kumar
2015-01-01
Separating an information-bearing signal from the background noise is a general problem in signal processing. In a clinical environment during acquisition of an electrocardiogram (ECG) signal, The ECG signal is corrupted by various noise sources such as powerline interference (PLI), baseline wander and muscle artifacts. This paper presents novel methods for reduction of powerline interference in ECG signals using empirical wavelet transform (EWT) and adaptive filtering. The proposed methods are compared with the empirical mode decomposition (EMD) based PLI cancellation methods. A total of six methods for PLI reduction based on EMD and EWT are analysed and their results are presented in this paper. The EWT-based de-noising methods have less computational complexity and are more efficient as compared with the EMD-based de-noising methods.
Wavelet-based Multiresolution Particle Methods
NASA Astrophysics Data System (ADS)
Bergdorf, Michael; Koumoutsakos, Petros
2006-03-01
Particle methods offer a robust numerical tool for solving transport problems across disciplines, such as fluid dynamics, quantitative biology or computer graphics. Their strength lies in their stability, as they do not discretize the convection operator, and appealing numerical properties, such as small dissipation and dispersion errors. Many problems of interest are inherently multiscale, and their efficient solution requires either multiscale modeling approaches or spatially adaptive numerical schemes. We present a hybrid particle method that employs a multiresolution analysis to identify and adapt to small scales in the solution. The method combines the versatility and efficiency of grid-based Wavelet collocation methods while retaining the numerical properties and stability of particle methods. The accuracy and efficiency of this method is then assessed for transport and interface capturing problems in two and three dimensions, illustrating the capabilities and limitations of our approach.
NASA Astrophysics Data System (ADS)
Hejazialhosseini, Babak; Rossinelli, Diego; Bergdorf, Michael; Koumoutsakos, Petros
2010-11-01
We present a space-time adaptive solver for single- and multi-phase compressible flows that couples average interpolating wavelets with high-order finite volume schemes. The solver introduces the concept of wavelet blocks, handles large jumps in resolution and employs local time-stepping for efficient time integration. We demonstrate that the inherently sequential wavelet-based adaptivity can be implemented efficiently in multicore computer architectures using task-based parallelism and introducing the concept of wavelet blocks. We validate our computational method on a number of benchmark problems and we present simulations of shock-bubble interaction at different Mach numbers, demonstrating the accuracy and computational performance of the method.
NASA Astrophysics Data System (ADS)
Rastigejev, Y.; Semakin, A. N.
2013-12-01
Accurate numerical simulations of global scale three-dimensional atmospheric chemical transport models (CTMs) are essential for studies of many important atmospheric chemistry problems such as adverse effect of air pollutants on human health, ecosystems and the Earth's climate. These simulations usually require large CPU time due to numerical difficulties associated with a wide range of spatial and temporal scales, nonlinearity and large number of reacting species. In our previous work we have shown that in order to achieve adequate convergence rate and accuracy, the mesh spacing in numerical simulation of global synoptic-scale pollution plume transport must be decreased to a few kilometers. This resolution is difficult to achieve for global CTMs on uniform or quasi-uniform grids. To address the described above difficulty we developed a three-dimensional Wavelet-based Adaptive Mesh Refinement (WAMR) algorithm. The method employs a highly non-uniform adaptive grid with fine resolution over the areas of interest without requiring small grid-spacing throughout the entire domain. The method uses multi-grid iterative solver that naturally takes advantage of a multilevel structure of the adaptive grid. In order to represent the multilevel adaptive grid efficiently, a dynamic data structure based on indirect memory addressing has been developed. The data structure allows rapid access to individual points, fast inter-grid operations and re-gridding. The WAMR method has been implemented on parallel computer architectures. The parallel algorithm is based on run-time partitioning and load-balancing scheme for the adaptive grid. The partitioning scheme maintains locality to reduce communications between computing nodes. The parallel scheme was found to be cost-effective. Specifically we obtained an order of magnitude increase in computational speed for numerical simulations performed on a twelve-core single processor workstation. We have applied the WAMR method for numerical
Are Nonadjacent Collocations Processed Faster?
ERIC Educational Resources Information Center
Vilkaite, Laura
2016-01-01
Numerous studies have shown processing advantages for collocations, but they only investigated processing of adjacent collocations (e.g., "provide information"). However, in naturally occurring language, nonadjacent collocations ("provide" some of the "information") are equally, if not more frequent. This raises the…
NASA Technical Reports Server (NTRS)
Hussaini, M. Y.; Kopriva, D. A.; Patera, A. T.
1987-01-01
This review covers the theory and application of spectral collocation methods. Section 1 describes the fundamentals, and summarizes results pertaining to spectral approximations of functions. Some stability and convergence results are presented for simple elliptic, parabolic, and hyperbolic equations. Applications of these methods to fluid dynamics problems are discussed in Section 2.
V S, Unni; Mishra, Deepak; Subrahmanyam, G R K S
2016-12-01
The need for image fusion in current image processing systems is increasing mainly due to the increased number and variety of image acquisition techniques. Image fusion is the process of combining substantial information from several sensors using mathematical techniques in order to create a single composite image that will be more comprehensive and thus more useful for a human operator or other computer vision tasks. This paper presents a new approach to multifocus image fusion based on sparse signal representation. Block-based compressive sensing integrated with a projection-driven compressive sensing (CS) recovery that encourages sparsity in the wavelet domain is used as a method to get the focused image from a set of out-of-focus images. Compression is achieved during the image acquisition process using a block compressive sensing method. An adaptive thresholding technique within the smoothed projected Landweber recovery process reconstructs high-resolution focused images from low-dimensional CS measurements of out-of-focus images. Discrete wavelet transform and dual-tree complex wavelet transform are used as the sparsifying basis for the proposed fusion. The main finding lies in the fact that sparsification enables a better selection of the fusion coefficients and hence better fusion. A Laplacian mixture model fit is done in the wavelet domain and estimation of the probability density function (pdf) parameters by expectation maximization leads us to the proper selection of the coefficients of the fused image. Using the proposed method compared with the fusion scheme without employing the projected Landweber (PL) scheme and the other existing CS-based fusion approaches, it is observed that with fewer samples itself, the proposed method outperforms other approaches.
ERIC Educational Resources Information Center
Kita, Kenji; Ogata, Hiroaki
1997-01-01
Presents an efficient method for extracting collocations from corpora, which uses the cost criteria measure and a tree-based data structure. Proposes a bilingual collocation concordancer, a tool that provides language learners with collocation correspondences between a native and foreign language. (Eight references) (Author/CK)
Anatomically-adapted graph wavelets for improved group-level fMRI activation mapping.
Behjat, Hamid; Leonardi, Nora; Sörnmo, Leif; Van De Ville, Dimitri
2015-12-01
A graph based framework for fMRI brain activation mapping is presented. The approach exploits the spectral graph wavelet transform (SGWT) for the purpose of defining an advanced multi-resolutional spatial transformation for fMRI data. The framework extends wavelet based SPM (WSPM), which is an alternative to the conventional approach of statistical parametric mapping (SPM), and is developed specifically for group-level analysis. We present a novel procedure for constructing brain graphs, with subgraphs that separately encode the structural connectivity of the cerebral and cerebellar gray matter (GM), and address the inter-subject GM variability by the use of template GM representations. Graph wavelets tailored to the convoluted boundaries of GM are then constructed as a means to implement a GM-based spatial transformation on fMRI data. The proposed approach is evaluated using real as well as semi-synthetic multi-subject data. Compared to SPM and WSPM using classical wavelets, the proposed approach shows superior type-I error control. The results on real data suggest a higher detection sensitivity as well as the capability to capture subtle, connected patterns of brain activity.
NASA Astrophysics Data System (ADS)
Rangel, T.; Caliste, D.; Genovese, L.; Torrent, M.
2016-11-01
We present a Projector Augmented-Wave (PAW) method based on a wavelet basis set. We implemented our wavelet-PAW method as a PAW library in the ABINIT package [http://www.abinit.org] and into BigDFT [http://www.bigdft.org]. We test our implementation in prototypical systems to illustrate the potential usage of our code. By using the wavelet-PAW method, we can simulate charged and special boundary condition systems with frozen-core all-electron precision. Furthermore, our work paves the way to large-scale and potentially order- N simulations within a PAW method.
NASA Astrophysics Data System (ADS)
Wang, Shibin; Zhu, Z. K.; He, Yingping; Huang, Weiguo
2010-12-01
Localized defects in rotating mechanical parts tend to result in impulse response in vibration signal, which contain important information about system dynamics being analyzed. Thus, parameter identification of impulse response provides a potential approach for localized fault diagnosis. A method combining the Morlet wavelet and correlation filtering, named Cyclic Morlet Wavelet Correlation Filtering (CMWCF), is proposed for identifying both parameters of impulse response and the cyclic period between adjacent impulses. Simulation study concerning cyclic impulse response signal with different SNR shows that CMWCF is effective in identifying the impulse response parameters and the cyclic period. Applications in parameter identification of gearbox vibration signal for localized fault diagnosis show that CMWCF is effective in identifying the parameters and thus provides a feature detection method for gearbox fault diagnosis.
NASA Astrophysics Data System (ADS)
Goossens, Bart; Aelterman, Jan; Luong, Hiep; Pizurica, Aleksandra; Philips, Wilfried
2013-02-01
In digital cameras and mobile phones, there is an ongoing trend to increase the image resolution, decrease the sensor size and to use lower exposure times. Because smaller sensors inherently lead to more noise and a worse spatial resolution, digital post-processing techniques are required to resolve many of the artifacts. Color filter arrays (CFAs), which use alternating patterns of color filters, are very popular because of price and power consumption reasons. However, color filter arrays require the use of a post-processing technique such as demosaicing to recover full resolution RGB images. Recently, there has been some interest in techniques that jointly perform the demosaicing and denoising. This has the advantage that the demosaicing and denoising can be performed optimally (e.g. in the MSE sense) for the considered noise model, while avoiding artifacts introduced when using demosaicing and denoising sequentially. In this paper, we will continue the research line of the wavelet-based demosaicing techniques. These approaches are computationally simple and very suited for combination with denoising. Therefore, we will derive Bayesian Minimum Squared Error (MMSE) joint demosaicing and denoising rules in the complex wavelet packet domain, taking local adaptivity into account. As an image model, we will use Gaussian Scale Mixtures, thereby taking advantage of the directionality of the complex wavelets. Our results show that this technique is well capable of reconstructing fine details in the image, while removing all of the noise, at a relatively low computational cost. In particular, the complete reconstruction (including color correction, white balancing etc) of a 12 megapixel RAW image takes 3.5 sec on a recent mid-range GPU.
A wavelet-MRA-based adaptive semi-Lagrangian method for the relativistic Vlasov-Maxwell system
Besse, Nicolas Latu, Guillaume Ghizzo, Alain Sonnendruecker, Eric Bertrand, Pierre
2008-08-10
In this paper we present a new method for the numerical solution of the relativistic Vlasov-Maxwell system on a phase-space grid using an adaptive semi-Lagrangian method. The adaptivity is performed through a wavelet multiresolution analysis, which gives a powerful and natural refinement criterion based on the local measurement of the approximation error and regularity of the distribution function. Therefore, the multiscale expansion of the distribution function allows to get a sparse representation of the data and thus save memory space and CPU time. We apply this numerical scheme to reduced Vlasov-Maxwell systems arising in laser-plasma physics. Interaction of relativistically strong laser pulses with overdense plasma slabs is investigated. These Vlasov simulations revealed a rich variety of phenomena associated with the fast particle dynamics induced by electromagnetic waves as electron trapping, particle acceleration, and electron plasma wavebreaking. However, the wavelet based adaptive method that we developed here, does not yield significant improvements compared to Vlasov solvers on a uniform mesh due to the substantial overhead that the method introduces. Nonetheless they might be a first step towards more efficient adaptive solvers based on different ideas for the grid refinement or on a more efficient implementation. Here the Vlasov simulations are performed in a two-dimensional phase-space where the development of thin filaments, strongly amplified by relativistic effects requires an important increase of the total number of points of the phase-space grid as they get finer as time goes on. The adaptive method could be more useful in cases where these thin filaments that need to be resolved are a very small fraction of the hyper-volume, which arises in higher dimensions because of the surface-to-volume scaling and the essentially one-dimensional structure of the filaments. Moreover, the main way to improve the efficiency of the adaptive method is to
Rezaee, Kh.; Haddadnia, J.
2013-01-01
Background: Breast cancer is currently one of the leading causes of death among women worldwide. The diagnosis and separation of cancerous tumors in mammographic images require accuracy, experience and time, and it has always posed itself as a major challenge to the radiologists and physicians. Objective: This paper proposes a new algorithm which draws on discrete wavelet transform and adaptive K-means techniques to transmute the medical images implement the tumor estimation and detect breast cancer tumors in mammograms in early stages. It also allows the rapid processing of the input data. Method: In the first step, after designing a filter, the discrete wavelet transform is applied to the input images and the approximate coefficients of scaling components are constructed. Then, the different parts of image are classified in continuous spectrum. In the next step, by using adaptive K-means algorithm for initializing and smart choice of clusters’ number, the appropriate threshold is selected. Finally, the suspicious cancerous mass is separated by implementing the image processing techniques. Results: We Received 120 mammographic images in LJPEG format, which had been scanned in Gray-Scale with 50 microns size, 3% noise and 20% INU from clinical data taken from two medical databases (mini-MIAS and DDSM). The proposed algorithm detected tumors at an acceptable level with an average accuracy of 92.32% and sensitivity of 90.24%. Also, the Kappa coefficient was approximately 0.85, which proved the suitable reliability of the system performance. Conclusion: The exact positioning of the cancerous tumors allows the radiologist to determine the stage of disease progression and suggest an appropriate treatment in accordance with the tumor growth. The low PPV and high NPV of the system is a warranty of the system and both clinical specialists and patients can trust its output. PMID:25505753
Avci, Derya; Leblebicioglu, Mehmet Kemal; Poyraz, Mustafa; Dogantekin, Esin
2014-02-01
So far, analysis and classification of urine cells number has become an important topic for medical diagnosis of some diseases. Therefore, in this study, we suggest a new technique based on Adaptive Discrete Wavelet Entropy Energy and Neural Network Classifier (ADWEENN) for Recognition of Urine Cells from Microscopic Images Independent of Rotation and Scaling. Some digital image processing methods such as noise reduction, contrast enhancement, segmentation, and morphological process are used for feature extraction stage of this ADWEENN in this study. Nowadays, the image processing and pattern recognition topics have come into prominence. The image processing concludes operation and design of systems that recognize patterns in data sets. In the past years, very difficulty in classification of microscopic images was the deficiency of enough methods to characterize. Lately, it is seen that, multi-resolution image analysis methods such as Gabor filters, discrete wavelet decompositions are superior to other classic methods for analysis of these microscopic images. In this study, the structure of the ADWEENN method composes of four stages. These are preprocessing stage, feature extraction stage, classification stage and testing stage. The Discrete Wavelet Transform (DWT) and adaptive wavelet entropy and energy is used for adaptive feature extraction in feature extraction stage to strengthen the premium features of the Artificial Neural Network (ANN) classifier in this study. Efficiency of the developed ADWEENN method was tested showing that an avarage of 97.58% recognition succes was obtained.
Adaptive fusion of multisensor precipitation using Gaussian-scale mixtures in the wavelet domain
NASA Astrophysics Data System (ADS)
Ebtehaj, Ardeshir Mohammad; Foufoula-Georgiou, Efi
2011-11-01
The past decades have witnessed a remarkable emergence of new sources of multiscale multisensor precipitation data, including global spaceborne active and passive sensors, regional ground-based weather surveillance radars, and local rain gauges. Optimal integration of these multisensor data promises a posteriori estimates of precipitation fluxes with increased accuracy and resolution to be used in hydrologic applications. In this context, a new framework is proposed for multiscale multisensor precipitation data fusion which capitalizes on two main observations: (1) non-Gaussian statistics of precipitation images, which are concisely parameterized in the wavelet domain via a class of Gaussian-scale mixtures, and (2) the conditionally Gaussian and weakly correlated local representation of remotely sensed precipitation data in the wavelet domain, which allows for exploiting the efficient linear estimation methodologies while capturing the non-Gaussian data structure of rainfall. The proposed methodology is demonstrated using a data set of coincidental observations of precipitation reflectivity images by the spaceborne precipitation radar aboard the Tropical Rainfall Measurement Mission satellite and by ground-based weather surveillance Doppler radars.
Enhancing P300 Wave of BCI Systems Via Negentropy in Adaptive Wavelet Denoising.
Vahabi, Z; Amirfattahi, R; Mirzaei, Ar
2011-07-01
Brian Computer Interface (BCI) is a direct communication pathway between the brain and an external device. BCIs are often aimed at assisting, augmenting or repairing human cognitive or sensory-motor functions. EEG separation into target and non-target ones based on presence of P300 signal is of difficult task mainly due to their natural low signal to noise ratio. In this paper a new algorithm is introduced to enhance EEG signals and improve their SNR. Our denoising method is based on multi-resolution analysis via Independent Component Analysis (ICA) Fundamentals. We have suggested combination of negentropy as a feature of signal and subband information from wavelet transform. The proposed method is finally tested with dataset from BCI Competition 2003 and gives results that compare favorably.
Spectral-collocation variational integrators
NASA Astrophysics Data System (ADS)
Li, Yiqun; Wu, Boying; Leok, Melvin
2017-03-01
Spectral methods are a popular choice for constructing numerical approximations for smooth problems, as they can achieve geometric rates of convergence and have a relatively small memory footprint. In this paper, we introduce a general framework to convert a spectral-collocation method into a shooting-based variational integrator for Hamiltonian systems. We also compare the proposed spectral-collocation variational integrators to spectral-collocation methods and Galerkin spectral variational integrators in terms of their ability to reproduce accurate trajectories in configuration and phase space, their ability to conserve momentum and energy, as well as the relative computational efficiency of these methods when applied to some classical Hamiltonian systems. In particular, we note that spectrally-accurate variational integrators, such as the Galerkin spectral variational integrators and the spectral-collocation variational integrators, combine the computational efficiency of spectral methods together with the geometric structure-preserving and long-time structural stability properties of symplectic integrators.
NASA Astrophysics Data System (ADS)
Li, Xueyang; Xiao, Aiguo
2014-06-01
The Gross-Pitaevskii equation is the model equation of the single-particle wave function in a Bose-Einstein condensation. A computation difficulty of the Gross-Pitaevskii equation comes from the semiclassical problem in supercritical case. In this paper, we apply a diffeomorphism to transform the original one-dimensional Gross-Pitaevskii equation into a modified equation. The adaptive grids are constructed through the interpolating wavelet method. Then, we use the time-splitting finite difference method with the wavelet-adaptive grids to solve the modified Gross-Pitaevskii equation, where the approximation to the second-order derivative is given by the Lagrange interpolation method. At last, the numerical results are given. It is shown that the obtained time-splitting finite difference method with the wavelet-adaptive grids is very efficient for solving the one-dimensional semiclassical Gross-Pitaevskii equation in supercritical case and it is suitable to deal with the local high oscillation of the solution.
Graham, Ryan B.; Wachowiak, Mark P.; Gurd, Brendon J.
2015-01-01
Peroxisome proliferator-activated receptor gamma coactivator 1 alpha (PGC-1α) is a transcription factor co-activator that helps coordinate mitochondrial biogenesis within skeletal muscle following exercise. While evidence gleaned from submaximal exercise suggests that intracellular pathways associated with the activation of PGC-1α, as well as the expression of PGC-1α itself are activated to a greater extent following higher intensities of exercise, we have recently shown that this effect does not extend to supramaximal exercise, despite corresponding increases in muscle activation amplitude measured with electromyography (EMG). Spectral analyses of EMG data may provide a more in-depth assessment of changes in muscle electrophysiology occurring across different exercise intensities, and therefore the goal of the present study was to apply continuous wavelet transforms (CWTs) to our previous data to comprehensively evaluate: 1) differences in muscle electrophysiological properties at different exercise intensities (i.e. 73%, 100%, and 133% of peak aerobic power), and 2) muscular effort and fatigue across a single interval of exercise at each intensity, in an attempt to shed mechanistic insight into our previous observations that the increase in PGC-1α is dissociated from exercise intensity following supramaximal exercise. In general, the CWTs revealed that localized muscle fatigue was only greater than the 73% condition in the 133% exercise intensity condition, which directly matched the work rate results. Specifically, there were greater drop-offs in frequency, larger changes in burst power, as well as greater changes in burst area under this intensity, which were already observable during the first interval. As a whole, the results from the present study suggest that supramaximal exercise causes extreme localized muscular fatigue, and it is possible that the blunted PGC-1α effects observed in our previous study are the result of fatigue-associated increases in
NASA Astrophysics Data System (ADS)
Chamundeeswari, V. V.; Singh, D.; Singh, K.
2007-12-01
In single band and single polarized synthetic aperture radar (SAR) images, the information is limited to intensity and texture only and it is very difficult to interpret such SAR images without any a priori information. For unsupervised classification of SAR images, M-band wavelet decomposition is performed on the SAR image and sub-band selection on the basis of energy levels is applied to improve the classification results since sparse representation of sub-bands degrades the performance of classification. Then, textural features are obtained from selected sub-bands and integrated with intensity features. An adaptive neuro-fuzzy algorithm is used to improve computational efficiency by extracting significant features. K-means classification is performed on the extracted features and land features are labeled. This classification algorithm involves user defined parameters. To remove the user dependency and to obtain maximum achievable classification accuracy, an algorithm is developed in this paper for classification accuracy in terms of the parameters involved in the segmentation process. This is very helpful to develop the automated land-cover monitoring system with SAR, where optimized parameters are to be identified only once and these parameters can be applied to SAR imagery of the same scene obtained year after year. A single band, single polarized SAR image is classified into water, urban and vegetation areas using this method and overall classification accuracy is obtained in the range of 85.92%-93.70% by comparing with ground truth data.
NASA Astrophysics Data System (ADS)
Ji, Yanju; Li, Dongsheng; Yu, Mingmei; Wang, Yuan; Wu, Qiong; Lin, Jun
2016-05-01
The ground electrical source airborne transient electromagnetic system (GREATEM) on an unmanned aircraft enjoys considerable prospecting depth, lateral resolution and detection efficiency, etc. In recent years it has become an important technical means of rapid resources exploration. However, GREATEM data are extremely vulnerable to stationary white noise and non-stationary electromagnetic noise (sferics noise, aircraft engine noise and other human electromagnetic noises). These noises will cause degradation of the imaging quality for data interpretation. Based on the characteristics of the GREATEM data and major noises, we propose a de-noising algorithm utilizing wavelet threshold method and exponential adaptive window width-fitting. Firstly, the white noise is filtered in the measured data using the wavelet threshold method. Then, the data are segmented using data window whose step length is even logarithmic intervals. The data polluted by electromagnetic noise are identified within each window based on the discriminating principle of energy detection, and the attenuation characteristics of the data slope are extracted. Eventually, an exponential fitting algorithm is adopted to fit the attenuation curve of each window, and the data polluted by non-stationary electromagnetic noise are replaced with their fitting results. Thus the non-stationary electromagnetic noise can be effectively removed. The proposed algorithm is verified by the synthetic and real GREATEM signals. The results show that in GREATEM signal, stationary white noise and non-stationary electromagnetic noise can be effectively filtered using the wavelet threshold-exponential adaptive window width-fitting algorithm, which enhances the imaging quality.
NASA Astrophysics Data System (ADS)
Pan, Jun; Chen, Jinglong; Zi, Yanyang; Li, Yueming; He, Zhengjia
2016-05-01
Due to the multi-modulation feature in most of the vibration signals, the extraction of embedded fault information from condition monitoring data for mechanical fault diagnosis still is not a relaxed task. Despite the reported achievements, Wavelet transform follows the dyadic partition scheme and would not allow a data-driven frequency partition. And then Empirical Wavelet Transform (EWT) is used to extract inherent modulation information by decomposing signal into mono-components under an orthogonal basis and non-dyadic partition scheme. However, the pre-defined segment way of Fourier spectrum without dependence on analyzed signals may result in inaccurate mono-component identification. In this paper, the modified EWT (MEWT) method via data-driven adaptive Fourier spectrum segment is proposed for mechanical fault identification. First, inner product is calculated between the Fourier spectrum of analyzed signal and Gaussian function for scale representation. Then, adaptive spectrum segment is achieved by detecting local minima of the scale representation. Finally, empirical modes can be obtained by adaptively merging mono-components based on their envelope spectrum similarity. The adaptively extracted empirical modes are analyzed for mechanical fault identification. A simulation experiment and two application cases are used to verify the effectiveness of the proposed method and the results show its outstanding performance.
Mr. Stockdale's Dictionary of Collocations.
ERIC Educational Resources Information Center
Stockdale, Joseph Gagen, III
This dictionary of collocations was compiled by an English-as-a-Second-Language (ESL) teacher in Saudi Arabia who teaches adult, native speakers of Arabic. The dictionary is practical in teaching English because it helps to focus on everyday events and situations. The dictionary works as follows: the teacher looks up a word, such as…
Interlanguage Development and Collocational Clash
ERIC Educational Resources Information Center
Shahheidaripour, Gholamabbass
2000-01-01
Background: Persian English learners committed mistakes and errors which were due to insufficient knowledge of different senses of the words and collocational structures they formed. Purpose: The study reported here was conducted for a thesis submitted in partial fulfillment of the requirements for The Master of Arts degree, School of Graduate…
Schlossnagle, G.; Restrepo, J.M.; Leaf, G.K.
1993-12-01
The properties of periodized Daubechies wavelets on [0,1] are detailed and contrasted against their counterparts which form a basis for L{sup 2}(R). Numerical examples illustrate the analytical estimates for convergence and demonstrate by comparison with Fourier spectral methods the superiority of wavelet projection methods for approximations. The analytical solution to inner products of periodized wavelets and their derivatives, which are known as connection coefficients, is presented, and several tabulated values are included.
NASA Astrophysics Data System (ADS)
Hortos, William S.
2008-04-01
Proposed distributed wavelet-based algorithms are a means to compress sensor data received at the nodes forming a wireless sensor network (WSN) by exchanging information between neighboring sensor nodes. Local collaboration among nodes compacts the measurements, yielding a reduced fused set with equivalent information at far fewer nodes. Nodes may be equipped with multiple sensor types, each capable of sensing distinct phenomena: thermal, humidity, chemical, voltage, or image signals with low or no frequency content as well as audio, seismic or video signals within defined frequency ranges. Compression of the multi-source data through wavelet-based methods, distributed at active nodes, reduces downstream processing and storage requirements along the paths to sink nodes; it also enables noise suppression and more energy-efficient query routing within the WSN. Targets are first detected by the multiple sensors; then wavelet compression and data fusion are applied to the target returns, followed by feature extraction from the reduced data; feature data are input to target recognition/classification routines; targets are tracked during their sojourns through the area monitored by the WSN. Algorithms to perform these tasks are implemented in a distributed manner, based on a partition of the WSN into clusters of nodes. In this work, a scheme of collaborative processing is applied for hierarchical data aggregation and decorrelation, based on the sensor data itself and any redundant information, enabled by a distributed, in-cluster wavelet transform with lifting that allows multiple levels of resolution. The wavelet-based compression algorithm significantly decreases RF bandwidth and other resource use in target processing tasks. Following wavelet compression, features are extracted. The objective of feature extraction is to maximize the probabilities of correct target classification based on multi-source sensor measurements, while minimizing the resource expenditures at
Wavelets based on Hermite cubic splines
NASA Astrophysics Data System (ADS)
Cvejnová, Daniela; Černá, Dana; Finěk, Václav
2016-06-01
In 2000, W. Dahmen et al. designed biorthogonal multi-wavelets adapted to the interval [0,1] on the basis of Hermite cubic splines. In recent years, several more simple constructions of wavelet bases based on Hermite cubic splines were proposed. We focus here on wavelet bases with respect to which both the mass and stiffness matrices are sparse in the sense that the number of nonzero elements in any column is bounded by a constant. Then, a matrix-vector multiplication in adaptive wavelet methods can be performed exactly with linear complexity for any second order differential equation with constant coefficients. In this contribution, we shortly review these constructions and propose a new wavelet which leads to improved Riesz constants. Wavelets have four vanishing wavelet moments.
NASA Astrophysics Data System (ADS)
Richard, Nelly; Laursen, Bettina; Grupe, Morten; Drewes, Asbjørn M.; Graversen, Carina; Sørensen, Helge B. D.; Bastlund, Jesper F.
2017-04-01
Objective. Active auditory oddball paradigms are simple tone discrimination tasks used to study the P300 deflection of event-related potentials (ERPs). These ERPs may be quantified by time-frequency analysis. As auditory stimuli cause early high frequency and late low frequency ERP oscillations, the continuous wavelet transform (CWT) is often chosen for decomposition due to its multi-resolution properties. However, as the conventional CWT traditionally applies only one mother wavelet to represent the entire spectrum, the time-frequency resolution is not optimal across all scales. To account for this, we developed and validated a novel method specifically refined to analyse P300-like ERPs in rats. Approach. An adapted CWT (aCWT) was implemented to preserve high time-frequency resolution across all scales by commissioning of multiple wavelets operating at different scales. First, decomposition of simulated ERPs was illustrated using the classical CWT and the aCWT. Next, the two methods were applied to EEG recordings obtained from prefrontal cortex in rats performing a two-tone auditory discrimination task. Main results. While only early ERP frequency changes between responses to target and non-target tones were detected by the CWT, both early and late changes were successfully described with strong accuracy by the aCWT in rat ERPs. Increased frontal gamma power and phase synchrony was observed particularly within theta and gamma frequency bands during deviant tones. Significance. The study suggests superior performance of the aCWT over the CWT in terms of detailed quantification of time-frequency properties of ERPs. Our methodological investigation indicates that accurate and complete assessment of time-frequency components of short-time neural signals is feasible with the novel analysis approach which may be advantageous for characterisation of several types of evoked potentials in particularly rodents.
ERIC Educational Resources Information Center
Bosse-Andrieu, J.; Mareschal, G.
1998-01-01
Discusses the definition of collocation, demonstrates that associative word combinations do form a continuum, and proposes some parameters to help delimit the scope of collocations in everyday contemporary French. (Author/VWL)
A Stochastic Collocation Algorithm for Uncertainty Analysis
NASA Technical Reports Server (NTRS)
Mathelin, Lionel; Hussaini, M. Yousuff; Zang, Thomas A. (Technical Monitor)
2003-01-01
This report describes a stochastic collocation method to adequately handle a physically intrinsic uncertainty in the variables of a numerical simulation. For instance, while the standard Galerkin approach to Polynomial Chaos requires multi-dimensional summations over the stochastic basis functions, the stochastic collocation method enables to collapse those summations to a one-dimensional summation only. This report furnishes the essential algorithmic details of the new stochastic collocation method and provides as a numerical example the solution of the Riemann problem with the stochastic collocation method used for the discretization of the stochastic parameters.
Should We Teach EFL Students Collocations?
ERIC Educational Resources Information Center
Bahns, Jens; Eldaw, Moira
1993-01-01
German advanced English-as-a-foreign-language (EFL) students' productive knowledge of English collocations consisting of a verb and a noun were investigated in a translation task and a close task. Results suggest that EFL students should concentrate on collocations that cannot readily be paraphrased. The tasks are appended. (32 references)…
Supporting Collocation Learning with a Digital Library
ERIC Educational Resources Information Center
Wu, Shaoqun; Franken, Margaret; Witten, Ian H.
2010-01-01
Extensive knowledge of collocations is a key factor that distinguishes learners from fluent native speakers. Such knowledge is difficult to acquire simply because there is so much of it. This paper describes a system that exploits the facilities offered by digital libraries to provide a rich collocation-learning environment. The design is based on…
Collocation and Galerkin Time-Stepping Methods
NASA Technical Reports Server (NTRS)
Huynh, H. T.
2011-01-01
We study the numerical solutions of ordinary differential equations by one-step methods where the solution at tn is known and that at t(sub n+1) is to be calculated. The approaches employed are collocation, continuous Galerkin (CG) and discontinuous Galerkin (DG). Relations among these three approaches are established. A quadrature formula using s evaluation points is employed for the Galerkin formulations. We show that with such a quadrature, the CG method is identical to the collocation method using quadrature points as collocation points. Furthermore, if the quadrature formula is the right Radau one (including t(sub n+1)), then the DG and CG methods also become identical, and they reduce to the Radau IIA collocation method. In addition, we present a generalization of DG that yields a method identical to CG and collocation with arbitrary collocation points. Thus, the collocation, CG, and generalized DG methods are equivalent, and the latter two methods can be formulated using the differential instead of integral equation. Finally, all schemes discussed can be cast as s-stage implicit Runge-Kutta methods.
NASA Astrophysics Data System (ADS)
Isah, Abdulnasir; Chang, Phang
2016-06-01
In this article we propose the wavelet operational method based on shifted Legendre polynomial to obtain the numerical solutions of non-linear systems of fractional order differential equations (NSFDEs). The operational matrix of fractional derivative derived through wavelet-polynomial transformation are used together with the collocation method to turn the NSFDEs to a system of non-linear algebraic equations. Illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques.
A multilevel stochastic collocation method for SPDEs
Gunzburger, Max; Jantsch, Peter; Teckentrup, Aretha; Webster, Clayton
2015-03-10
We present a multilevel stochastic collocation method that, as do multilevel Monte Carlo methods, uses a hierarchy of spatial approximations to reduce the overall computational complexity when solving partial differential equations with random inputs. For approximation in parameter space, a hierarchy of multi-dimensional interpolants of increasing fidelity are used. Rigorous convergence and computational cost estimates for the new multilevel stochastic collocation method are derived and used to demonstrate its advantages compared to standard single-level stochastic collocation approximations as well as multilevel Monte Carlo methods.
A Wavelet Perspective on the Allan Variance.
Percival, Donald B
2016-04-01
The origins of the Allan variance trace back 50 years ago to two seminal papers, one by Allan (1966) and the other by Barnes (1966). Since then, the Allan variance has played a leading role in the characterization of high-performance time and frequency standards. Wavelets first arose in the early 1980s in the geophysical literature, and the discrete wavelet transform (DWT) became prominent in the late 1980s in the signal processing literature. Flandrin (1992) briefly documented a connection between the Allan variance and a wavelet transform based upon the Haar wavelet. Percival and Guttorp (1994) noted that one popular estimator of the Allan variance-the maximal overlap estimator-can be interpreted in terms of a version of the DWT now widely referred to as the maximal overlap DWT (MODWT). In particular, when the MODWT is based on the Haar wavelet, the variance of the resulting wavelet coefficients-the wavelet variance-is identical to the Allan variance when the latter is multiplied by one-half. The theory behind the wavelet variance can thus deepen our understanding of the Allan variance. In this paper, we review basic wavelet variance theory with an emphasis on the Haar-based wavelet variance and its connection to the Allan variance. We then note that estimation theory for the wavelet variance offers a means of constructing asymptotically correct confidence intervals (CIs) for the Allan variance without reverting to the common practice of specifying a power-law noise type a priori. We also review recent work on specialized estimators of the wavelet variance that are of interest when some observations are missing (gappy data) or in the presence of contamination (rogue observations or outliers). It is a simple matter to adapt these estimators to become estimators of the Allan variance. Finally we note that wavelet variances based upon wavelets other than the Haar offer interesting generalizations of the Allan variance.
Wavelet Local Extrema Applied to Image Processing
1992-12-01
The research project had two components. In the first part, we developed a numerical method, based on the wavelet transform , for the solution of...on the orthogonal wavelet transform , that adapts the computational resolution in space and time to the regularity of the solution. This scheme saves
LUPOD: Collocation in POD via LU decomposition
NASA Astrophysics Data System (ADS)
Rapún, M.-L.; Terragni, F.; Vega, J. M.
2017-04-01
A collocation method is developed for the (truncated) POD of a set of snapshots. In other words, POD computations are performed using only a set of collocation points, whose number is comparable to the number of retained modes, in a similar fashion as in collocation spectral methods. Intending to rely on simple ideas which, moreover, are consistent with the essence of POD, collocation points are computed via the LU decomposition with pivoting of the snapshot matrix. The new method is illustrated in simple applications in which POD is used as a data-processing method. The performance of the method is tested in the computationally efficient construction of reduced order models based on POD plus Galerkin projection for the complex Ginzburg-Landau equation in one and two space dimensions.
Wavelet and wavelet packet compression of electrocardiograms.
Hilton, M L
1997-05-01
Wavelets and wavelet packets have recently emerged as powerful tools for signal compression. Wavelet and wavelet packet-based compression algorithms based on embedded zerotree wavelet (EZW) coding are developed for electrocardiogram (ECG) signals, and eight different wavelets are evaluated for their ability to compress Holter ECG data. Pilot data from a blind evaluation of compressed ECG's by cardiologists suggest that the clinically useful information present in original ECG signals is preserved by 8:1 compression, and in most cases 16:1 compressed ECG's are clinically useful.
Perceptually Lossless Wavelet Compression
NASA Technical Reports Server (NTRS)
Watson, Andrew B.; Yang, Gloria Y.; Solomon, Joshua A.; Villasenor, John
1996-01-01
The Discrete Wavelet Transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter, which we call DWT uniform quantization noise. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2(exp -1), where r is display visual resolution in pixels/degree, and L is the wavelet level. Amplitude thresholds increase rapidly with spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from low-pass to horizontal/vertical to diagonal. We propose a mathematical model for DWT noise detection thresholds that is a function of level, orientation, and display visual resolution. This allows calculation of a 'perceptually lossless' quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.
Optimization of dynamic systems using collocation methods
NASA Astrophysics Data System (ADS)
Holden, Michael Eric
The time-based simulation is an important tool for the engineer. Often a time-domain simulation is the most expedient to construct, the most capable of handling complex modeling issues, or the most understandable with an engineer's physical intuition. Aeroelastic systems, for example, are often most easily solved with a nonlinear time-based approach to allow the use of high fidelity models. Simulations of automatic flight control systems can also be easier to model in the time domain, especially when nonlinearities are present. Collocation is an optimization method for systems that incorporate a time-domain simulation. Instead of integrating the equations of motion for each design iteration, the optimizer iteratively solves the simulation as it finds the optimal design. This forms a smooth, well-posed, sparse optimization problem, transforming the numerical integration's sequential calculation into a set of constraints that can be evaluated in any order, or even in parallel. The collocation method used in this thesis has been improved from existing techniques in several ways, in particular with a very simple and computationally inexpensive method of applying dynamic constraints, such as damping, that are more traditionally calculated with linear models in the frequency domain. This thesis applies the collocation method to a range of aircraft design problems, from minimizing the weight of a wing with a flutter constraint, to gain-scheduling the stability augmentation system of a small-scale flight control testbed, to aeroservoelastic design of a large aircraft concept. Collocation methods have not been applied to aeroelastic simulations in the past, although the combination of nonlinear aerodynamic analyses with structural dynamics and stability constraints is well-suited to collocation. The results prove the collocation method's worth as a tool for aircraft design, particularly when applied to the multidisciplinary numerical models used today.
NASA Astrophysics Data System (ADS)
Swaidan, Waleeda; Hussin, Amran
2015-10-01
Most direct methods solve finite time horizon optimal control problems with nonlinear programming solver. In this paper, we propose a numerical method for solving nonlinear optimal control problem with state and control inequality constraints. This method used quasilinearization technique and Haar wavelet operational matrix to convert the nonlinear optimal control problem into a quadratic programming problem. The linear inequality constraints for trajectories variables are converted to quadratic programming constraint by using Haar wavelet collocation method. The proposed method has been applied to solve Optimal Control of Multi-Item Inventory Model. The accuracy of the states, controls and cost can be improved by increasing the Haar wavelet resolution.
Stochastic Collocation Method for Three-dimensional Groundwater Flow
NASA Astrophysics Data System (ADS)
Shi, L.; Zhang, D.
2008-12-01
The stochastic collocation method (SCM) has recently gained extensive attention in several disciplines. The numerical implementation of SCM only requires repetitive runs of an existing deterministic solver or code as in the Monte Carlo simulation. But it is generally much more efficient than the Monte Carlo method. In this paper, the stochastic collocation method is used to efficiently qualify uncertainty of three-dimensional groundwater flow. We introduce the basic principles of common collocation methods, i.e., the tensor product collocation method (TPCM), Smolyak collocation method (SmCM), Stround-2 collocation method (StCM), and probability collocation method (PCM). Their accuracy, computational cost, and limitation are discussed. Illustrative examples reveal that the seamless combination of collocation techniques and existing simulators makes the new framework possible to efficiently handle complex stochastic problems.
Zhang, Qiushi; Yang, Xueqian; Yao, Li; Zhao, Xiaojie
2017-03-27
Working memory (WM) refers to the holding and manipulation of information during cognitive tasks. Its underlying neural mechanisms have been explored through both functional magnetic resonance imaging (fMRI) and electroencephalography (EEG). Trial-by-trial coupling of simultaneously collected EEG and fMRI signals has become an important and promising approach to study the spatio-temporal dynamics of such cognitive processes. Previous studies have demonstrated a modulation effect of the WM load on both the BOLD response in certain brain areas and the amplitude of P3. However, much remains to be explored regarding the WM load-dependent relationship between the amplitude of ERP components and cortical activities, and the low signal-to-noise ratio (SNR) of the EEG signal still poses a challenge to performing single-trial analyses. In this paper, we investigated the spatio-temporal activities of P3 during an n-back verbal WM task by introducing an adaptive wavelet denoiser into the extraction of single-trial P3 features and using general linear model (GLM) to integrate simultaneously collected EEG and fMRI data. Our results replicated the modulation effect of the WM load on the P3 amplitude. Additionally, the activation of single-trial P3 amplitudes was detected in multiple brain regions, including the insula, the cuneus, the lingual gyrus (LG), and the middle occipital gyrus (MOG). Moreover, we found significant correlations between P3 features and behavioral performance. These findings suggest that the single-trial integration of simultaneous EEG and fMRI signals may provide new insights into classical cognitive functions.
NASA Astrophysics Data System (ADS)
Yang, Huijuan; Guan, Cuntai; Sui Geok Chua, Karen; San Chok, See; Wang, Chuan Chu; Kok Soon, Phua; Tang, Christina Ka Yin; Keng Ang, Kai
2014-06-01
Objective. Detection of motor imagery of hand/arm has been extensively studied for stroke rehabilitation. This paper firstly investigates the detection of motor imagery of swallow (MI-SW) and motor imagery of tongue protrusion (MI-Ton) in an attempt to find a novel solution for post-stroke dysphagia rehabilitation. Detection of MI-SW from a simple yet relevant modality such as MI-Ton is then investigated, motivated by the similarity in activation patterns between tongue movements and swallowing and there being fewer movement artifacts in performing tongue movements compared to swallowing. Approach. Novel features were extracted based on the coefficients of the dual-tree complex wavelet transform to build multiple training models for detecting MI-SW. The session-to-session classification accuracy was boosted by adaptively selecting the training model to maximize the ratio of between-classes distances versus within-class distances, using features of training and evaluation data. Main results. Our proposed method yielded averaged cross-validation (CV) classification accuracies of 70.89% and 73.79% for MI-SW and MI-Ton for ten healthy subjects, which are significantly better than the results from existing methods. In addition, averaged CV accuracies of 66.40% and 70.24% for MI-SW and MI-Ton were obtained for one stroke patient, demonstrating the detectability of MI-SW and MI-Ton from the idle state. Furthermore, averaged session-to-session classification accuracies of 72.08% and 70% were achieved for ten healthy subjects and one stroke patient using the MI-Ton model. Significance. These results and the subjectwise strong correlations in classification accuracies between MI-SW and MI-Ton demonstrated the feasibility of detecting MI-SW from MI-Ton models.
Gauging the Effects of Exercises on Verb-Noun Collocations
ERIC Educational Resources Information Center
Boers, Frank; Demecheleer, Murielle; Coxhead, Averil; Webb, Stuart
2014-01-01
Many contemporary textbooks for English as a foreign language (EFL) and books for vocabulary study contain exercises with a focus on collocations, with verb-noun collocations (e.g. "make a mistake") being particularly popular as targets for collocation learning. Common exercise formats used in textbooks and other pedagogic materials…
Corpus-Based versus Traditional Learning of Collocations
ERIC Educational Resources Information Center
Daskalovska, Nina
2015-01-01
One of the aspects of knowing a word is the knowledge of which words it is usually used with. Since knowledge of collocations is essential for appropriate and fluent use of language, learning collocations should have a central place in the study of vocabulary. There are different opinions about the best ways of learning collocations. This study…
3D steerable wavelets in practice.
Chenouard, Nicolas; Unser, Michael
2012-11-01
We introduce a systematic and practical design for steerable wavelet frames in 3D. Our steerable wavelets are obtained by applying a 3D version of the generalized Riesz transform to a primary isotropic wavelet frame. The novel transform is self-reversible (tight frame) and its elementary constituents (Riesz wavelets) can be efficiently rotated in any 3D direction by forming appropriate linear combinations. Moreover, the basis functions at a given location can be linearly combined to design custom (and adaptive) steerable wavelets. The features of the proposed method are illustrated with the processing and analysis of 3D biomedical data. In particular, we show how those wavelets can be used to characterize directional patterns and to detect edges by means of a 3D monogenic analysis. We also propose a new inverse-problem formalism along with an optimization algorithm for reconstructing 3D images from a sparse set of wavelet-domain edges. The scheme results in high-quality image reconstructions which demonstrate the feature-reduction ability of the steerable wavelets as well as their potential for solving inverse problems.
Research of Gear Fault Detection in Morphological Wavelet Domain
NASA Astrophysics Data System (ADS)
Hong, Shi; Fang-jian, Shan; Bo, Cong; Wei, Qiu
2016-02-01
For extracting mutation information from gear fault signal and achieving a valid fault diagnosis, a gear fault diagnosis method based on morphological mean wavelet transform was designed. Morphological mean wavelet transform is a linear wavelet in the framework of morphological wavelet. Decomposing gear fault signal by this morphological mean wavelet transform could produce signal synthesis operators and detailed synthesis operators. For signal synthesis operators, it was just close to orginal signal, and for detailed synthesis operators, it contained fault impact signal or interference signal and could be catched. The simulation experiment result indicates that, compared with Fourier transform, the morphological mean wavelet transform method can do time-frequency analysis for original signal, effectively catch impact signal appears position; and compared with traditional linear wavelet transform, it has simple structure, easy realization, signal local extremum sensitivity and high denoising ability, so it is more adapted to gear fault real-time detection.
Higher Order B-Spline Collocation at the Greville Abscissae
Johnson, Richard Wayne
2005-01-01
Collocation methods are investigated because of their simplicity and inherent efficiency for application to a model problem with similarities to the equations of fluid dynamics. The model problem is a steady, one-dimensional convection-diffusion equation with constant coefficients. The objective of the present research is to compare the efficiency and accuracy of several collocation schemes as applied to the model problem for values of 15 and 50 for the associated Peclet number. The application of standard nodal and orthogonal collocation is compared to the use of the Greville abscissae for the collocation points, in conjunction with cubic and quartic B-splines. The continuity of the B-spline curve solution is varied from C1 continuity for traditional orthogonal collocation of cubic and quartic splines to C2-C3 continuity for cubic and quartic splines employing nodal, orthogonal and Greville point collocation. The application of nodal, one-point orthogonal, and Greville collocation for smoothest quartic B-splines is found to be as accurate as for traditional two-point orthogonal collocation using cubics, while having comparable or better efficiency based on operation count. Greville collocation is more convenient than nodal or 1-point orthogonal collocation because exactly the correct number of collocation points is available.
Schwarz and multilevel methods for quadratic spline collocation
Christara, C.C.; Smith, B.
1994-12-31
Smooth spline collocation methods offer an alternative to Galerkin finite element methods, as well as to Hermite spline collocation methods, for the solution of linear elliptic Partial Differential Equations (PDEs). Recently, optimal order of convergence spline collocation methods have been developed for certain degree splines. Convergence proofs for smooth spline collocation methods are generally more difficult than for Galerkin finite elements or Hermite spline collocation, and they require stronger assumptions and more restrictions. However, numerical tests indicate that spline collocation methods are applicable to a wider class of problems, than the analysis requires, and are very competitive to finite element methods, with respect to efficiency. The authors will discuss Schwarz and multilevel methods for the solution of elliptic PDEs using quadratic spline collocation, and compare these with domain decomposition methods using substructuring. Numerical tests on a variety of parallel machines will also be presented. In addition, preliminary convergence analysis using Schwarz and/or maximum principle techniques will be presented.
Brechet, Laurent; Lucas, Marie-Françoise; Doncarli, Christian; Farina, Dario
2007-12-01
We propose a novel scheme for signal compression based on the discrete wavelet packet transform (DWPT) decompositon. The mother wavelet and the basis of wavelet packets were optimized and the wavelet coefficients were encoded with a modified version of the embedded zerotree algorithm. This signal dependant compression scheme was designed by a two-step process. The first (internal optimization) was the best basis selection that was performed for a given mother wavelet. For this purpose, three additive cost functions were applied and compared. The second (external optimization) was the selection of the mother wavelet based on the minimal distortion of the decoded signal given a fixed compression ratio. The mother wavelet was parameterized in the multiresolution analysis framework by the scaling filter, which is sufficient to define the entire decomposition in the orthogonal case. The method was tested on two sets of ten electromyographic (EMG) and ten electrocardiographic (ECG) signals that were compressed with compression ratios in the range of 50%-90%. For 90% compression ratio of EMG (ECG) signals, the percent residual difference after compression decreased from (mean +/- SD) 48.6 +/- 9.9% (21.5 +/- 8.4%) with discrete wavelet transform (DWT) using the wavelet leading to poorest performance to 28.4 +/- 3.0% (6.7 +/- 1.9%) with DWPT, with optimal basis selection and wavelet optimization. In conclusion, best basis selection and optimization of the mother wavelet through parameterization led to substantial improvement of performance in signal compression with respect to DWT and randon selection of the mother wavelet. The method provides an adaptive approach for optimal signal representation for compression and can thus be applied to any type of biomedical signal.
Evaluating techniques for multivariate classification of non-collocated spatial data.
McKenna, Sean Andrew
2004-09-01
Multivariate spatial classification schemes such as regionalized classification or principal components analysis combined with kriging rely on all variables being collocated at the sample locations. In these approaches, classification of the multivariate data into a finite number of groups is done prior to the spatial estimation. However, in some cases, the variables may be sampled at different locations with the extreme case being complete heterotopy of the data set. In these situations, it is necessary to adapt existing techniques to work with non-collocated data. Two approaches are considered: (1) kriging of existing data onto a series of 'collection points' where the classification into groups is completed and a measure of the degree of group membership is kriged to all other locations; and (2) independent kriging of all attributes to all locations after which the classification is done at each location. Calculations are conducted using an existing groundwater chemistry data set in the upper Dakota aquifer in Kansas (USA) and previously examined using regionalized classification (Bohling, 1997). This data set has all variables measured at all locations. To test the ability of the first approach for dealing with non-collocated data, each variable is reestimated at each sample location through a cross-validation process and the reestimated values are then used in the regionalized classification. The second approach for non-collocated data requires independent kriging of each attribute across the entire domain prior to classification. Hierarchical and non-hierarchical classification of all vectors is completed and a computationally less burdensome classification approach, 'sequential discrimination', is developed that constrains the classified vectors to be chosen from those with a minimal multivariate kriging variance. Resulting classification and uncertainty maps are compared between all non-collocated approaches as well as to the original collocated approach
Multiwavelets on the interval and divergence-free wavelets
NASA Astrophysics Data System (ADS)
Lakey, Joseph D.; Pereyra, M. Cristina
1999-10-01
This manuscript gives a construction of divergence-free multiwavelets which combines the Hardin-Marasovich (HM) construction with a recipe of Strela for increasing or decreasing regularity of biorthogonal wavelets. Strela's process preserves symmetry of the HM wavelets. This enables the divergence-free wavelets to be suitably adapted to the analysis of divergence-free vector fields whose boundary traces are tangent vectors.
NOKIN1D: one-dimensional neutron kinetics based on a nodal collocation method
NASA Astrophysics Data System (ADS)
Verdú, G.; Ginestar, D.; Miró, R.; Jambrina, A.; Barrachina, T.; Soler, Amparo; Concejal, Alberto
2014-06-01
The TRAC-BF1 one-dimensional kinetic model is a formulation of the neutron diffusion equation in the two energy groups' approximation, based on the analytical nodal method (ANM). The advantage compared with a zero-dimensional kinetic model is that the axial power profile may vary with time due to thermal-hydraulic parameter changes and/or actions of the control systems but at has the disadvantages that in unusual situations it fails to converge. The nodal collocation method developed for the neutron diffusion equation and applied to the kinetics resolution of TRAC-BF1 thermal-hydraulics, is an adaptation of the traditional collocation methods for the discretization of partial differential equations, based on the development of the solution as a linear combination of analytical functions. It has chosen to use a nodal collocation method based on a development of Legendre polynomials of neutron fluxes in each cell. The qualification is carried out by the analysis of the turbine trip transient from the NEA benchmark in Peach Bottom NPP using both the original 1D kinetics implemented in TRAC-BF1 and the 1D nodal collocation method.
NASA Astrophysics Data System (ADS)
Jones, B. J. T.
Wavelet analysis has become a major tool in many aspects of data handling, whether it be statistical analysis, noise removal or image reconstruction. Wavelet analysis has worked its way into fields as diverse as economics, medicine, geophysics, music and cosmology.
Visibility of wavelet quantization noise
NASA Technical Reports Server (NTRS)
Watson, A. B.; Yang, G. Y.; Solomon, J. A.; Villasenor, J.
1997-01-01
The discrete wavelet transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that we call DWT uniform quantization noise; it is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2-lambda, where r is display visual resolution in pixels/degree, and lambda is the wavelet level. Thresholds increase rapidly with wavelet spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from lowpass to horizontal/vertical to diagonal. We construct a mathematical model for DWT noise detection thresholds that is a function of level, orientation, and display visual resolution. This allows calculation of a "perceptually lossless" quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.
Wavelet Approximation in Data Assimilation
NASA Technical Reports Server (NTRS)
Tangborn, Andrew; Atlas, Robert (Technical Monitor)
2002-01-01
Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation.
Review of wavelet transforms for pattern recognitions
NASA Astrophysics Data System (ADS)
Szu, Harold H.
1996-03-01
After relating the adaptive wavelet transform to the human visual and hearing systems, we exploit the synergism between such a smart sensor processing with brain-style neural network computing. The freedom of choosing an appropriate kernel of a linear transform, which is given to us by the recent mathematical foundation of the wavelet transform, is exploited fully and is generally called the adaptive wavelet transform (WT). However, there are several levels of adaptivity: (1) optimum coefficients: adjustable transform coefficients chosen with respect to a fixed mother kernel for better invariant signal representation, (2) super-mother: grouping different scales of daughter wavelets of same or different mother wavelets at different shift location into a new family called a superposition mother kernel for better speech signal classification, (3) variational calculus to determine ab initio a constraint optimization mother for a specific task. The tradeoff between the mathematical rigor of the complete orthonormality and the speed of order (N) with the adaptive flexibility is finally up to the user's needs. Then, to illustrate (1), a new invariant optoelectronic architecture of a wedge- shape filter in the WT domain is given for scale-invariant signal classification by neural networks.
Transient Detection Using Wavelets.
1995-03-01
signaL and transients are nonstationary. A new technique for the analysis of this type of signal, called the Wavelet Transform , was applied to artificial...and real signals. A brief theoretical comparison between the Short Time Fourier Transform and the Wavelet Transform is introduced A multisolution...analysis approach for implementing the transform was used. Computer code for the Discrete Wavelet Transform was implemented. Different types of wavelets to use as basis functions were evaluated. (KAR) P. 2
Rotation and Scale Invariant Wavelet Feature for Content-Based Texture Image Retrieval.
ERIC Educational Resources Information Center
Lee, Moon-Chuen; Pun, Chi-Man
2003-01-01
Introduces a rotation and scale invariant log-polar wavelet texture feature for image retrieval. The underlying feature extraction process involves a log-polar transform followed by an adaptive row shift invariant wavelet packet transform. Experimental results show that this rotation and scale invariant wavelet feature is quite effective for image…
Biorthogonal wavelet-based method of moments for electromagnetic scattering
NASA Astrophysics Data System (ADS)
Zhang, Qinke
Wavelet analysis is a technique developed in recent years in mathematics and has found usefulness in signal processing and many other engineering areas. The practical use of wavelets for the solution of partial differential and integral equations in computational electromagnetics has been investigated in this dissertation, with the emphasis on development of biorthogonal wavelet based method of moments for the solution of electric and magnetic field integral equations. The fundamentals and numerical analysis aspects of wavelet theory have been studied. In particular, a family of compactly supported biorthogonal spline wavelet bases on the n-cube (0,1) n has been studied in detail. The wavelet bases were used in this work as a building block to construct biorthogonal wavelet bases on general domain geometry. A specific and practical way of adapting the wavelet bases to certain n- dimensional blocks or elements is proposed based on the domain decomposition and local transformation techniques used in traditional finite element methods and computer aided graphics. The element, with the biorthogonal wavelet base embedded in it, is called a wavelet element in this work. The physical domains which can be treated with this method include general curves, surfaces in 2D and 3D, and 3D volume domains. A two-step mapping is proposed for the purpose of taking full advantage of the zero-moments of wavelets. The wavelet element approach appears to offer several important advantages. It avoids the need of generating very complicated meshes required in traditional finite element based methods, and makes the adaptive analysis easy to implement. A specific implementation procedure for performing adaptive analysis is proposed. The proposed biorthogonal wavelet based method of moments (BWMoM) has been implemented by using object-oriented programming techniques. The main computational issues have been detailed, discussed, and implemented in the whole package. Numerical examples show
Wavelet based image visibility enhancement of IR images
NASA Astrophysics Data System (ADS)
Jiang, Qin; Owechko, Yuri; Blanton, Brendan
2016-05-01
Enhancing the visibility of infrared images obtained in a degraded visibility environment is very important for many applications such as surveillance, visual navigation in bad weather, and helicopter landing in brownout conditions. In this paper, we present an IR image visibility enhancement system based on adaptively modifying the wavelet coefficients of the images. In our proposed system, input images are first filtered by a histogram-based dynamic range filter in order to remove sensor noise and convert the input images into 8-bit dynamic range for efficient processing and display. By utilizing a wavelet transformation, we modify the image intensity distribution and enhance image edges simultaneously. In the wavelet domain, low frequency wavelet coefficients contain original image intensity distribution while high frequency wavelet coefficients contain edge information for the original images. To modify the image intensity distribution, an adaptive histogram equalization technique is applied to the low frequency wavelet coefficients while to enhance image edges, an adaptive edge enhancement technique is applied to the high frequency wavelet coefficients. An inverse wavelet transformation is applied to the modified wavelet coefficients to obtain intensity images with enhanced visibility. Finally, a Gaussian filter is used to remove blocking artifacts introduced by the adaptive techniques. Since wavelet transformation uses down-sampling to obtain low frequency wavelet coefficients, histogram equalization of low-frequency coefficients is computationally more efficient than histogram equalization of the original images. We tested the proposed system with degraded IR images obtained from a helicopter landing in brownout conditions. Our experimental results show that the proposed system is effective for enhancing the visibility of degraded IR images.
NASA Astrophysics Data System (ADS)
van den Berg, J. C.
1999-08-01
A guided tour J. C. van den Berg; 1. Wavelet analysis, a new tool in physics J.-P. Antoine; 2. The 2-D wavelet transform, physical applications J.-P. Antoine; 3. Wavelets and astrophysical applications A. Bijaoui; 4. Turbulence analysis, modelling and computing using wavelets M. Farge, N. K.-R. Kevlahan, V. Perrier and K. Schneider; 5. Wavelets and detection of coherent structures in fluid turbulence L. Hudgins and J. H. Kaspersen; 6. Wavelets, non-linearity and turbulence in fusion plasmas B. Ph. van Milligen; 7. Transfers and fluxes of wind kinetic energy between orthogonal wavelet components during atmospheric blocking A. Fournier; 8. Wavelets in atomic physics and in solid state physics J.-P. Antoine, Ph. Antoine and B. Piraux; 9. The thermodynamics of fractals revisited with wavelets A. Arneodo, E. Bacry and J. F. Muzy; 10. Wavelets in medicine and physiology P. Ch. Ivanov, A. L. Goldberger, S. Havlin, C.-K. Peng, M. G. Rosenblum and H. E. Stanley; 11. Wavelet dimension and time evolution Ch.-A. Guérin and M. Holschneider.
NASA Astrophysics Data System (ADS)
van den Berg, J. C.
2004-03-01
A guided tour J. C. van den Berg; 1. Wavelet analysis, a new tool in physics J.-P. Antoine; 2. The 2-D wavelet transform, physical applications J.-P. Antoine; 3. Wavelets and astrophysical applications A. Bijaoui; 4. Turbulence analysis, modelling and computing using wavelets M. Farge, N. K.-R. Kevlahan, V. Perrier and K. Schneider; 5. Wavelets and detection of coherent structures in fluid turbulence L. Hudgins and J. H. Kaspersen; 6. Wavelets, non-linearity and turbulence in fusion plasmas B. Ph. van Milligen; 7. Transfers and fluxes of wind kinetic energy between orthogonal wavelet components during atmospheric blocking A. Fournier; 8. Wavelets in atomic physics and in solid state physics J.-P. Antoine, Ph. Antoine and B. Piraux; 9. The thermodynamics of fractals revisited with wavelets A. Arneodo, E. Bacry and J. F. Muzy; 10. Wavelets in medicine and physiology P. Ch. Ivanov, A. L. Goldberger, S. Havlin, C.-K. Peng, M. G. Rosenblum and H. E. Stanley; 11. Wavelet dimension and time evolution Ch.-A. Guérin and M. Holschneider.
Code of Federal Regulations, 2012 CFR
2012-10-01
... Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION... the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal Communications Commission, the National Conference of State...
Code of Federal Regulations, 2011 CFR
2011-10-01
... Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION... the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal Communications Commission, the National Conference of State...
Code of Federal Regulations, 2014 CFR
2014-10-01
... Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION... the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal Communications Commission, the National Conference of State...
Code of Federal Regulations, 2010 CFR
2010-10-01
... Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION... the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal Communications Commission, the National Conference of State...
Code of Federal Regulations, 2013 CFR
2013-10-01
... Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION... the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal Communications Commission, the National Conference of State...
Relative orbit control of collocated geostationary spacecraft
NASA Astrophysics Data System (ADS)
Rausch, Raoul R.
A relative orbit control concept for collocated geostationary spacecraft is presented. One chief spacecraft, controlled from the ground, is responsible for the orbit determination and control of the remaining vehicles. Any orbit relative to the chief is described in terms of equinoctial orbit element differences and a linear mapping is employed for quick transformation from relative orbit measurements to orbit element differences. It is demonstrated that the concept is well-suited for spacecraft that are collocated using eccentricity-inclination vector separation and this formulation still allows for the continued use of well established and currently employed stationkeeping schemes, such as the Sun-pointing-perigee strategy. The relative approach allows to take determinisitc thruster cross-coupling effects in the computation of stationkeeping corrections into account. The control cost for the proposed concept is comparable to ground-based stationkeeping. A relative line-of-sight constraint between spacecraft separated in longitude is also considered and an algorithm is developed to provide enforcement options. The proposed on-board control approach maintains the deputy spacecraft relative orbit, is competitive in terms of propellant consumption, allows enforcement of a relative line-of-sight constraint and offers increased autonomy and flexibility for future missions.
Subcell resolution in simplex stochastic collocation for spatial discontinuities
NASA Astrophysics Data System (ADS)
Witteveen, Jeroen A. S.; Iaccarino, Gianluca
2013-10-01
Subcell resolution has been used in the Finite Volume Method (FVM) to obtain accurate approximations of discontinuities in the physical space. Stochastic methods are usually based on local adaptivity for resolving discontinuities in the stochastic dimensions. However, the adaptive refinement in the probability space is ineffective in the non-intrusive uncertainty quantification framework, if the stochastic discontinuity is caused by a discontinuity in the physical space with a random location. The dependence of the discontinuity location in the probability space on the spatial coordinates then results in a staircase approximation of the statistics, which leads to first-order error convergence and an underprediction of the maximum standard deviation. To avoid these problems, we introduce subcell resolution into the Simplex Stochastic Collocation (SSC) method for obtaining a truly discontinuous representation of random spatial discontinuities in the interior of the cells discretizing the probability space. The presented SSC-SR method is based on resolving the discontinuity location in the probability space explicitly as function of the spatial coordinates and extending the stochastic response surface approximations up to the predicted discontinuity location. The applications to a linear advection problem, the inviscid Burgers' equation, a shock tube problem, and the transonic flow over the RAE 2822 airfoil show that SSC-SR resolves random spatial discontinuities with multiple stochastic and spatial dimensions accurately using a minimal number of samples.
The Effect of Grouping and Presenting Collocations on Retention
ERIC Educational Resources Information Center
Akpinar, Kadriye Dilek; Bardakçi, Mehmet
2015-01-01
The aim of this study is two-fold. Firstly, it attempts to determine the role of presenting collocations by organizing them based on (i) the keyword, (ii) topic related and (iii) grammatical aspect on retention of collocations. Secondly, it investigates the relationship between participants' general English proficiency and the presentation types…
Collocations of High Frequency Noun Keywords in Prescribed Science Textbooks
ERIC Educational Resources Information Center
Menon, Sujatha; Mukundan, Jayakaran
2012-01-01
This paper analyses the discourse of science through the study of collocational patterns of high frequency noun keywords in science textbooks used by upper secondary students in Malaysia. Research has shown that one of the areas of difficulty in science discourse concerns lexis, especially that of collocations. This paper describes a corpus-based…
A Study of Strategy Use in Producing Lexical Collocations.
ERIC Educational Resources Information Center
Liu, Candi Chen-Pin
This study examined strategy use in producing lexical collocations among freshman English majors at the Chinese Culture University. Divided into two groups by English writing proficiency, students completed three tasks: a collocation test, an optimal revision task, and a task-based structured questionnaire regarding their actions and mental…
Profiling the Collocation Use in ELT Textbooks and Learner Writing
ERIC Educational Resources Information Center
Tsai, Kuei-Ju
2015-01-01
The present study investigates the collocational profiles of (1) three series of graded textbooks for English as a foreign language (EFL) commonly used in Taiwan, (2) the written productions of EFL learners, and (3) the written productions of native speakers (NS) of English. These texts were examined against a purpose-built collocation list. Based…
Wavelet-Based Signal and Image Processing for Target Recognition
2002-01-01
in target recognition applications. Classical spatial and frequency domain image processing algorithms were generalized to process discrete wavelet ... transform (DWT) data. Results include adaptation of classical filtering, smoothing and interpolation techniques to DWT. From 2003 the research
ERIC Educational Resources Information Center
Varlamova, Elena V.; Naciscione, Anita; Tulusina, Elena A.
2016-01-01
Relevance of the issue stated in the article is determined by the fact that there is a lack of research devoted to the methods of teaching English and German collocations. The aim of our work is to determine methods of teaching English and German collocations to Russian university students studying foreign languages through experimental testing.…
Collocation points distributions for optimal spacecraft trajectories
NASA Astrophysics Data System (ADS)
Fumenti, Federico; Circi, Christian; Romagnoli, Daniele
2013-03-01
The method of direct collocation with nonlinear programming (DCNLP) is a powerful tool to solve optimal control problems (OCP). In this method the solution time history is approximated with piecewise polynomials, which are constructed using interpolation points deriving from the Jacobi polynomials. Among the Jacobi polynomials family, Legendre and Chebyshev polynomials are the most used, but there is no evidence that they offer the best performance with respect to other family members. By solving different OCPs with interpolation points not only taken within the Jacoby family, the behavior of the Jacobi polynomials in the optimization problems is discussed. This paper focuses on spacecraft trajectories optimization problems. In particular orbit transfers, interplanetary transfers and station keepings are considered.
Visibility of Wavelet Quantization Noise
NASA Technical Reports Server (NTRS)
Watson, Andrew B.; Yang, Gloria Y.; Solomon, Joshua A.; Villasenor, John; Null, Cynthia H. (Technical Monitor)
1995-01-01
The Discrete Wavelet Transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter, which we call DWT uniform quantization noise. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2(exp)-L , where r is display visual resolution in pixels/degree, and L is the wavelet level. Amplitude thresholds increase rapidly with spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from low-pass to horizontal/vertical to diagonal. We describe a mathematical model to predict DWT noise detection thresholds as a function of level, orientation, and display visual resolution. This allows calculation of a "perceptually lossless" quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.
NASA Astrophysics Data System (ADS)
Li, Hong; Ding, Xue
2017-03-01
This paper combines wavelet analysis and wavelet transform theory with artificial neural network, through the pretreatment on point feature attributes before in intrusion detection, to make them suitable for improvement of wavelet neural network. The whole intrusion classification model gets the better adaptability, self-learning ability, greatly enhances the wavelet neural network for solving the problem of field detection invasion, reduces storage space, contributes to improve the performance of the constructed neural network, and reduces the training time. Finally the results of the KDDCup99 data set simulation experiment shows that, this method reduces the complexity of constructing wavelet neural network, but also ensures the accuracy of the intrusion classification.
Wavelet Analyses and Applications
ERIC Educational Resources Information Center
Bordeianu, Cristian C.; Landau, Rubin H.; Paez, Manuel J.
2009-01-01
It is shown how a modern extension of Fourier analysis known as wavelet analysis is applied to signals containing multiscale information. First, a continuous wavelet transform is used to analyse the spectrum of a nonstationary signal (one whose form changes in time). The spectral analysis of such a signal gives the strength of the signal in each…
1994-07-29
Douglas (MDA). This has been extended to the use of local SVD methods and the use of wavelet packets to provide a controlled sparsening. The goal is to be...possibilities for segmenting, compression and denoising signals and one of us (GVW) is using these wavelets to study edge sets with Prof. B. Jawerth. The
Developing and Evaluating a Chinese Collocation Retrieval Tool for CFL Students and Teachers
ERIC Educational Resources Information Center
Chen, Howard Hao-Jan; Wu, Jian-Cheng; Yang, Christine Ting-Yu; Pan, Iting
2016-01-01
The development of collocational knowledge is important for foreign language learners; unfortunately, learners often have difficulties producing proper collocations in the target language. Among the various ways of collocation learning, the DDL (data-driven learning) approach encourages the independent learning of collocations and allows learners…
The Learning Burden of Collocations: The Role of Interlexical and Intralexical Factors
ERIC Educational Resources Information Center
Peters, Elke
2016-01-01
This study investigates whether congruency (+/- literal translation equivalent), collocate-node relationship (adjective-noun, verb-noun, phrasal-verb-noun collocations), and word length influence the learning burden of EFL learners' learning collocations at the initial stage of form-meaning mapping. Eighteen collocations were selected on the basis…
Predictive depth coding of wavelet transformed images
NASA Astrophysics Data System (ADS)
Lehtinen, Joonas
1999-10-01
In this paper, a new prediction based method, predictive depth coding, for lossy wavelet image compression is presented. It compresses a wavelet pyramid composition by predicting the number of significant bits in each wavelet coefficient quantized by the universal scalar quantization and then by coding the prediction error with arithmetic coding. The adaptively found linear prediction context covers spatial neighbors of the coefficient to be predicted and the corresponding coefficients on lower scale and in the different orientation pyramids. In addition to the number of significant bits, the sign and the bits of non-zero coefficients are coded. The compression method is tested with a standard set of images and the results are compared with SFQ, SPIHT, EZW and context based algorithms. Even though the algorithm is very simple and it does not require any extra memory, the compression results are relatively good.
Usability Study of Two Collocated Prototype System Displays
NASA Technical Reports Server (NTRS)
Trujillo, Anna C.
2007-01-01
Currently, most of the displays in control rooms can be categorized as status screens, alerts/procedures screens (or paper), or control screens (where the state of a component is changed by the operator). The primary focus of this line of research is to determine which pieces of information (status, alerts/procedures, and control) should be collocated. Two collocated displays were tested for ease of understanding in an automated desktop survey. This usability study was conducted as a prelude to a larger human-in-the-loop experiment in order to verify that the 2 new collocated displays were easy to learn and usable. The results indicate that while the DC display was preferred and yielded better performance than the MDO display, both collocated displays can be easily learned and used.
Hermite cubic spline multi-wavelets on the cube
NASA Astrophysics Data System (ADS)
Cvejnová, Daniela; Černá, Dana; Finěk, Václav
2015-11-01
In 2000, W. Dahmen et al. proposed a construction of Hermite cubic spline multi-wavelets adapted to the interval [0, 1]. Later, several more simple constructions of wavelet bases based on Hermite cubic splines were proposed. We focus here on wavelet basis with respect to which both the mass and stiffness matrices are sparse in the sense that the number of non-zero elements in each column is bounded by a constant. Then, a matrix-vector multiplication in adaptive wavelet methods can be performed exactly with linear complexity for any second order differential equation with constant coefficients. In this contribution, we shortly review these constructions, use an anisotropic tensor product to obtain bases on the cube [0, 1]3, and compare their condition numbers.
Wavelet analysis in neurodynamics
NASA Astrophysics Data System (ADS)
Pavlov, Aleksei N.; Hramov, Aleksandr E.; Koronovskii, Aleksei A.; Sitnikova, Evgenija Yu; Makarov, Valeri A.; Ovchinnikov, Alexey A.
2012-09-01
Results obtained using continuous and discrete wavelet transforms as applied to problems in neurodynamics are reviewed, with the emphasis on the potential of wavelet analysis for decoding signal information from neural systems and networks. The following areas of application are considered: (1) the microscopic dynamics of single cells and intracellular processes, (2) sensory data processing, (3) the group dynamics of neuronal ensembles, and (4) the macrodynamics of rhythmical brain activity (using multichannel EEG recordings). The detection and classification of various oscillatory patterns of brain electrical activity and the development of continuous wavelet-based brain activity monitoring systems are also discussed as possibilities.
EEG Artifact Removal Using a Wavelet Neural Network
NASA Technical Reports Server (NTRS)
Nguyen, Hoang-Anh T.; Musson, John; Li, Jiang; McKenzie, Frederick; Zhang, Guangfan; Xu, Roger; Richey, Carl; Schnell, Tom
2011-01-01
!n this paper we developed a wavelet neural network. (WNN) algorithm for Electroencephalogram (EEG) artifact removal without electrooculographic (EOG) recordings. The algorithm combines the universal approximation characteristics of neural network and the time/frequency property of wavelet. We. compared the WNN algorithm with .the ICA technique ,and a wavelet thresholding method, which was realized by using the Stein's unbiased risk estimate (SURE) with an adaptive gradient-based optimal threshold. Experimental results on a driving test data set show that WNN can remove EEG artifacts effectively without diminishing useful EEG information even for very noisy data.
Continuous Groundwater Monitoring Collocated at USGS Streamgages
NASA Astrophysics Data System (ADS)
Constantz, J. E.; Eddy-Miller, C.; Caldwell, R.; Wheeer, J.; Barlow, J.
2012-12-01
USGS Office of Groundwater funded a 2-year pilot study collocating groundwater wells for monitoring water level and temperature at several existing continuous streamgages in Montana and Wyoming, while U.S. Army Corps of Engineers funded enhancement to streamgages in Mississippi. To increase spatial relevance with in a given watershed, study sites were selected where near-stream groundwater was in connection with an appreciable aquifer, and where logistics and cost of well installations were considered representative. After each well installation and surveying, groundwater level and temperature were easily either radio-transmitted or hardwired to existing data acquisition system located in streamgaging shelter. Since USGS field personnel regularly visit streamgages during routine streamflow measurements and streamgage maintenance, the close proximity of observation wells resulted in minimum extra time to verify electronically transmitted measurements. After field protocol was tuned, stream and nearby groundwater information were concurrently acquired at streamgages and transmitted to satellite from seven pilot-study sites extending over nearly 2,000 miles (3,200 km) of the central US from October 2009 until October 2011, for evaluating the scientific and engineering add-on value of the enhanced streamgage design. Examination of the four-parameter transmission from the seven pilot study groundwater gaging stations reveals an internally consistent, dynamic data suite of continuous groundwater elevation and temperature in tandem with ongoing stream stage and temperature data. Qualitatively, the graphical information provides appreciation of seasonal trends in stream exchanges with shallow groundwater, as well as thermal issues of concern for topics ranging from ice hazards to suitability of fish refusia, while quantitatively this information provides a means for estimating flux exchanges through the streambed via heat-based inverse-type groundwater modeling. In June
Wavelet transforms with discrete-time continuous-dilation wavelets
NASA Astrophysics Data System (ADS)
Zhao, Wei; Rao, Raghuveer M.
1999-03-01
Wavelet constructions and transforms have been confined principally to the continuous-time domain. Even the discrete wavelet transform implemented through multirate filter banks is based on continuous-time wavelet functions that provide orthogonal or biorthogonal decompositions. This paper provides a novel wavelet transform construction based on the definition of discrete-time wavelets that can undergo continuous parameter dilations. The result is a transformation that has the advantage of discrete-time or digital implementation while circumventing the problem of inadequate scaling resolution seen with conventional dyadic or M-channel constructions. Examples of constructing such wavelets are presented.
The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
Foo, Jasmine; Wan Xiaoliang; Karniadakis, George Em
2008-11-20
Stochastic spectral methods are numerical techniques for approximating solutions to partial differential equations with random parameters. In this work, we present and examine the multi-element probabilistic collocation method (ME-PCM), which is a generalized form of the probabilistic collocation method. In the ME-PCM, the parametric space is discretized and a collocation/cubature grid is prescribed on each element. Both full and sparse tensor product grids based on Gauss and Clenshaw-Curtis quadrature rules are considered. We prove analytically and observe in numerical tests that as the parameter space mesh is refined, the convergence rate of the solution depends on the quadrature rule of each element only through its degree of exactness. In addition, the L{sup 2} error of the tensor product interpolant is examined and an adaptivity algorithm is provided. Numerical examples demonstrating adaptive ME-PCM are shown, including low-regularity problems and long-time integration. We test the ME-PCM on two-dimensional Navier-Stokes examples and a stochastic diffusion problem with various random input distributions and up to 50 dimensions. While the convergence rate of ME-PCM deteriorates in 50 dimensions, the error in the mean and variance is two orders of magnitude lower than the error obtained with the Monte Carlo method using only a small number of samples (e.g., 100). The computational cost of ME-PCM is found to be favorable when compared to the cost of other methods including stochastic Galerkin, Monte Carlo and quasi-random sequence methods.
The Discrete Wavelet Transform
1991-06-01
Split- Band Coding," Proc. ICASSP, May 1977, pp 191-195. 12. Vetterli, M. "A Theory of Multirate Filter Banks ," IEEE Trans. ASSP, 35, March 1987, pp 356...both special cases of a single filter bank structure, the discrete wavelet transform, the behavior of which is governed by one’s choice of filters . In...B-1 ,.iii FIGURES 1.1 A wavelet filter bank structure ..................................... 2 2.1 Diagram illustrating the dialation and
Wavelet despiking of fractographs
NASA Astrophysics Data System (ADS)
Aubry, Jean-Marie; Saito, Naoki
2000-12-01
Fractographs are elevation maps of the fracture zone of some broken material. The technique employed to create these maps often introduces noise composed of positive or negative 'spikes' that must be removed before further analysis. Since the roughness of these maps contains useful information, it must be preserved. Consequently, conventional denoising techniques cannot be employed. We use continuous and discrete wavelet transforms of these images, and the properties of wavelet coefficients related to pointwise Hoelder regularity, to detect and remove the spikes.
Wavelets and Multifractal Analysis
2004-07-01
distribution unlimited 13. SUPPLEMENTARY NOTES See also ADM001750, Wavelets and Multifractal Analysis (WAMA) Workshop held on 19-31 July 2004., The original...f)] . . . 16 2.5.4 Detrended Fluctuation Analysis [DFA(m)] . . . . . . . . . . . . . . . 17 2.6 Scale-Independent Measures...18 2.6.1 Detrended -Fluctuation- Analysis Power-Law Exponent (αD) . . . . . . 18 2.6.2 Wavelet-Transform Power-Law Exponent
Collocation and Pattern Recognition Effects on System Failure Remediation
NASA Technical Reports Server (NTRS)
Trujillo, Anna C.; Press, Hayes N.
2007-01-01
Previous research found that operators prefer to have status, alerts, and controls located on the same screen. Unfortunately, that research was done with displays that were not designed specifically for collocation. In this experiment, twelve subjects evaluated two displays specifically designed for collocating system information against a baseline that consisted of dial status displays, a separate alert area, and a controls panel. These displays differed in the amount of collocation, pattern matching, and parameter movement compared to display size. During the data runs, subjects kept a randomly moving target centered on a display using a left-handed joystick and they scanned system displays to find a problem in order to correct it using the provided checklist. Results indicate that large parameter movement aided detection and then pattern recognition is needed for diagnosis but the collocated displays centralized all the information subjects needed, which reduced workload. Therefore, the collocated display with large parameter movement may be an acceptable display after familiarization because of the possible pattern recognition developed with training and its use.
Riesz wavelets and multiresolution structures
NASA Astrophysics Data System (ADS)
Larson, David R.; Tang, Wai-Shing; Weber, Eric
2001-12-01
Multiresolution structures are important in applications, but they are also useful for analyzing properties of associated wavelets. Given a nonorthogonal (multi-) wavelet in a Hilbert space, we construct a core subspace. Subsequently, the dilates of the core subspace defines a ladder of nested subspaces. Of fundamental importance are two questions: 1) when is the core subspace shift invariant; and if yes, then 2) when is the core subspace generated by shifts of a single vector, i.e. there exists a scaling vector. If the wavelet generates a Riesz basis then the answer to question 1) is yes if and only if the wavelet is a biorthogonal wavelet. Additionally, if the wavelet generates a tight frame of arbitrary frame constant, then the core subspace is shift invariant. Question 1) is still open in case the wavelet generates a non-tight frame. We also present some known results to question 2) and provide some preliminary improvements. Our analysis here arises from investigating the dimension function and the multiplicity function of a wavelet. These two functions agree if the wavelet is orthogonal. Finally, we discuss how these questions are important for considering linear perturbation of wavelets. Utilizing the idea of the local commutant of a unitary system developed by Dai and Larson, we show that nearly all linear perturbations of two orthonormal wavelets form a Riesz wavelet. If in fact these wavelets correspond to a von Neumann algebra in the local commutant of a base wavelet, then the interpolated wavelet is biorthogonal. Moreover, we demonstrate that in this case the interpolated wavelets have a scaling vector if the base wavelet has a scaling vector.
Wavelet-based functional mixed models
Morris, Jeffrey S.; Carroll, Raymond J.
2009-01-01
Summary Increasingly, scientific studies yield functional data, in which the ideal units of observation are curves and the observed data consist of sets of curves that are sampled on a fine grid. We present new methodology that generalizes the linear mixed model to the functional mixed model framework, with model fitting done by using a Bayesian wavelet-based approach. This method is flexible, allowing functions of arbitrary form and the full range of fixed effects structures and between-curve covariance structures that are available in the mixed model framework. It yields nonparametric estimates of the fixed and random-effects functions as well as the various between-curve and within-curve covariance matrices. The functional fixed effects are adaptively regularized as a result of the non-linear shrinkage prior that is imposed on the fixed effects’ wavelet coefficients, and the random-effect functions experience a form of adaptive regularization because of the separately estimated variance components for each wavelet coefficient. Because we have posterior samples for all model quantities, we can perform pointwise or joint Bayesian inference or prediction on the quantities of the model. The adaptiveness of the method makes it especially appropriate for modelling irregular functional data that are characterized by numerous local features like peaks. PMID:19759841
Advantage of collocating research facilities The administrator's point of view
NASA Astrophysics Data System (ADS)
Spilker, H.-M.; Blomeyer, C.
1995-02-01
Research facilities are collocated in order to create a maximum of synergy. This also requires a close cooperation of the administration concerned leading to advantages, in particular with regards to infrastructure and cost effectiveness. Faced with the specificities of the research facilities involved, administrators feel challenged to find appropriate solutions. The successive establishment of research institutes on the Polygone Scientifique in Grenoble is described. Forms and content of administrative collaboration between the Institut Max von Laue-Paul Langevin and the European Synchrotron Radiation Facility are analysed, where collocation has led to intensive cooperation.
Comparison of Implicit Collocation Methods for the Heat Equation
NASA Technical Reports Server (NTRS)
Kouatchou, Jules; Jezequel, Fabienne; Zukor, Dorothy (Technical Monitor)
2001-01-01
We combine a high-order compact finite difference scheme to approximate spatial derivatives arid collocation techniques for the time component to numerically solve the two dimensional heat equation. We use two approaches to implement the collocation methods. The first one is based on an explicit computation of the coefficients of polynomials and the second one relies on differential quadrature. We compare them by studying their merits and analyzing their numerical performance. All our computations, based on parallel algorithms, are carried out on the CRAY SV1.
Wavelet Approach for Operational Gamma Spectral Peak Detection - Preliminary Assessment
,
2012-02-01
Gamma spectroscopy for radionuclide identifications typically involves locating spectral peaks and matching the spectral peaks with known nuclides in the knowledge base or database. Wavelet analysis, due to its ability for fitting localized features, offers the potential for automatic detection of spectral peaks. Past studies of wavelet technologies for gamma spectra analysis essentially focused on direct fitting of raw gamma spectra. Although most of those studies demonstrated the potentials of peak detection using wavelets, they often failed to produce new benefits to operational adaptations for radiological surveys. This work presents a different approach with the operational objective being to detect only the nuclides that do not exist in the environment (anomalous nuclides). With this operational objective, the raw-count spectrum collected by a detector is first converted to a count-rate spectrum and is then followed by background subtraction prior to wavelet analysis. The experimental results suggest that this preprocess is independent of detector type and background radiation, and is capable of improving the peak detection rates using wavelets. This process broadens the doors for a practical adaptation of wavelet technologies for gamma spectral surveying devices.
Three-dimensional compression scheme based on wavelet transform
NASA Astrophysics Data System (ADS)
Yang, Wu; Xu, Hui; Liao, Mengyang
1999-03-01
In this paper, a 3D compression method based on separable wavelet transform is discussed in detail. The most commonly used digital modalities generate multiple slices in a single examination, which are normally anatomically or physiologically correlated to each other. 3D wavelet compression methods can achieve more efficient compression by exploring the correlation between slices. The first step is based on a separable 3D wavelet transform. Considering the difference between pixel distances within a slice and those between slices, one biorthogonal Antoninin filter bank is applied within 2D slices and a second biorthogonal Villa4 filter bank on the slice direction. Then, S+P transform is applied in the low-resolution wavelet components and an optimal quantizer is presented after analysis of the quantization noise. We use an optimal bit allocation algorithm, which, instead of eliminating the coefficients of high-resolution components in smooth areas, minimizes the system reconstruction distortion at a given bit-rate. Finally, to remain high coding efficiency and adapt to different properties of each component, a comprehensive entropy coding method is proposed, in which arithmetic coding method is applied in high-resolution components and adaptive Huffman coding method in low-resolution components. Our experimental results are evaluated by several image measures and our 3D wavelet compression scheme is proved to be more efficient than 2D wavelet compression.
Broom, Donald M
2006-01-01
The term adaptation is used in biology in three different ways. It may refer to changes which occur at the cell and organ level, or at the individual level, or at the level of gene action and evolutionary processes. Adaptation by cells, especially nerve cells helps in: communication within the body, the distinguishing of stimuli, the avoidance of overload and the conservation of energy. The time course and complexity of these mechanisms varies. Adaptive characters of organisms, including adaptive behaviours, increase fitness so this adaptation is evolutionary. The major part of this paper concerns adaptation by individuals and its relationships to welfare. In complex animals, feed forward control is widely used. Individuals predict problems and adapt by acting before the environmental effect is substantial. Much of adaptation involves brain control and animals have a set of needs, located in the brain and acting largely via motivational mechanisms, to regulate life. Needs may be for resources but are also for actions and stimuli which are part of the mechanism which has evolved to obtain the resources. Hence pigs do not just need food but need to be able to carry out actions like rooting in earth or manipulating materials which are part of foraging behaviour. The welfare of an individual is its state as regards its attempts to cope with its environment. This state includes various adaptive mechanisms including feelings and those which cope with disease. The part of welfare which is concerned with coping with pathology is health. Disease, which implies some significant effect of pathology, always results in poor welfare. Welfare varies over a range from very good, when adaptation is effective and there are feelings of pleasure or contentment, to very poor. A key point concerning the concept of individual adaptation in relation to welfare is that welfare may be good or poor while adaptation is occurring. Some adaptation is very easy and energetically cheap and
Wavelet differential neural network observer.
Chairez, Isaac
2009-09-01
State estimation for uncertain systems affected by external noises is an important problem in control theory. This paper deals with a state observation problem when the dynamic model of a plant contains uncertainties or it is completely unknown. Differential neural network (NN) approach is applied in this uninformative situation but with activation functions described by wavelets. A new learning law, containing an adaptive adjustment rate, is suggested to imply the stability condition for the free parameters of the observer. Nominal weights are adjusted during the preliminary training process using the least mean square (LMS) method. Lyapunov theory is used to obtain the upper bounds for the weights dynamics as well as for the mean squared estimation error. Two numeric examples illustrate this approach: first, a nonlinear electric system, governed by the Chua's equation and second the Lorentz oscillator. Both systems are assumed to be affected by external perturbations and their parameters are unknown.
Adaptive multiresolution modeling of groundwater flow in heterogeneous porous media
NASA Astrophysics Data System (ADS)
Malenica, Luka; Gotovac, Hrvoje; Srzic, Veljko; Andric, Ivo
2016-04-01
different temporal lines and local time stepping control. Critical aspect of time integration accuracy is construction of spatial stencil due to accurate calculation of spatial derivatives. Since common approach applied for wavelets and splines uses a finite difference operator, we developed here collocation one including solution values and differential operator. In this way, new improved algorithm is adaptive in space and time enabling accurate solution for groundwater flow problems, especially in highly heterogeneous porous media with large lnK variances and different correlation length scales. In addition, differences between collocation and finite volume approaches are discussed. Finally, results show application of methodology to the groundwater flow problems in highly heterogeneous confined and unconfined aquifers.
Wavelets on Planar Tesselations
Bertram, M.; Duchaineau, M.A.; Hamann, B.; Joy, K.I.
2000-02-25
We present a new technique for progressive approximation and compression of polygonal objects in images. Our technique uses local parameterizations defined by meshes of convex polygons in the plane. We generalize a tensor product wavelet transform to polygonal domains to perform multiresolution analysis and compression of image regions. The advantage of our technique over conventional wavelet methods is that the domain is an arbitrary tessellation rather than, for example, a uniform rectilinear grid. We expect that this technique has many applications image compression, progressive transmission, radiosity, virtual reality, and image morphing.
Beyond Single Words: The Most Frequent Collocations in Spoken English
ERIC Educational Resources Information Center
Shin, Dongkwang; Nation, Paul
2008-01-01
This study presents a list of the highest frequency collocations of spoken English based on carefully applied criteria. In the literature, more than forty terms have been used for designating multi-word units, which are generally not well defined. To avoid this confusion, six criteria are strictly applied. The ten million word BNC spoken section…
Spline collocation method for linear singular hyperbolic systems
NASA Astrophysics Data System (ADS)
Gaidomak, S. V.
2008-07-01
Some classes of singular systems of partial differential equations with variable matrix coefficients and internal hyperbolic structure are considered. The spline collocation method is used to numerically solve such systems. Sufficient conditions for the convergence of the numerical procedure are obtained. Numerical results are presented.
Redefining Creativity--Analyzing Definitions, Collocations, and Consequences
ERIC Educational Resources Information Center
Kampylis, Panagiotis G.; Valtanen, Juri
2010-01-01
How holistically is human creativity defined, investigated, and understood? Until recently, most scientific research on creativity has focused on its positive side. However, creativity might not only be a desirable resource but also be a potential threat. In order to redefine creativity we need to analyze and understand definitions, collocations,…
A multidomain spectral collocation method for the Stokes problem
NASA Technical Reports Server (NTRS)
Landriani, G. Sacchi; Vandeven, H.
1989-01-01
A multidomain spectral collocation scheme is proposed for the approximation of the two-dimensional Stokes problem. It is shown that the discrete velocity vector field is exactly divergence-free and we prove error estimates both for the velocity and the pressure.
Domain identification in impedance computed tomography by spline collocation method
NASA Technical Reports Server (NTRS)
Kojima, Fumio
1990-01-01
A method for estimating an unknown domain in elliptic boundary value problems is considered. The problem is formulated as an inverse problem of integral equations of the second kind. A computational method is developed using a splice collocation scheme. The results can be applied to the inverse problem of impedance computed tomography (ICT) for image reconstruction.
Beyond triple collocation: Applications to satellite soil moisture
Technology Transfer Automated Retrieval System (TEKTRAN)
Triple collocation is now routinely used to resolve the exact (linear) relationships between multiple measurements and/or representations of a geophysical variable that are subject to errors. It has been utilized in the context of calibration, rescaling and error characterisation to allow comparison...
Evaluation of assumptions in soil moisture triple collocation analysis
Technology Transfer Automated Retrieval System (TEKTRAN)
Triple collocation analysis (TCA) enables estimation of error variances for three or more products that retrieve or estimate the same geophysical variable using mutually-independent methods. Several statistical assumptions regarding the statistical nature of errors (e.g., mutual independence and ort...
Target profile identification of step frequency MMW radar based on wavelet neural network
NASA Astrophysics Data System (ADS)
Li, Yuehua; Gao, Duntang; Shen, Qinghong; Li, Xingguo
2001-11-01
With the increased availability of coherent wide band radar, there has been a renewed interest in the target recognition of MMW frequency step radar. A large bandwidth gives high resolution in range which means target recognition may be possible. In this paper, by integrating wavelet with neural network, a new adaptive wavelet function neural network is proposed. An artificial neural network with wavelet as weight coefficients is developed for pattern recognition. It is inspired by wavelet transform theory and feed forward neural network. The good localization characteristics of wavelet functions in both time and frequency space allow hierarchical multi-resolution learning of input-output data mappings. The wavelet shapes are adaptively computed to minimize an energy function for a specific application of radar targets. The mathematical frame of the neural network is introduced and error back propagation algorithm is used. The procedure of using wavelet neural network for identification is described in detail. Based on the target specific information offered by the range profiles of step frequency MMW radar targets, the wavelet neural network is applied to recognition of three kinds of practical radar targets. We find that we can reliably distinguish for three targets over a range of aspect angle. Experiment results indicate that the new feature vector in low dimension is valuable for target recognition, the wavelet neural network has faster convergence speed and higher correct recognition rate and the noise resistance character is good.
A Fourth-Order Spline Collocation Approach for the Solution of a Boundary Layer Problem
NASA Astrophysics Data System (ADS)
Sayfy, Khoury, S.
2011-09-01
A finite element approach, based on cubic B-spline collocation, is presented for the numerical solution of a class of singularly perturbed two-point boundary value problems that possess a boundary layer at one or two end points. Due to the existence of a layer, the problem is handled using an adaptive spline collocation approach constructed over a non-uniform Shishkin-like meshes, defined via a carefully selected generating function. To tackle the case of nonlinearity, if it exists, an iterative scheme arising from Newton's method is employed. The rate of convergence is verified to be of fourth-order and is calculated using the double-mesh principle. The efficiency and applicability of the method are demonstrated by applying it to a number of linear and nonlinear examples. The numerical solutions are compared with both analytical and other existing numerical solutions in the literature. The numerical results confirm that this method is superior when contrasted with other accessible approaches and yields more accurate solutions.
Sankaran, Sethuraman; Marsden, Alison L
2011-03-01
Simulations of blood flow in both healthy and diseased vascular models can be used to compute a range of hemodynamic parameters including velocities, time varying wall shear stress, pressure drops, and energy losses. The confidence in the data output from cardiovascular simulations depends directly on our level of certainty in simulation input parameters. In this work, we develop a general set of tools to evaluate the sensitivity of output parameters to input uncertainties in cardiovascular simulations. Uncertainties can arise from boundary conditions, geometrical parameters, or clinical data. These uncertainties result in a range of possible outputs which are quantified using probability density functions (PDFs). The objective is to systemically model the input uncertainties and quantify the confidence in the output of hemodynamic simulations. Input uncertainties are quantified and mapped to the stochastic space using the stochastic collocation technique. We develop an adaptive collocation algorithm for Gauss-Lobatto-Chebyshev grid points that significantly reduces computational cost. This analysis is performed on two idealized problems--an abdominal aortic aneurysm and a carotid artery bifurcation, and one patient specific problem--a Fontan procedure for congenital heart defects. In each case, relevant hemodynamic features are extracted and their uncertainty is quantified. Uncertainty quantification of the hemodynamic simulations is done using (a) stochastic space representations, (b) PDFs, and (c) the confidence intervals for a specified level of confidence in each problem.
ERIC Educational Resources Information Center
Leonardi, Magda
1977-01-01
Discusses the importance of two Firthian themes for language teaching. The first theme, "Restricted Languages," concerns the "microlanguages" of every language (e.g., literary language, scientific, etc.). The second theme, "Collocation," shows that equivalent words in two languages rarely have the same position in…
NASA Astrophysics Data System (ADS)
Bargatze, L. F.
2015-12-01
Active Data Archive Product Tracking (ADAPT) is a collection of software routines that permits one to generate XML metadata files to describe and register data products in support of the NASA Heliophysics Virtual Observatory VxO effort. ADAPT is also a philosophy. The ADAPT concept is to use any and all available metadata associated with scientific data to produce XML metadata descriptions in a consistent, uniform, and organized fashion to provide blanket access to the full complement of data stored on a targeted data server. In this poster, we present an application of ADAPT to describe all of the data products that are stored by using the Common Data File (CDF) format served out by the CDAWEB and SPDF data servers hosted at the NASA Goddard Space Flight Center. These data servers are the primary repositories for NASA Heliophysics data. For this purpose, the ADAPT routines have been used to generate data resource descriptions by using an XML schema named Space Physics Archive, Search, and Extract (SPASE). SPASE is the designated standard for documenting Heliophysics data products, as adopted by the Heliophysics Data and Model Consortium. The set of SPASE XML resource descriptions produced by ADAPT includes high-level descriptions of numerical data products, display data products, or catalogs and also includes low-level "Granule" descriptions. A SPASE Granule is effectively a universal access metadata resource; a Granule associates an individual data file (e.g. a CDF file) with a "parent" high-level data resource description, assigns a resource identifier to the file, and lists the corresponding assess URL(s). The CDAWEB and SPDF file systems were queried to provide the input required by the ADAPT software to create an initial set of SPASE metadata resource descriptions. Then, the CDAWEB and SPDF data repositories were queried subsequently on a nightly basis and the CDF file lists were checked for any changes such as the occurrence of new, modified, or deleted
Oriented wavelet transform for image compression and denoising.
Chappelier, Vivien; Guillemot, Christine
2006-10-01
In this paper, we introduce a new transform for image processing, based on wavelets and the lifting paradigm. The lifting steps of a unidimensional wavelet are applied along a local orientation defined on a quincunx sampling grid. To maximize energy compaction, the orientation minimizing the prediction error is chosen adaptively. A fine-grained multiscale analysis is provided by iterating the decomposition on the low-frequency band. In the context of image compression, the multiresolution orientation map is coded using a quad tree. The rate allocation between the orientation map and wavelet coefficients is jointly optimized in a rate-distortion sense. For image denoising, a Markov model is used to extract the orientations from the noisy image. As long as the map is sufficiently homogeneous, interesting properties of the original wavelet are preserved such as regularity and orthogonality. Perfect reconstruction is ensured by the reversibility of the lifting scheme. The mutual information between the wavelet coefficients is studied and compared to the one observed with a separable wavelet transform. The rate-distortion performance of this new transform is evaluated for image coding using state-of-the-art subband coders. Its performance in a denoising application is also assessed against the performance obtained with other transforms or denoising methods.
Myoelectric signal compression using zero-trees of wavelet coefficients.
Norris, Jason A; Englehart, Kevin B; Lovely, Dennis F
2003-11-01
Recent progress in the diagnostic use of the myoelectric signal for neuromuscular diseases, coupled with increasing interests in telemedicine applications, mandate the need for an effective compression technique. The efficacy of the embedded zero-tree wavelet compression algorithm is examined with respect to some important analysis parameters (the length of the analysis segment and wavelet type) and measurement conditions (muscle type and contraction type). It is shown that compression performance improves with segment length, and that good choices of wavelet type include the Meyer wavelet and the fifth order biorthogonal wavelet. The effects of different muscle sites and contraction types on compression performance are less conclusive.A comparison of a number of lossy compression techniques has revealed that the EZW algorithm exhibits superior performance to a hard thresholding wavelet approach, but falls short of adaptive differential pulse code modulation. The bit prioritization capability of the EZW algorithm allows one to specify the compression factor online, making it an appealing technique for streaming data applications, as often encountered in telemedicine.
Wavelet Signal Processing for Transient Feature Extraction
1992-03-15
Research was conducted to evaluate the feasibility of applying Wavelets and Wavelet Transform methods to transient signal feature extraction problems... Wavelet transform techniques were developed to extract low dimensional feature data that allowed a simple classification scheme to easily separate
NASA Technical Reports Server (NTRS)
Zhang, Yiqiang; Alexander, J. I. D.; Ouazzani, J.
1994-01-01
Free and moving boundary problems require the simultaneous solution of unknown field variables and the boundaries of the domains on which these variables are defined. There are many technologically important processes that lead to moving boundary problems associated with fluid surfaces and solid-fluid boundaries. These include crystal growth, metal alloy and glass solidification, melting and name propagation. The directional solidification of semi-conductor crystals by the Bridgman-Stockbarger method is a typical example of such a complex process. A numerical model of this growth method must solve the appropriate heat, mass and momentum transfer equations and determine the location of the melt-solid interface. In this work, a Chebyshev pseudospectra collocation method is adapted to the problem of directional solidification. Implementation involves a solution algorithm that combines domain decomposition, finite-difference preconditioned conjugate minimum residual method and a Picard type iterative scheme.
An iterative finite-element collocation method for parabolic problems using domain decomposition
Curran, M.C.
1992-01-01
Advection-dominated flows occur widely in the transport of groundwater contaminants, the movements of fluids in enhanced oil recovery projects, and many other contexts. In numerical models of such flows, adaptive local grid refinement is a conceptually attractive approach for resolving the sharp fronts or layers that tend to characterize the solutions. However, this approach can be difficult to implement in practice. A domain decomposition method developed by Bramble, Ewing, Pasciak, and Schatz, known as the BEPS method, overcomes many of the difficulties. We demonstrate the applicability of the iterative BEPS ideas to finite-element collocation on trial spaces of piecewise Hermite bicubics. The resulting scheme allows one to refine selected parts of a spatial grid without destroying algebraic efficiencies associated with the original coarse grid. We apply the method to two dimensional time-dependent advection-diffusion problems.
An iterative finite-element collocation method for parabolic problems using domain decomposition
Curran, M.C.
1992-11-01
Advection-dominated flows occur widely in the transport of groundwater contaminants, the movements of fluids in enhanced oil recovery projects, and many other contexts. In numerical models of such flows, adaptive local grid refinement is a conceptually attractive approach for resolving the sharp fronts or layers that tend to characterize the solutions. However, this approach can be difficult to implement in practice. A domain decomposition method developed by Bramble, Ewing, Pasciak, and Schatz, known as the BEPS method, overcomes many of the difficulties. We demonstrate the applicability of the iterative BEPS ideas to finite-element collocation on trial spaces of piecewise Hermite bicubics. The resulting scheme allows one to refine selected parts of a spatial grid without destroying algebraic efficiencies associated with the original coarse grid. We apply the method to two dimensional time-dependent advection-diffusion problems.
Radiation energy budget studies using collocated AVHRR and ERBE observations
Ackerman, S.A.; Inoue, Toshiro
1994-03-01
Changes in the energy balance at the top of the atmosphere are specified as a function of atmospheric and surface properties using observations from the Advanced Very High Resolution Radiometer (AVHRR) and the Earth Radiation Budget Experiment (ERBE) scanner. By collocating the observations from the two instruments, flown on NOAA-9, the authors take advantage of the remote-sensing capabilities of each instrument. The AVHRR spectral channels were selected based on regions that are strongly transparent to clear sky conditions and are therefore useful for characterizing both surface and cloud-top conditions. The ERBE instruments make broadband observations that are important for climate studies. The approach of collocating these observations in time and space is used to study the radiative energy budget of three geographic regions: oceanic, savanna, and desert. 25 refs., 8 figs.
Locating CVBEM collocation points for steady state heat transfer problems
Hromadka, T.V.
1985-01-01
The Complex Variable Boundary Element Method or CVBEM provides a highly accurate means of developing numerical solutions to steady state two-dimensional heat transfer problems. The numerical approach exactly solves the Laplace equation and satisfies the boundary conditions at specified points on the boundary by means of collocation. The accuracy of the approximation depends upon the nodal point distribution specified by the numerical analyst. In order to develop subsequent, refined approximation functions, four techniques for selecting additional collocation points are presented. The techniques are compared as to the governing theory, representation of the error of approximation on the problem boundary, the computational costs, and the ease of use by the numerical analyst. ?? 1985.
Mining visual collocation patterns via self-supervised subspace learning.
Yuan, Junsong; Wu, Ying
2012-04-01
Traditional text data mining techniques are not directly applicable to image data which contain spatial information and are characterized by high-dimensional visual features. It is not a trivial task to discover meaningful visual patterns from images because the content variations and spatial dependence in visual data greatly challenge most existing data mining methods. This paper presents a novel approach to coping with these difficulties for mining visual collocation patterns. Specifically, the novelty of this work lies in the following new contributions: 1) a principled solution to the discovery of visual collocation patterns based on frequent itemset mining and 2) a self-supervised subspace learning method to refine the visual codebook by feeding back discovered patterns via subspace learning. The experimental results show that our method can discover semantically meaningful patterns efficiently and effectively.
A Christoffel function weighted least squares algorithm for collocation approximations
Narayan, Akil; Jakeman, John D.; Zhou, Tao
2016-11-28
Here, we propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation framework. Our investigation is motivated by applications in the collocation approximation of parametric functions, which frequently entails construction of surrogates via orthogonal polynomials. A standard Monte Carlo approach would draw samples according to the density defining the orthogonal polynomial family. Our proposed algorithm instead samples with respect to the (weighted) pluripotential equilibrium measure of the domain, and subsequently solves a weighted least-squares problem, with weights given by evaluations of the Christoffel function. We present theoretical analysis tomore » motivate the algorithm, and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest.« less
A Christoffel function weighted least squares algorithm for collocation approximations
Narayan, Akil; Jakeman, John D.; Zhou, Tao
2016-11-28
Here, we propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation framework. Our investigation is motivated by applications in the collocation approximation of parametric functions, which frequently entails construction of surrogates via orthogonal polynomials. A standard Monte Carlo approach would draw samples according to the density defining the orthogonal polynomial family. Our proposed algorithm instead samples with respect to the (weighted) pluripotential equilibrium measure of the domain, and subsequently solves a weighted least-squares problem, with weights given by evaluations of the Christoffel function. We present theoretical analysis to motivate the algorithm, and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest.
Wavelet Preprocessing of Acoustic Signals
1991-12-01
wavelet transform to preprocess acoustic broadband signals in a system that discriminates between different classes of acoustic bursts. This is motivated by the similarity between the proportional bandwidth filters provided by the wavelet transform and those found in biological hearing systems. The experiment involves comparing statistical pattern classifier effects of wavelet and FFT preprocessed acoustic signals. The data used was from the DARPA Phase I database, which consists of artificially generated signals with real ocean background. The
Domain decomposition preconditioners for the spectral collocation method
NASA Technical Reports Server (NTRS)
Quarteroni, Alfio; Sacchilandriani, Giovanni
1988-01-01
Several block iteration preconditioners are proposed and analyzed for the solution of elliptic problems by spectral collocation methods in a region partitioned into several rectangles. It is shown that convergence is achieved with a rate which does not depend on the polynomial degree of the spectral solution. The iterative methods here presented can be effectively implemented on multiprocessor systems due to their high degree of parallelism.
Weak transient fault feature extraction based on an optimized Morlet wavelet and kurtosis
NASA Astrophysics Data System (ADS)
Qin, Yi; Xing, Jianfeng; Mao, Yongfang
2016-08-01
Aimed at solving the key problem in weak transient detection, the present study proposes a new transient feature extraction approach using the optimized Morlet wavelet transform, kurtosis index and soft-thresholding. Firstly, a fast optimization algorithm based on the Shannon entropy is developed to obtain the optimized Morlet wavelet parameter. Compared to the existing Morlet wavelet parameter optimization algorithm, this algorithm has lower computation complexity. After performing the optimized Morlet wavelet transform on the analyzed signal, the kurtosis index is used to select the characteristic scales and obtain the corresponding wavelet coefficients. From the time-frequency distribution of the periodic impulsive signal, it is found that the transient signal can be reconstructed by the wavelet coefficients at several characteristic scales, rather than the wavelet coefficients at just one characteristic scale, so as to improve the accuracy of transient detection. Due to the noise influence on the characteristic wavelet coefficients, the adaptive soft-thresholding method is applied to denoise these coefficients. With the denoised wavelet coefficients, the transient signal can be reconstructed. The proposed method was applied to the analysis of two simulated signals, and the diagnosis of a rolling bearing fault and a gearbox fault. The superiority of the method over the fast kurtogram method was verified by the results of simulation analysis and real experiments. It is concluded that the proposed method is extremely suitable for extracting the periodic impulsive feature from strong background noise.
Steerable pyramids and tight wavelet frames in L2(R(d)).
Unser, Michael; Chenouard, Nicolas; Van de Ville, Dimitri
2011-10-01
We present a functional framework for the design of tight steerable wavelet frames in any number of dimensions. The 2-D version of the method can be viewed as a generalization of Simoncelli's steerable pyramid that gives access to a larger palette of steerable wavelets via a suitable parametrization. The backbone of our construction is a primal isotropic wavelet frame that provides the multiresolution decomposition of the signal. The steerable wavelets are obtained by applying a one-to-many mapping (Nth-order generalized Riesz transform) to the primal ones. The shaping of the steerable wavelets is controlled by an M×M unitary matrix (where M is the number of wavelet channels) that can be selected arbitrarily; this allows for a much wider range of solutions than the traditional equiangular configuration (steerable pyramid). We give a complete functional description of these generalized wavelet transforms and derive their steering equations. We describe some concrete examples of transforms, including some built around a Mallat-type multiresolution analysis of L(2)(R(d)), and provide a fast Fourier transform-based decomposition algorithm. We also propose a principal-component-based method for signal-adapted wavelet design. Finally, we present some illustrative examples together with a comparison of the denoising performance of various brands of steerable transforms. The results are in favor of an optimized wavelet design (equalized principal component analysis), which consistently performs best.
2007-11-02
Daubechies-DeVore (Cohen-Daubechies-Gulleryuz-Orchard) This encoder is optimal on all Besov classes compactly embedded into L2 EZW , Said-Pearlman...DeVore (Cohen-Daubechies-Gulleryuz-Orchard) This encoder is optimal on all Besov classes compactly embedded into L2 EZW , Said-Pearlman, Cargese – p.49...Cohen-Daubechies-Gulleryuz-Orchard) This encoder is optimal on all Besov classes compactly embedded into L2 EZW , Said-Pearlman, Cargese – p.49/49 Wavelet
Wavelet phase synchronization and chaoticity.
Postnikov, E B
2009-11-01
It has been shown that the so-called "wavelet phase" (or "time-scale") synchronization of chaotic signals is actually synchronization of smoothed functions with reduced chaotic fluctuations. This fact is based on the representation of the wavelet transform with the Morlet wavelet as a solution of the Cauchy problem for a simple diffusion equation with initial condition in a form of harmonic function modulated by a given signal. The topological background of the resulting effect is discussed. It is argued that the wavelet phase synchronization provides information about the synchronization of an averaged motion described by bounding tori instead of the fine-level classical chaotic phase synchronization.
Pseudospectral collocation methods for fourth order differential equations
NASA Technical Reports Server (NTRS)
Malek, Alaeddin; Phillips, Timothy N.
1994-01-01
Collocation schemes are presented for solving linear fourth order differential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalent to this discrete variational problem. An efficient preconditioner based on a low-order finite difference approximation to the same differential operator is presented. The corresponding multidomain problem is also considered and interface conditions are derived. Pseudospectral approximations which are C1 continuous at the interfaces are used in each subdomain to approximate the solution. The approximations are also shown to be C3 continuous at the interfaces asymptotically. A complete analysis of the collocation scheme for the multidomain problem is provided. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a nonrectangular domain.
ERIC Educational Resources Information Center
Walker, Crayton Phillip
2011-01-01
In this article I examine the collocational behaviour of groups of semantically related verbs (e.g., "head, run, manage") and nouns (e.g., "issue, factor, aspect") from the domain of business English. The results of this corpus-based study show that much of the collocational behaviour exhibited by these lexical items can be explained by examining…
Zahra, Noor e; Sevindir, Huliya A.; Aslan, Zafar; Siddiqi, A. H.
2012-07-17
The aim of this study is to provide emerging applications of wavelet methods to medical signals and images, such as electrocardiogram, electroencephalogram, functional magnetic resonance imaging, computer tomography, X-ray and mammography. Interpretation of these signals and images are quite important. Nowadays wavelet methods have a significant impact on the science of medical imaging and the diagnosis of disease and screening protocols. Based on our initial investigations, future directions include neurosurgical planning and improved assessment of risk for individual patients, improved assessment and strategies for the treatment of chronic pain, improved seizure localization, and improved understanding of the physiology of neurological disorders. We look ahead to these and other emerging applications as the benefits of this technology become incorporated into current and future patient care. In this chapter by applying Fourier transform and wavelet transform, analysis and denoising of one of the important biomedical signals like EEG is carried out. The presence of rhythm, template matching, and correlation is discussed by various method. Energy of EEG signal is used to detect seizure in an epileptic patient. We have also performed denoising of EEG signals by SWT.
NASA Astrophysics Data System (ADS)
Zahra, Noor e.; Sevindir, Hulya Kodal; Aslan, Zafer; Siddiqi, A. H.
2012-07-01
The aim of this study is to provide emerging applications of wavelet methods to medical signals and images, such as electrocardiogram, electroencephalogram, functional magnetic resonance imaging, computer tomography, X-ray and mammography. Interpretation of these signals and images are quite important. Nowadays wavelet methods have a significant impact on the science of medical imaging and the diagnosis of disease and screening protocols. Based on our initial investigations, future directions include neurosurgical planning and improved assessment of risk for individual patients, improved assessment and strategies for the treatment of chronic pain, improved seizure localization, and improved understanding of the physiology of neurological disorders. We look ahead to these and other emerging applications as the benefits of this technology become incorporated into current and future patient care. In this chapter by applying Fourier transform and wavelet transform, analysis and denoising of one of the important biomedical signals like EEG is carried out. The presence of rhythm, template matching, and correlation is discussed by various method. Energy of EEG signal is used to detect seizure in an epileptic patient. We have also performed denoising of EEG signals by SWT.
Narayan, Akil; Jakeman, John D.; Zhou, Tao
2016-11-28
Here, we propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation framework. Our investigation is motivated by applications in the collocation approximation of parametric functions, which frequently entails construction of surrogates via orthogonal polynomials. A standard Monte Carlo approach would draw samples according to the density defining the orthogonal polynomial family. Our proposed algorithm instead samples with respect to the (weighted) pluripotential equilibrium measure of the domain, and subsequently solves a weighted least-squares problem, with weights given by evaluations of the Christoffel function. We present theoretical analysis tomore » motivate the algorithm, and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest.« less
The berkeley wavelet transform: a biologically inspired orthogonal wavelet transform.
Willmore, Ben; Prenger, Ryan J; Wu, Michael C-K; Gallant, Jack L
2008-06-01
We describe the Berkeley wavelet transform (BWT), a two-dimensional triadic wavelet transform. The BWT comprises four pairs of mother wavelets at four orientations. Within each pair, one wavelet has odd symmetry, and the other has even symmetry. By translation and scaling of the whole set (plus a single constant term), the wavelets form a complete, orthonormal basis in two dimensions. The BWT shares many characteristics with the receptive fields of neurons in mammalian primary visual cortex (V1). Like these receptive fields, BWT wavelets are localized in space, tuned in spatial frequency and orientation, and form a set that is approximately scale invariant. The wavelets also have spatial frequency and orientation bandwidths that are comparable with biological values. Although the classical Gabor wavelet model is a more accurate description of the receptive fields of individual V1 neurons, the BWT has some interesting advantages. It is a complete, orthonormal basis and is therefore inexpensive to compute, manipulate, and invert. These properties make the BWT useful in situations where computational power or experimental data are limited, such as estimation of the spatiotemporal receptive fields of neurons.
Nonlocal hierarchical dictionary learning using wavelets for image denoising.
Yan, Ruomei; Shao, Ling; Liu, Yan
2013-12-01
Exploiting the sparsity within representation models for images is critical for image denoising. The best currently available denoising methods take advantage of the sparsity from image self-similarity, pre-learned, and fixed representations. Most of these methods, however, still have difficulties in tackling high noise levels or noise models other than Gaussian. In this paper, the multiresolution structure and sparsity of wavelets are employed by nonlocal dictionary learning in each decomposition level of the wavelets. Experimental results show that our proposed method outperforms two state-of-the-art image denoising algorithms on higher noise levels. Furthermore, our approach is more adaptive to the less extensively researched uniform noise.
Wavelet analysis of discharge dynamics of fusimotor neurons
NASA Astrophysics Data System (ADS)
Stratimirović, Dj.; Milošević, S.; Blesić, S.; Ljubisavljević, M.
2001-03-01
We study the interspike intervals (ISI) time series of the spontaneous fusimotor neuron activity by applying the wavelet transform analysis and confirm the existence of the white noise characteristics of the ISI time series. This means that the neuron activity may serve as the requisite noisy component for occurrence of the stochastic resonance mechanism in the neural coordination of muscle spindles. Besides, we apply the multifractal formalism adapted for the wavelet transform time series analysis. Thus, we have established the multifractality of the ISI data and achieved an additional insight into fusimotor discharge dynamics.
Speckle Suppression in Ultrasonic Images Based on Undecimated Wavelets
NASA Astrophysics Data System (ADS)
Argenti, Fabrizio; Torricelli, Gionatan
2003-12-01
An original method to denoise ultrasonic images affected by speckle is presented. Speckle is modeled as a signal-dependent noise corrupting the image. Noise reduction is approached as a Wiener-like filtering performed in a shift-invariant wavelet domain by means of an adaptive rescaling of the coefficients of an undecimated octave decomposition. The scaling factor of each coefficient is calculated from local statistics of the degraded image, the parameters of the noise model, and the wavelet filters. Experimental results demonstrate that excellent background smoothing as well as preservation of edge sharpness and fine details can be obtained.
Object-based wavelet compression using coefficient selection
NASA Astrophysics Data System (ADS)
Zhao, Lifeng; Kassim, Ashraf A.
1998-12-01
In this paper, we present a novel approach to code image regions of arbitrary shapes. The proposed algorithm combines a coefficient selection scheme with traditional wavelet compression for coding arbitrary regions and uses a shape adaptive embedded zerotree wavelet coding (SA-EZW) to quantize the selected coefficients. Since the shape information is implicitly encoded by the SA-EZW, our decoder can reconstruct the arbitrary region without separate shape coding. This makes the algorithm simple to implement and avoids the problem of contour coding. Our algorithm also provides a sufficient framework to address content-based scalability and improved coding efficiency as described by MPEG-4.
Data compression by wavelet transforms
NASA Technical Reports Server (NTRS)
Shahshahani, M.
1992-01-01
A wavelet transform algorithm is applied to image compression. It is observed that the algorithm does not suffer from the blockiness characteristic of the DCT-based algorithms at compression ratios exceeding 25:1, but the edges do not appear as sharp as they do with the latter method. Some suggestions for the improved performance of the wavelet transform method are presented.
Finite element-wavelet hybrid algorithm for atmospheric tomography.
Yudytskiy, Mykhaylo; Helin, Tapio; Ramlau, Ronny
2014-03-01
Reconstruction of the refractive index fluctuations in the atmosphere, or atmospheric tomography, is an underlying problem of many next generation adaptive optics (AO) systems, such as the multiconjugate adaptive optics or multiobject adaptive optics (MOAO). The dimension of the problem for the extremely large telescopes, such as the European Extremely Large Telescope (E-ELT), suggests the use of iterative schemes as an alternative to the matrix-vector multiply (MVM) methods. Recently, an algorithm based on the wavelet representation of the turbulence has been introduced in [Inverse Probl.29, 085003 (2013)] by the authors to solve the atmospheric tomography using the conjugate gradient iteration. The authors also developed an efficient frequency-dependent preconditioner for the wavelet method in a later work. In this paper we study the computational aspects of the wavelet algorithm. We introduce three new techniques, the dual domain discretization strategy, a scale-dependent preconditioner, and a ground layer multiscale method, to derive a method that is globally O(n), parallelizable, and compact with respect to memory. We present the computational cost estimates and compare the theoretical numerical performance of the resulting finite element-wavelet hybrid algorithm with the MVM. The quality of the method is evaluated in terms of an MOAO simulation for the E-ELT on the European Southern Observatory (ESO) end-to-end simulation system OCTOPUS. The method is compared to the ESO version of the Fractal Iterative Method [Proc. SPIE7736, 77360X (2010)] in terms of quality.
A generalized wavelet extrema representation
Lu, Jian; Lades, M.
1995-10-01
The wavelet extrema representation originated by Stephane Mallat is a unique framework for low-level and intermediate-level (feature) processing. In this paper, we present a new form of wavelet extrema representation generalizing Mallat`s original work. The generalized wavelet extrema representation is a feature-based multiscale representation. For a particular choice of wavelet, our scheme can be interpreted as representing a signal or image by its edges, and peaks and valleys at multiple scales. Such a representation is shown to be stable -- the original signal or image can be reconstructed with very good quality. It is further shown that a signal or image can be modeled as piecewise monotonic, with all turning points between monotonic segments given by the wavelet extrema. A new projection operator is introduced to enforce piecewise inonotonicity of a signal in its reconstruction. This leads to an enhancement to previously developed algorithms in preventing artifacts in reconstructed signal.
NASA Technical Reports Server (NTRS)
Jameson, Leland
1996-01-01
Wavelets can provide a basis set in which the basis functions are constructed by dilating and translating a fixed function known as the mother wavelet. The mother wavelet can be seen as a high pass filter in the frequency domain. The process of dilating and expanding this high-pass filter can be seen as altering the frequency range that is 'passed' or detected. The process of translation moves this high-pass filter throughout the domain, thereby providing a mechanism to detect the frequencies or scales of information at every location. This is exactly the type of information that is needed for effective grid generation. This paper provides motivation to use wavelets for grid generation in addition to providing the final product: source code for wavelet-based grid generation.
Wavelet preprocessing of acoustic signals
NASA Astrophysics Data System (ADS)
Huang, W. Y.; Solorzano, M. R.
1991-12-01
This paper describes results using the wavelet transform to preprocess acoustic broadband signals in a system that discriminates between different classes of acoustic bursts. This is motivated by the similarity between the proportional bandwidth filters provided by the wavelet transform and those found in biological hearing systems. The experiment involves comparing statistical pattern classifier effects of wavelet and FFT preprocessed acoustic signals. The data used was from the DARPA Phase 1 database, which consists of artificially generated signals with real ocean background. The results show that the wavelet transform did provide improved performance when classifying in a frame-by-frame basis. The DARPA Phase 1 database is well matched to proportional bandwidth filtering; i.e., signal classes that contain high frequencies do tend to have shorter duration in this database. It is also noted that the decreasing background levels at high frequencies compensate for the poor match of the wavelet transform for long duration (high frequency) signals.
Video coding with lifted wavelet transforms and complementary motion-compensated signals
NASA Astrophysics Data System (ADS)
Flierl, Markus H.; Vandergheynst, Pierre; Girod, Bernd
2004-01-01
This paper investigates video coding with wavelet transforms applied in the temporal direction of a video sequence. The wavelets are implemented with the lifting scheme in order to permit motion compensation between successive pictures. We improve motion compensation in the lifting steps and utilize complementary motion-compensated signals. Similar to superimposed predictive coding with complementary signals, this approach improves compression efficiency. We investigate experimentally and theoretically complementary motion-compensated signals for lifted wavelet transforms. Experimental results with the complementary motion-compensated Haar wavelet and frame-adaptive motion compensation show improvements in coding efficiency of up to 3 dB. The theoretical results demonstrate that the lifted Haar wavelet scheme with complementary motion-compensated signals is able to approach the bound for bit-rate savings of 2 bits per sample and motion-accuracy step when compared to optimum intra-frame coding of the input pictures.
Wavelet Analysis of Bioacoustic Scattering and Marine Mammal Vocalizations
2005-09-01
17 B. DISCRETE WAVELET TRANSFORM .....................................................17 1. Mother Wavelet ...LEFT BLANK 11 III. WAVELET THEORY There are two distinct classes of wavelet transforms : the continuous wavelet transform (CWT) and the discrete ... wavelet transform (DWT). The discrete wavelet transform is a compact representation of the data and is particularly useful for noise reduction and
A Wavelet-Based Methodology for Grinding Wheel Condition Monitoring
Liao, T. W.; Ting, C.F.; Qu, Jun; Blau, Peter Julian
2007-01-01
Grinding wheel surface condition changes as more material is removed. This paper presents a wavelet-based methodology for grinding wheel condition monitoring based on acoustic emission (AE) signals. Grinding experiments in creep feed mode were conducted to grind alumina specimens with a resinoid-bonded diamond wheel using two different conditions. During the experiments, AE signals were collected when the wheel was 'sharp' and when the wheel was 'dull'. Discriminant features were then extracted from each raw AE signal segment using the discrete wavelet decomposition procedure. An adaptive genetic clustering algorithm was finally applied to the extracted features in order to distinguish different states of grinding wheel condition. The test results indicate that the proposed methodology can achieve 97% clustering accuracy for the high material removal rate condition, 86.7% for the low material removal rate condition, and 76.7% for the combined grinding conditions if the base wavelet, the decomposition level, and the GA parameters are properly selected.
Content based image retrieval based on wavelet transform coefficients distribution.
Lamard, Mathieu; Cazuguel, Guy; Quellec, Gwénolé; Bekri, Lynda; Roux, Christian; Cochener, Béatrice
2007-01-01
In this paper we propose a content based image retrieval method for diagnosis aid in medical fields. We characterize images without extracting significant features by using distribution of coefficients obtained by building signatures from the distribution of wavelet transform. The research is carried out by computing signature distances between the query and database images. Several signatures are proposed; they use a model of wavelet coefficient distribution. To enhance results, a weighted distance between signatures is used and an adapted wavelet base is proposed. Retrieval efficiency is given for different databases including a diabetic retinopathy, a mammography and a face database. Results are promising: the retrieval efficiency is higher than 95% for some cases using an optimization process.
Wavelets and spacetime squeeze
NASA Technical Reports Server (NTRS)
Han, D.; Kim, Y. S.; Noz, Marilyn E.
1993-01-01
It is shown that the wavelet is the natural language for the Lorentz covariant description of localized light waves. A model for covariant superposition is constructed for light waves with different frequencies. It is therefore possible to construct a wave function for light waves carrying a covariant probability interpretation. It is shown that the time-energy uncertainty relation (Delta(t))(Delta(w)) is approximately 1 for light waves is a Lorentz-invariant relation. The connection between photons and localized light waves is examined critically.
Wavelet Packets in Wideband Multiuser Communications
2004-11-01
developed doubly orthogonal CDMA user spreading waveforms based on wavelet packets. We have also developed and evaluated a wavelet packet based ...inter symbol interferences. Compared with the existing DFT based multicarrier CDMA systems, better performance is achieved with the wavelet packet...23 3.4 Over Loaded Waveform Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4. Wavelet Packet Based Time-Varying
An Introduction to Wavelet Theory and Analysis
Miner, N.E.
1998-10-01
This report reviews the history, theory and mathematics of wavelet analysis. Examination of the Fourier Transform and Short-time Fourier Transform methods provides tiormation about the evolution of the wavelet analysis technique. This overview is intended to provide readers with a basic understanding of wavelet analysis, define common wavelet terminology and describe wavelet amdysis algorithms. The most common algorithms for performing efficient, discrete wavelet transforms for signal analysis and inverse discrete wavelet transforms for signal reconstruction are presented. This report is intended to be approachable by non- mathematicians, although a basic understanding of engineering mathematics is necessary.
Fourier analysis of finite element preconditioned collocation schemes
NASA Technical Reports Server (NTRS)
Deville, Michel O.; Mund, Ernest H.
1990-01-01
The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.
Simplex-stochastic collocation method with improved scalability
Edeling, W.N.; Dwight, R.P.; Cinnella, P.
2016-04-01
The Simplex-Stochastic Collocation (SSC) method is a robust tool used to propagate uncertain input distributions through a computer code. However, it becomes prohibitively expensive for problems with dimensions higher than 5. The main purpose of this paper is to identify bottlenecks, and to improve upon this bad scalability. In order to do so, we propose an alternative interpolation stencil technique based upon the Set-Covering problem, and we integrate the SSC method in the High-Dimensional Model-Reduction framework. In addition, we address the issue of ill-conditioned sample matrices, and we present an analytical map to facilitate uniformly-distributed simplex sampling.
Wavelet Transform Signal Processing Applied to Ultrasonics.
1995-05-01
THE WAVELET TRANSFORM IS APPLIED TO THE ANALYSIS OF ULTRASONIC WAVES FOR IMPROVED SIGNAL DETECTION AND ANALYSIS OF THE SIGNALS. In instances where...the mother wavelet is well defined, the wavelet transform has relative insensitivity to noise and does not need windowing. Peak detection of...ultrasonic pulses using the wavelet transform is described and results show good detection even when large white noise was added. The use of the wavelet
Spherical 3D isotropic wavelets
NASA Astrophysics Data System (ADS)
Lanusse, F.; Rassat, A.; Starck, J.-L.
2012-04-01
Context. Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D spherical Fourier-Bessel (SFB) analysis in spherical coordinates is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. Aims: The aim of this paper is to present a new formalism for a spherical 3D isotropic wavelet, i.e. one based on the SFB decomposition of a 3D field and accompany the formalism with a public code to perform wavelet transforms. Methods: We describe a new 3D isotropic spherical wavelet decomposition based on the undecimated wavelet transform (UWT) described in Starck et al. (2006). We also present a new fast discrete spherical Fourier-Bessel transform (DSFBT) based on both a discrete Bessel transform and the HEALPIX angular pixelisation scheme. We test the 3D wavelet transform and as a toy-application, apply a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and find we can successfully remove noise without much loss to the large scale structure. Results: We have described a new spherical 3D isotropic wavelet transform, ideally suited to analyse and denoise future 3D spherical cosmological surveys, which uses a novel DSFBT. We illustrate its potential use for denoising using a toy model. All the algorithms presented in this paper are available for download as a public code called MRS3D at http://jstarck.free.fr/mrs3d.html
Tailoring wavelets for chaos control.
Wei, G W; Zhan, Meng; Lai, C-H
2002-12-31
Chaos is a class of ubiquitous phenomena and controlling chaos is of great interest and importance. In this Letter, we introduce wavelet controlled dynamics as a new paradigm of dynamical control. We find that by modifying a tiny fraction of the wavelet subspaces of a coupling matrix, we could dramatically enhance the transverse stability of the synchronous manifold of a chaotic system. Wavelet controlled Hopf bifurcation from chaos is observed. Our approach provides a robust strategy for controlling chaos and other dynamical systems in nature.
Peak finding using biorthogonal wavelets
Tan, C.Y.
2000-02-01
The authors show in this paper how they can find the peaks in the input data if the underlying signal is a sum of Lorentzians. In order to project the data into a space of Lorentzian like functions, they show explicitly the construction of scaling functions which look like Lorentzians. From this construction, they can calculate the biorthogonal filter coefficients for both the analysis and synthesis functions. They then compare their biorthogonal wavelets to the FBI (Federal Bureau of Investigations) wavelets when used for peak finding in noisy data. They will show that in this instance, their filters perform much better than the FBI wavelets.
Blind source separation of multichannel electroencephalogram based on wavelet transform and ICA
NASA Astrophysics Data System (ADS)
You, Rong-Yi; Chen, Zhong
2005-11-01
Combination of the wavelet transform and independent component analysis (ICA) was employed for blind source separation (BSS) of multichannel electroencephalogram (EEG). After denoising the original signals by discrete wavelet transform, high frequency components of some noises and artifacts were removed from the original signals. The denoised signals were reconstructed again for the purpose of ICA, such that the drawback that ICA cannot distinguish noises from source signals can be overcome effectively. The practical processing results showed that this method is an effective way to BSS of multichannel EEG. The method is actually a combination of wavelet transform with adaptive neural network, so it is also useful for BBS of other complex signals.
The Differential Pressure Signal De-noised by Domain Transform Combined with Wavelet Threshold
NASA Astrophysics Data System (ADS)
Zhang, Yuhao; Wang, Haihui; Li, Chao
2017-01-01
In the process of estimating the thrust of an aircraft engine, there is a big problem that the differential pressure signal has large fluctuation. To deal with this problem, we develop an effective and robust adaptive de-noising algorithm based on domain transform combined with wavelet transform (D-WT). First, we do the domain transform for the signal, then sample the transformed signal, and finally the wavelet threshold transform is performed for the signal. Compared with the traditional wavelet transforms, the D-WT method filters the noise effectively and keeps more details.
Accuracy and speed in computing the Chebyshev collocation derivative
NASA Technical Reports Server (NTRS)
Don, Wai-Sun; Solomonoff, Alex
1991-01-01
We studied several algorithms for computing the Chebyshev spectral derivative and compare their roundoff error. For a large number of collocation points, the elements of the Chebyshev differentiation matrix, if constructed in the usual way, are not computed accurately. A subtle cause is is found to account for the poor accuracy when computing the derivative by the matrix-vector multiplication method. Methods for accurately computing the elements of the matrix are presented, and we find that if the entities of the matrix are computed accurately, the roundoff error of the matrix-vector multiplication is as small as that of the transform-recursion algorithm. Results of CPU time usage are shown for several different algorithms for computing the derivative by the Chebyshev collocation method for a wide variety of two-dimensional grid sizes on both an IBM and a Cray 2 computer. We found that which algorithm is fastest on a particular machine depends not only on the grid size, but also on small details of the computer hardware as well. For most practical grid sizes used in computation, the even-odd decomposition algorithm is found to be faster than the transform-recursion method.
A stochastic collocation approach for efficient integrated gear health prognosis
NASA Astrophysics Data System (ADS)
Zhao, Fuqiong; Tian, Zhigang; Zeng, Yong
2013-08-01
Uncertainty quantification in damage growth is critical in equipment health prognosis and condition based maintenance. Integrated health prognostics has recently drawn growing attention due to its capability to produce more accurate predictions through integrating physical models and real-time condition monitoring data. In the existing literature, simulation is commonly used to account for the uncertainty in prognostics, which is inefficient. In this paper, instead of using simulation, a stochastic collocation approach is developed for efficient integrated gear health prognosis. Based on generalized polynomial chaos expansion, the approach is utilized to evaluate the uncertainty in gear remaining useful life prediction as well as the likelihood function in Bayesian inference. The collected condition monitoring data are incorporated into prognostics via Bayesian inference to update the distributions of uncertainties at given inspection times. Accordingly, the distribution of the remaining useful life is updated. Compared to conventional simulation methods, the stochastic collocation approach is much more efficient, and is capable of dealing with high dimensional probability space. An example is used to demonstrate the effectiveness and efficiency of the proposed approach.
Wavelets for approximate Fourier transform and data compression
NASA Astrophysics Data System (ADS)
Guo, Haitao
This dissertation has two parts. In the first part, we develop a wavelet-based fast approximate Fourier transform algorithm. The second part is devoted to the developments of several wavelet-based data compression techniques for image and seismic data. We propose an algorithm that uses the discrete wavelet transform (DWT) as a tool to compute the discrete Fourier transform (DFT). The classical Cooley-Tukey FFT is shown to be a special case of the proposed algorithm when the wavelets in use are trivial. The main advantage of our algorithm is that the good time and frequency localization of wavelets can be exploited to approximate the Fourier transform for many classes of signals, resulting in much less computation. Thus the new algorithm provides an efficient complexity versus accuracy tradeoff. When approximations are allowed, under certain sparsity conditions, the algorithm can achieve linear complexity, i.e. O(N). The proposed algorithm also has built-in noise reduction capability. For waveform and image compression, we propose a novel scheme using the recently developed Burrows-Wheeler transform (BWT). We show that the discrete wavelet transform (DWT) should be used before the Burrows-Wheeler transform to improve the compression performance for many natural signals and images. We demonstrate that the simple concatenation of the DWT and BWT coding performs comparably as the embedded zerotree wavelet (EZW) compression for images. Various techniques that significantly improve the performance of our compression scheme are also discussed. The phase information is crucial for seismic data processing. However, traditional compression schemes do not pay special attention to preserving the phase of the seismic data, resulting in the loss of critical information. We propose a lossy compression method that preserves the phase as much as possible. The method is based on the self-adjusting wavelet transform that adapts to the locations of the significant signal components
Hill, Paul; Achim, Alin; Al-Mualla, Mohammed Ebrahim; Bull, David
2016-04-11
Accurate estimation of the contrast sensitivity of the human visual system is crucial for perceptually based image processing in applications such as compression, fusion and denoising. Conventional Contrast Sensitivity Functions (CSFs) have been obtained using fixed sized Gabor functions. However, the basis functions of multiresolution decompositions such as wavelets often resemble Gabor functions but are of variable size and shape. Therefore to use conventional contrast sensitivity functions in such cases is not appropriate. We have therefore conducted a set of psychophysical tests in order to obtain the contrast sensitivity function for a range of multiresolution transforms: the Discrete Wavelet Transform (DWT), the Steerable Pyramid, the Dual-Tree Complex Wavelet Transform (DT-CWT) and the Curvelet Transform. These measures were obtained using contrast variation of each transforms' basis functions in a 2AFC experiment combined with an adapted version of the QUEST psychometric function method. The results enable future image processing applications that exploit these transforms such as signal fusion, super-resolution processing, denoising and motion estimation, to be perceptually optimised in a principled fashion. The results are compared to an existing vision model (HDR-VDP2) and are used to show quantitative improvements within a denoising application compared to using conventional CSF values.
The wavelet/scalar quantization compression standard for digital fingerprint images
Bradley, J.N.; Brislawn, C.M.
1994-04-01
A new digital image compression standard has been adopted by the US Federal Bureau of Investigation for use on digitized gray-scale fingerprint images. The algorithm is based on adaptive uniform scalar quantization of a discrete wavelet transform image decomposition and is referred to as the wavelet/scalar quantization standard. The standard produces archival quality images at compression ratios of around 20:1 and will allow the FBI to replace their current database of paper fingerprint cards with digital imagery.
Investigating the Impact of Explicit Collocation Instruction on ESL Learners' Writing Ability
ERIC Educational Resources Information Center
Adhami-O'Brian, Soolmaz
2014-01-01
The present study was conducted to explore the impact of explicit collocation instruction on the ESL learners' writing ability. Furthermore, this study was an attempt to find if there is any significant difference between male and female learners on their use of collocations in writing tasks. In so doing, 63 advanced English as a Second Language…
Corpora and Collocations in Chinese-English Dictionaries for Chinese Users
ERIC Educational Resources Information Center
Xia, Lixin
2015-01-01
The paper identifies the major problems of the Chinese-English dictionary in representing collocational information after an extensive survey of nine dictionaries popular among Chinese users. It is found that the Chinese-English dictionary only provides the collocation types of "v+n" and "v+n," but completely ignores those of…
English Collocation Learning through Corpus Data: On-Line Concordance and Statistical Information
ERIC Educational Resources Information Center
Ohtake, Hiroshi; Fujita, Nobuyuki; Kawamoto, Takeshi; Morren, Brian; Ugawa, Yoshihiro; Kaneko, Shuji
2012-01-01
We developed an English Collocations On Demand system offering on-line corpus and concordance information to help Japanese researchers acquire a better command of English collocation patterns. The Life Science Dictionary Corpus consists of approximately 90,000,000 words collected from life science related research papers published in academic…
Study on the Causes and Countermeasures of the Lexical Collocation Mistakes in College English
ERIC Educational Resources Information Center
Yan, Hansheng
2010-01-01
The lexical collocation in English is an important content in the linguistics theory, and also a research topic which is more and more emphasized in English teaching practice of China. The collocation ability of English decides whether learners could masterly use real English in effective communication. In many years' English teaching practice,…
Triple collocation: beyond three estimates and separation of structural/non-structural errors
Technology Transfer Automated Retrieval System (TEKTRAN)
This study extends the popular triple collocation method for error assessment from three source estimates to an arbitrary number of source estimates, i.e., to solve the “multiple” collocation problem. The error assessment problem is solved through Pythagorean constraints in Hilbert space, which is s...
Symmetrical and Asymmetrical Scaffolding of L2 Collocations in the Context of Concordancing
ERIC Educational Resources Information Center
Rezaee, Abbas Ali; Marefat, Hamideh; Saeedakhtar, Afsaneh
2015-01-01
Collocational competence is recognized to be integral to native-like L2 performance, and concordancing can be of assistance in gaining this competence. This study reports on an investigation into the effect of symmetrical and asymmetrical scaffolding on the collocational competence of Iranian intermediate learners of English in the context of…
Going beyond Patterns: Involving Cognitive Analysis in the Learning of Collocations
ERIC Educational Resources Information Center
Liu, Dilin
2010-01-01
Since the late 1980s, collocations have received increasing attention in applied linguistics, especially language teaching, as is evidenced by the many publications on the topic. These works fall roughly into two lines of research (a) those focusing on the identification and use of collocations (Benson, 1989; Hunston, 2002; Hunston & Francis,…
Birdsong Denoising Using Wavelets
Priyadarshani, Nirosha; Marsland, Stephen; Castro, Isabel; Punchihewa, Amal
2016-01-01
Automatic recording of birdsong is becoming the preferred way to monitor and quantify bird populations worldwide. Programmable recorders allow recordings to be obtained at all times of day and year for extended periods of time. Consequently, there is a critical need for robust automated birdsong recognition. One prominent obstacle to achieving this is low signal to noise ratio in unattended recordings. Field recordings are often very noisy: birdsong is only one component in a recording, which also includes noise from the environment (such as wind and rain), other animals (including insects), and human-related activities, as well as noise from the recorder itself. We describe a method of denoising using a combination of the wavelet packet decomposition and band-pass or low-pass filtering, and present experiments that demonstrate an order of magnitude improvement in noise reduction over natural noisy bird recordings. PMID:26812391
Wavelet theory and its applications
Faber, V.; Bradley, JJ.; Brislawn, C.; Dougherty, R.; Hawrylycz, M.
1996-07-01
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). We investigated the theory of wavelet transforms and their relation to Laboratory applications. The investigators have had considerable success in the past applying wavelet techniques to the numerical solution of optimal control problems for distributed- parameter systems, nonlinear signal estimation, and compression of digital imagery and multidimensional data. Wavelet theory involves ideas from the fields of harmonic analysis, numerical linear algebra, digital signal processing, approximation theory, and numerical analysis, and the new computational tools arising from wavelet theory are proving to be ideal for many Laboratory applications. 10 refs.
Wavelet entropy of stochastic processes
NASA Astrophysics Data System (ADS)
Zunino, L.; Pérez, D. G.; Garavaglia, M.; Rosso, O. A.
2007-06-01
We compare two different definitions for the wavelet entropy associated to stochastic processes. The first one, the normalized total wavelet entropy (NTWS) family [S. Blanco, A. Figliola, R.Q. Quiroga, O.A. Rosso, E. Serrano, Time-frequency analysis of electroencephalogram series, III. Wavelet packets and information cost function, Phys. Rev. E 57 (1998) 932-940; O.A. Rosso, S. Blanco, J. Yordanova, V. Kolev, A. Figliola, M. Schürmann, E. Başar, Wavelet entropy: a new tool for analysis of short duration brain electrical signals, J. Neurosci. Method 105 (2001) 65-75] and a second introduced by Tavares and Lucena [Physica A 357(1) (2005) 71-78]. In order to understand their advantages and disadvantages, exact results obtained for fractional Gaussian noise ( -1<α< 1) and fractional Brownian motion ( 1<α< 3) are assessed. We find out that the NTWS family performs better as a characterization method for these stochastic processes.
Wavelet Analysis of Protein Motion
BENSON, NOAH C.
2014-01-01
As high-throughput molecular dynamics simulations of proteins become more common and the databases housing the results become larger and more prevalent, more sophisticated methods to quickly and accurately mine large numbers of trajectories for relevant information will have to be developed. One such method, which is only recently gaining popularity in molecular biology, is the continuous wavelet transform, which is especially well-suited for time course data such as molecular dynamics simulations. We describe techniques for the calculation and analysis of wavelet transforms of molecular dynamics trajectories in detail and present examples of how these techniques can be useful in data mining. We demonstrate that wavelets are sensitive to structural rearrangements in proteins and that they can be used to quickly detect physically relevant events. Finally, as an example of the use of this approach, we show how wavelet data mining has led to a novel hypothesis related to the mechanism of the protein γδ resolvase. PMID:25484480
A new fractional wavelet transform
NASA Astrophysics Data System (ADS)
Dai, Hongzhe; Zheng, Zhibao; Wang, Wei
2017-03-01
The fractional Fourier transform (FRFT) is a potent tool to analyze the time-varying signal. However, it fails in locating the fractional Fourier domain (FRFD)-frequency contents which is required in some applications. A novel fractional wavelet transform (FRWT) is proposed to solve this problem. It displays the time and FRFD-frequency information jointly in the time-FRFD-frequency plane. The definition, basic properties, inverse transform and reproducing kernel of the proposed FRWT are considered. It has been shown that an FRWT with proper order corresponds to the classical wavelet transform (WT). The multiresolution analysis (MRA) associated with the developed FRWT, together with the construction of the orthogonal fractional wavelets are also presented. Three applications are discussed: the analysis of signal with time-varying frequency content, the FRFD spectrum estimation of signals that involving noise, and the construction of fractional Harr wavelet. Simulations verify the validity of the proposed FRWT.
A wavelet phase filter for emission tomography
Olsen, E.T.; Lin, B.
1995-07-01
The presence of a high level of noise is a characteristic in some tomographic imaging techniques such as positron emission tomography (PET). Wavelet methods can smooth out noise while preserving significant features of images. Mallat et al. proposed a wavelet based denoising scheme exploiting wavelet modulus maxima, but the scheme is sensitive to noise. In this study, the authors explore the properties of wavelet phase, with a focus on reconstruction of emission tomography images. Specifically, they show that the wavelet phase of regular Poisson noise under a Haar-type wavelet transform converges in distribution to a random variable uniformly distributed on [0, 2{pi}). They then propose three wavelet-phase-based denoising schemes which exploit this property: edge tracking, local phase variance thresholding, and scale phase variation thresholding. Some numerical results are also presented. The numerical experiments indicate that wavelet phase techniques show promise for wavelet based denoising methods.
Optical HAAR Wavelet Transforms using Computer Generated Holography
1992-12-17
This research introduces an optical implementation of the continuous wavelet transform to filter images. The wavelet transform is modeled as a...continuous wavelet transform was performed and that the results compared favorably to digital simulation. Wavelets, Holography, Optical correlators.
Collocation methods for index 1 DAEs with a singularity of the first kind
NASA Astrophysics Data System (ADS)
Koch, Othmar; Maerz, Roswitha; Praetorius, Dirk; Weinmueller, Ewa
2010-01-01
We study the convergence behavior of collocation schemes applied to approximate solutions of BVPs in linear index 1 DAEs which exhibit a critical point at the left boundary. Such a critical point of the DAE causes a singularity within the inherent ODE system. We focus our attention on the case when the inherent ODE system is singular with a singularity of the first kind, apply polynomial collocation to the original DAE system and consider different choices of the collocation points such as equidistant, Gaussian or Radau points. We show that for a well-posed boundary value problem for DAEs having a sufficiently smooth solution, the global error of the collocation scheme converges with the order O(h^s) , where s is the number of collocation points. Superconvergence cannot be expected in general due to the singularity, not even for the differential components of the solution. The theoretical results are illustrated by numerical experiments.
Heart Disease Detection Using Wavelets
NASA Astrophysics Data System (ADS)
González S., A.; Acosta P., J. L.; Sandoval M., M.
2004-09-01
We develop a wavelet based method to obtain standardized gray-scale chart of both healthy hearts and of hearts suffering left ventricular hypertrophy. The hypothesis that early bad functioning of heart can be detected must be tested by comparing the wavelet analysis of the corresponding ECD with the limit cases. Several important parameters shall be taken into account such as age, sex and electrolytic changes.
Wavelet transform for real-time detection of action potentials in neural signals.
Quotb, Adam; Bornat, Yannick; Renaud, Sylvie
2011-01-01
We present a study on wavelet detection methods of neuronal action potentials (APs). Our final goal is to implement the selected algorithms on custom integrated electronics for on-line processing of neural signals; therefore we take real-time computing as a hard specification and silicon area as a price to pay. Using simulated neural signals including APs, we characterize an efficient wavelet method for AP extraction by evaluating its detection rate and its implementation cost. We compare software implementation for three methods: adaptive threshold, discrete wavelet transform (DWT), and stationary wavelet transform (SWT). We evaluate detection rate and implementation cost for detection functions dynamically comparing a signal with an adaptive threshold proportional to its SD, where the signal is the raw neural signal, respectively: (i) non-processed; (ii) processed by a DWT; (iii) processed by a SWT. We also use different mother wavelets and test different data formats to set an optimal compromise between accuracy and silicon cost. Detection accuracy is evaluated together with false negative and false positive detections. Simulation results show that for on-line AP detection implemented on a configurable digital integrated circuit, APs underneath the noise level can be detected using SWT with a well-selected mother wavelet, combined to an adaptive threshold.
Wavelets in the solution of the volume integral equation: Application to eddy current modeling
Wang, B.; Moulder, J.C.; Basart, J.P.
1997-05-01
There is growing interest in the applications of wavelets as basis functions in solutions of integral equations, especially in the area of electromagnetic field problems. In this article we apply a wavelet expansion to the solution of the three-dimensional eddy current modeling problem based on the volume integral method. Although this method shows promise for eddy current modeling of three-dimensional flaws, it is restricted by the computing power required to solve a large linear system. In this article we show that applying a wavelet basis to the volume integral method can dramatically reduce the size of the linear system to be solved. In our approach, the unknown total field is expressed as a twofold summation of shifted and dilated forms of a properly chosen basis function that is often referred to as the mother wavelet. The wavelet expansion can adaptively fit itself to the total field distribution by distributing the localized functions near the flaw boundary, where the field change is large, and the more spatially diffused functions over the interior of the flaw where the total field tends to be smooth. The approach is thus best suited to modeling large three-dimensional flaws where the large number of elements used in the volume integral method requires extremely large memory space and computational capacity. The feasibility of the wavelet method is discussed in the context of the physical nature of eddy-current modeling problems. Numerical examples using both Haar wavelets and Daubechies compactly supported wavelets with periodic extension are given. The results of the wavelet method are also compared with experimental results from a cylindrical flat-bottom hole in an aluminum plate. These numerical examples and comparisons indicate that the wavelet method can greatly reduce the numerical complexity of the problem with negligible loss in accuracy. {copyright} {ital 1997 American Institute of Physics.}
Wavelets in the solution of the volume integral equation: Application to eddy current modeling
NASA Astrophysics Data System (ADS)
Wang, Bing; Moulder, John C.; Basart, John P.
1997-05-01
There is growing interest in the applications of wavelets as basis functions in solutions of integral equations, especially in the area of electromagnetic field problems. In this article we apply a wavelet expansion to the solution of the three-dimensional eddy current modeling problem based on the volume integral method. Although this method shows promise for eddy current modeling of three-dimensional flaws, it is restricted by the computing power required to solve a large linear system. In this article we show that applying a wavelet basis to the volume integral method can dramatically reduce the size of the linear system to be solved. In our approach, the unknown total field is expressed as a twofold summation of shifted and dilated forms of a properly chosen basis function that is often referred to as the mother wavelet. The wavelet expansion can adaptively fit itself to the total field distribution by distributing the localized functions near the flaw boundary, where the field change is large, and the more spatially diffused functions over the interior of the flaw where the total field tends to be smooth. The approach is thus best suited to modeling large three-dimensional flaws where the large number of elements used in the volume integral method requires extremely large memory space and computational capacity. The feasibility of the wavelet method is discussed in the context of the physical nature of eddy-current modeling problems. Numerical examples using both Haar wavelets and Daubechies compactly supported wavelets with periodic extension are given. The results of the wavelet method are also compared with experimental results from a cylindrical flat-bottom hole in an aluminum plate. These numerical examples and comparisons indicate that the wavelet method can greatly reduce the numerical complexity of the problem with negligible loss in accuracy.
A frequency dependent preconditioned wavelet method for atmospheric tomography
NASA Astrophysics Data System (ADS)
Yudytskiy, Mykhaylo; Helin, Tapio; Ramlau, Ronny
2013-12-01
Atmospheric tomography, i.e. the reconstruction of the turbulence in the atmosphere, is a main task for the adaptive optics systems of the next generation telescopes. For extremely large telescopes, such as the European Extremely Large Telescope, this problem becomes overly complex and an efficient algorithm is needed to reduce numerical costs. Recently, a conjugate gradient method based on wavelet parametrization of turbulence layers was introduced [5]. An iterative algorithm can only be numerically efficient when the number of iterations required for a sufficient reconstruction is low. A way to achieve this is to design an efficient preconditioner. In this paper we propose a new frequency-dependent preconditioner for the wavelet method. In the context of a multi conjugate adaptive optics (MCAO) system simulated on the official end-to-end simulation tool OCTOPUS of the European Southern Observatory we demonstrate robustness and speed of the preconditioned algorithm. We show that three iterations are sufficient for a good reconstruction.
A wavelet watermarking algorithm based on a tree structure
NASA Astrophysics Data System (ADS)
Guitart Pla, Oriol; Lin, Eugene T.; Delp, Edward J., III
2004-06-01
We describe a blind watermarking technique for digital images. Our technique constructs an image-dependent watermark in the discrete wavelet transform (DWT) domain and inserts the watermark in the most signifcant coefficients of the image. The watermarked coefficients are determined by using the hierarchical tree structure induced by the DWT, similar in concept to embedded zerotree wavelet (EZW) compression. If the watermarked image is attacked or manipulated such that the set of significant coefficients is changed, the tree structure allows the correlation-based watermark detector to recover synchronization. Our technique also uses a visual adaptive scheme to insert the watermark to minimize watermark perceptibility. The visual adaptive scheme also takes advantage of the tree structure. Finally, a template is inserted into the watermark to provide robustness against geometric attacks. The template detection uses the cross-ratio of four collinear points.
The chain collocation method: A spectrally accurate calculus of forms
NASA Astrophysics Data System (ADS)
Rufat, Dzhelil; Mason, Gemma; Mullen, Patrick; Desbrun, Mathieu
2014-01-01
Preserving in the discrete realm the underlying geometric, topological, and algebraic structures at stake in partial differential equations has proven to be a fruitful guiding principle for numerical methods in a variety of fields such as elasticity, electromagnetism, or fluid mechanics. However, structure-preserving methods have traditionally used spaces of piecewise polynomial basis functions for differential forms. Yet, in many problems where solutions are smoothly varying in space, a spectral numerical treatment is called for. In an effort to provide structure-preserving numerical tools with spectral accuracy on logically rectangular grids over periodic or bounded domains, we present a spectral extension of the discrete exterior calculus (DEC), with resulting computational tools extending well-known collocation-based spectral methods. Its efficient implementation using fast Fourier transforms is provided as well.
Optimization of Low-Thrust Spiral Trajectories by Collocation
NASA Technical Reports Server (NTRS)
Falck, Robert D.; Dankanich, John W.
2012-01-01
As NASA examines potential missions in the post space shuttle era, there has been a renewed interest in low-thrust electric propulsion for both crewed and uncrewed missions. While much progress has been made in the field of software for the optimization of low-thrust trajectories, many of the tools utilize higher-fidelity methods which, while excellent, result in extremely high run-times and poor convergence when dealing with planetocentric spiraling trajectories deep within a gravity well. Conversely, faster tools like SEPSPOT provide a reasonable solution but typically fail to account for other forces such as third-body gravitation, aerodynamic drag, solar radiation pressure. SEPSPOT is further constrained by its solution method, which may require a very good guess to yield a converged optimal solution. Here the authors have developed an approach using collocation intended to provide solution times comparable to those given by SEPSPOT while allowing for greater robustness and extensible force models.
Robust Stabilizing Compensators for Flexible Structures with Collocated Controls
NASA Technical Reports Server (NTRS)
Balakrishman, A. V.
1996-01-01
For flexible structures with collocated rate and attitude sensors/actuators, we characterize compensator transfer functions which guarantee modal stability even when stiffness/inertia parameters are uncertain. While the compensators are finite-dimensional, the structure models are allowed to be infinite-dimensional (continuum models), with attendant complexity of the notion of stability; thus exponential stability is not possible and the best we can obtain is strong stability. Robustness is interpreted essentially as maintaining stability in the worst case. The conditions require that the compensator transfer functions be positive real and use is made of the Kalman-Yakubovic lemma to characterize them further. The concept of positive realness is shown to be equivalent to dissipativity in infinite dimensions. In particular we show that for a subclass of compensators it is possible to make the system strongly stable as well as dissipative in an appropriate energy norm.
A Jacobi collocation approximation for nonlinear coupled viscous Burgers' equation
NASA Astrophysics Data System (ADS)
Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohamed A.; Hafez, Ramy M.
2014-02-01
This article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers' equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nyström (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers' equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.
Local validation of EU-DEM using Least Squares Collocation
NASA Astrophysics Data System (ADS)
Ampatzidis, Dimitrios; Mouratidis, Antonios; Gruber, Christian; Kampouris, Vassilios
2016-04-01
In the present study we are dealing with the evaluation of the European Digital Elevation Model (EU-DEM) in a limited area, covering few kilometers. We compare EU-DEM derived vertical information against orthometric heights obtained by classical trigonometric leveling for an area located in Northern Greece. We apply several statistical tests and we initially fit a surface model, in order to quantify the existing biases and outliers. Finally, we implement a methodology for orthometric heights prognosis, using the Least Squares Collocation for the remaining residuals of the first step (after the fitted surface application). Our results, taking into account cross validation points, reveal a local consistency between EU-DEM and official heights, which is better than 1.4 meters.
Robustness properties of LQG optimized compensators for collocated rate sensors
NASA Technical Reports Server (NTRS)
Balakrishnan, A. V.
1994-01-01
In this paper we study the robustness with respect to stability of the closed-loop system with collocated rate sensor using LQG (mean square rate) optimized compensators. Our main result is that the transmission zeros of the compensator are precisely the structure modes when the actuator/sensor locations are 'pinned' and/or 'clamped': i.e., motion in the direction sensed is not allowed. We have stability even under parameter mismatch, except in the unlikely situation where such a mode frequency of the assumed system coincides with an undamped mode frequency of the real system and the corresponding mode shape is an eigenvector of the compensator transfer function matrix at that frequency. For a truncated modal model - such as that of the NASA LaRC Phase Zero Evolutionary model - the transmission zeros of the corresponding compensator transfer function can be interpreted as the structure modes when motion in the directions sensed is prohibited.
The Rocchio classifier and second generation wavelets
NASA Astrophysics Data System (ADS)
Carter, Patricia H.
2007-04-01
Classification and characterization of text is of ever growing importance in defense and national security. The text classification task is an instance of classification using sparse features residing in a high dimensional feature space. Two standard (of a wide selection of available) algorithms for this task are the naive Bayes classifier and the Rocchio linear classifier. Naive Bayes classifiers are widely applied; the Rocchio algorithm is primarily used in document classification and information retrieval. Both these classifiers are popular because of their simplicity and ease of application, computational speed and reasonable performance. One aspect of the Rocchio approach, inherited from its information retrieval origin, is that it explicitly uses both positive and negative models. Parameters have been introduced which make it adaptive to the particulars of the corpora of interest and thereby improve its performance. The ideas inherent in these classifiers and in second generation wavelets can be recombined into new algorithms for classification. An example is a classifier using second generation wavelet-like functions for class probes that mimic the Rocchio positive template - negative template approach.
Improved Compression of Wavelet-Transformed Images
NASA Technical Reports Server (NTRS)
Kiely, Aaron; Klimesh, Matthew
2005-01-01
A recently developed data-compression method is an adaptive technique for coding quantized wavelet-transformed data, nominally as part of a complete image-data compressor. Unlike some other approaches, this method admits a simple implementation and does not rely on the use of large code tables. A common data compression approach, particularly for images, is to perform a wavelet transform on the input data, and then losslessly compress a quantized version of the wavelet-transformed data. Under this compression approach, it is common for the quantized data to include long sequences, or runs, of zeros. The new coding method uses prefixfree codes for the nonnegative integers as part of an adaptive algorithm for compressing the quantized wavelet-transformed data by run-length coding. In the form of run-length coding used here, the data sequence to be encoded is parsed into strings consisting of some number (possibly 0) of zeros, followed by a nonzero value. The nonzero value and the length of the run of zeros are encoded. For a data stream that contains a sufficiently high frequency of zeros, this method is known to be more effective than using a single variable length code to encode each symbol. The specific prefix-free codes used are from two classes of variable-length codes: a class known as Golomb codes, and a class known as exponential-Golomb codes. The codes within each class are indexed by a single integer parameter. The present method uses exponential-Golomb codes for the lengths of the runs of zeros, and Golomb codes for the nonzero values. The code parameters within each code class are determined adaptively on the fly as compression proceeds, on the basis of statistics from previously encoded values. In particular, a simple adaptive method has been devised to select the parameter identifying the particular exponential-Golomb code to use. The method tracks the average number of bits used to encode recent runlengths, and takes the difference between this average
A wavelet-based statistical analysis of FMRI data: I. motivation and data distribution modeling.
Dinov, Ivo D; Boscardin, John W; Mega, Michael S; Sowell, Elizabeth L; Toga, Arthur W
2005-01-01
We propose a new method for statistical analysis of functional magnetic resonance imaging (fMRI) data. The discrete wavelet transformation is employed as a tool for efficient and robust signal representation. We use structural magnetic resonance imaging (MRI) and fMRI to empirically estimate the distribution of the wavelet coefficients of the data both across individuals and spatial locations. An anatomical subvolume probabilistic atlas is used to tessellate the structural and functional signals into smaller regions each of which is processed separately. A frequency-adaptive wavelet shrinkage scheme is employed to obtain essentially optimal estimations of the signals in the wavelet space. The empirical distributions of the signals on all the regions are computed in a compressed wavelet space. These are modeled by heavy-tail distributions because their histograms exhibit slower tail decay than the Gaussian. We discovered that the Cauchy, Bessel K Forms, and Pareto distributions provide the most accurate asymptotic models for the distribution of the wavelet coefficients of the data. Finally, we propose a new model for statistical analysis of functional MRI data using this atlas-based wavelet space representation. In the second part of our investigation, we will apply this technique to analyze a large fMRI dataset involving repeated presentation of sensory-motor response stimuli in young, elderly, and demented subjects.
Validation of significant wave height product from Envisat ASAR using triple collocation
NASA Astrophysics Data System (ADS)
Wang, H.; Shi, C. Y.; Zhu, J. H.; Huang, X. Q.; Chen, C. T.
2014-03-01
Nowadays, spaceborne Synthetic Aperture Radar (SAR) has become a powerful tool for providing significant wave height. Traditionally, validation of SAR derived ocean wave height has been carried out against buoy measurements or model outputs, which only yield a inter-comparison, but not an 'absolute' validation. In this study, the triple collocation error model has been introduced in the validation of Envisat ASAR level 2 data. Significant wave height data from ASAR were validated against in situ buoy data, and wave model hindcast results from WaveWatch III, covering a period of six years. The impact of the collocation distance on the error of ASAR wave height was discussed. From the triple collocation validation analysis, it is found that the error of Envisat ASAR significant wave height product is linear to the collocation distance, and decrease with the decreasing collocation distance. Using the linear regression fit method, the absolute error of Envisat ASAR wave height was obtained with zero collocation distance. The absolute Envisat ASAR wave height error of 0.49m is presented in deep and open ocean from this triple collocation validation work.
Wavelet Transforms using VTK-m
Li, Shaomeng; Sewell, Christopher Meyer
2016-09-27
These are a set of slides that deal with the topics of wavelet transforms using VTK-m. First, wavelets are discussed and detailed, then VTK-m is discussed and detailed, then wavelets and VTK-m are looked at from a performance comparison, then from an accuracy comparison, and finally lessons learned, conclusion, and what is next. Lessons learned are the following: Launching worklets is expensive; Natural logic of performing 2D wavelet transform: Repeat the same 1D wavelet transform on every row, repeat the same 1D wavelet transform on every column, invoke the 1D wavelet worklet every time: num_rows x num_columns; VTK-m approach of performing 2D wavelet transform: Create a worklet for 2D that handles both rows and columns, invoke this new worklet only one time; Fast calculation, but cannot reuse 1D implementations.
Edge Detection Using a Complex Wavelet
1993-12-01
A complex wavelet of the form Psi(x, y) = C(x jy)exp(-p(x-sq+y-sq))) is used in the continuous wavelet transform to obtain edges from a digital image...and x and y are position variables. The square root of the sum of the squares of the real and imaginary parts of the wavelet transform are used to...radar images and the resulting images are shown. Continuous wavelet transform , Digital image.
Steerable dyadic wavelet transform and interval wavelets for enhancement of digital mammography
NASA Astrophysics Data System (ADS)
Laine, Andrew F.; Koren, Iztok; Yang, Wuhai; Taylor, Fred J.
1995-04-01
This paper describes two approaches for accomplishing interactive feature analysis by overcomplete multiresolution representations. We show quantitatively that transform coefficients, modified by an adaptive non-linear operator, can make more obvious unseen or barely seen features of mammography without requiring additional radiation. Our results are compared with traditional image enhancement techniques by measuring the local contrast of known mammographic features. We design a filter bank representing a steerable dyadic wavelet transform that can be used for multiresolution analysis along arbitrary orientations. Digital mammograms are enhanced by orientation analysis performed by a steerable dyadic wavelet transform. Arbitrary regions of interest (ROI) are enhanced by Deslauriers-Dubuc interpolation representations on an interval. We demonstrate that our methods can provide radiologists with an interactive capability to support localized processing of selected (suspicion) areas (lesions). Features extracted from multiscale representations can provide an adaptive mechanism for accomplishing local contrast enhancement. By improving the visualization of breast pathology can improve changes of early detection while requiring less time to evaluate mammograms for most patients.
Wei, Hua-Liang; Billings, Stephen A; Zhao, Yifan; Guo, Lingzhong
2009-01-01
In this brief, by combining an efficient wavelet representation with a coupled map lattice model, a new family of adaptive wavelet neural networks, called lattice dynamical wavelet neural networks (LDWNNs), is introduced for spatio-temporal system identification. A new orthogonal projection pursuit (OPP) method, coupled with a particle swarm optimization (PSO) algorithm, is proposed for augmenting the proposed network. A novel two-stage hybrid training scheme is developed for constructing a parsimonious network model. In the first stage, by applying the OPP algorithm, significant wavelet neurons are adaptively and successively recruited into the network, where adjustable parameters of the associated wavelet neurons are optimized using a particle swarm optimizer. The resultant network model, obtained in the first stage, however, may be redundant. In the second stage, an orthogonal least squares algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet neurons from the network. An example for a real spatio-temporal system identification problem is presented to demonstrate the performance of the proposed new modeling framework.
NASA Astrophysics Data System (ADS)
Xiao, Cheng-Nian; Denner, Fabian; van Wachem, Berend
2015-11-01
A pressure-based Navier-Stokes solver which is applicable to fluid flow problems of a wide range of speeds is presented. The novel solver is based on collocated variable arrangement and uses a modified Rhie-Chow interpolation method to assure implicit pressure-velocity coupling. A Mach number biased modification to the continuity equation as well as coupling of flow and thermodynamic variables via an energy equation and equation of state enable the simulation of compressible flows belonging to transonic or supersonic Mach number regimes. The flow equation systems are all solved simultaneously, thus guaranteeing strong coupling between pressure and velocity at each iteration step. Shock-capturing is accomplished via nonlinear spatial discretisation schemes which adaptively apply an appropriate blending of first-order upwind and second-order central schemes depending on the local smoothness of the flow field. A selection of standard test problems will be presented to demonstrate the solver's capability of handling incompressible as well as compressible flow fields of vastly different speed regimes on structured as well as unstructured meshes. The authors are grateful for the financial support of Shell.
Wavelet-Based Multiresolution Analyses of Signals
1992-06-01
classification. Some signals, notably those of a transient nature, are inherently difficult to analyze with these traditional tools. The Discrete Wavelet Transform has...scales. This thesis investigates dyadic discrete wavelet decompositions of signals. A new multiphase wavelet transform is proposed and investigated. The
A multiresolution analysis for tensor-product splines using weighted spline wavelets
NASA Astrophysics Data System (ADS)
Kapl, Mario; Jüttler, Bert
2009-09-01
We construct biorthogonal spline wavelets for periodic splines which extend the notion of "lazy" wavelets for linear functions (where the wavelets are simply a subset of the scaling functions) to splines of higher degree. We then use the lifting scheme in order to improve the approximation properties with respect to a norm induced by a weighted inner product with a piecewise constant weight function. Using the lifted wavelets we define a multiresolution analysis of tensor-product spline functions and apply it to image compression of black-and-white images. By performing-as a model problem-image compression with black-and-white images, we demonstrate that the use of a weight function allows to adapt the norm to the specific problem.
Recent advances in wavelet technology
NASA Technical Reports Server (NTRS)
Wells, R. O., Jr.
1994-01-01
Wavelet research has been developing rapidly over the past five years, and in particular in the academic world there has been significant activity at numerous universities. In the industrial world, there has been developments at Aware, Inc., Lockheed, Martin-Marietta, TRW, Kodak, Exxon, and many others. The government agencies supporting wavelet research and development include ARPA, ONR, AFOSR, NASA, and many other agencies. The recent literature in the past five years includes a recent book which is an index of citations in the past decade on this subject, and it contains over 1,000 references and abstracts.
Image Segmentation Using Affine Wavelets
1991-12-12
Fourier Transform [23:677] ........ .. 3-15 3.6. Typical Wavelet Function and its Fourier Transform [23:577] ............ 3-16 3.7. Orientation of...Wavelet Decomposition Filters ii the Fourier Dcmain [14:65] 3-18 4.1. Datafiow- Diagram of the Wa’velet Decompossii ’n Proga, F.r..t cvc.. A -•A 4.2...global spatial relationships, as does a Fourier transforn."[l 1] The main thrust of Daugman’s article [11] was to show the utility of a neural network
Wavelet filtering of chaotic data
NASA Astrophysics Data System (ADS)
Grzesiak, M.
Satisfactory method of removing noise from experimental chaotic data is still an open problem. Normally it is necessary to assume certain properties of the noise and dynamics, which one wants to extract, from time series. The wavelet based method of denoising of time series originating from low-dimensional dynamical systems and polluted by the Gaussian white noise is considered. Its efficiency is investigated by comparing the correlation dimension of clean and noisy data generated for some well-known dynamical systems. The wavelet method is contrasted with the singular value decomposition (SVD) and finite impulse response (FIR) filter methods.
NASA Technical Reports Server (NTRS)
Eren, K.
1980-01-01
The mathematical background in spectral analysis as applied to geodetic applications is summarized. The resolution (cut-off frequency) of the GEOS 3 altimeter data is examined by determining the shortest wavelength (corresponding to the cut-off frequency) recoverable. The data from some 18 profiles are used. The total power (variance) in the sea surface topography with respect to the reference ellipsoid as well as with respect to the GEM-9 surface is computed. A fast inversion algorithm for matrices of simple and block Toeplitz matrices and its application to least squares collocation is explained. This algorithm yields a considerable gain in computer time and storage in comparison with conventional least squares collocation. Frequency domain least squares collocation techniques are also introduced and applied to estimating gravity anomalies from GEOS 3 altimeter data. These techniques substantially reduce the computer time and requirements in storage associated with the conventional least squares collocation. Numerical examples given demonstrate the efficiency and speed of these techniques.
Collocation Schemes for Nonlinear Index 1 DAEs with a Singular Point
NASA Astrophysics Data System (ADS)
Dick, A.; Koch, O.; März, R.; Weinmüller, E.
2011-09-01
We discuss the convergence behavior of collocation schemes applied to approximate solutions of BVPs in nonlinear index 1 DAEs, which exhibit a critical point at the left boundary. Such a critical point of the DAE causes a singularity in the inherent nonlinear ODE system. In particular, we focus on the case when the inherent ODE system is singular with a singularity of the first kind and apply polynomial collocation to the original DAE system. We show that for a certain class of well-posed boundary value problems in DAEs having a sufficiently smooth solution, the global error of the collocation scheme converges in the collocation points with the so-called stage order. The theoretical results are supported by numerical experiments.
NASA Technical Reports Server (NTRS)
Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H.
2013-01-01
Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations.
Denoising and robust nonlinear wavelet analysis
NASA Astrophysics Data System (ADS)
Bruce, Andrew G.; Donoho, David L.; Gao, Hong-Ye; Martin, R. D.
1994-03-01
In a series of papers, Donoho and Johnstone develop a powerful theory based on wavelets for extracting non-smooth signals from noisy data. Several nonlinear smoothing algorithms are presented which provide high performance for removing Gaussian noise from a wide range of spatially inhomogeneous signals. However, like other methods based on the linear wavelet transform, these algorithms are very sensitive to certain types of non-Gaussian noise, such as outliers. In this paper, we develop outlier resistant wavelet transforms. In these transforms, outliers and outlier patches are localized to just a few scales. By using the outlier resistant wavelet transform, we improve upon the Donoho and Johnstone nonlinear signal extraction methods. The outlier resistant wavelet algorithms are included with the 'S+WAVELETS' object-oriented toolkit for wavelet analysis.
Multi-element probabilistic collocation method in high dimensions
Foo, Jasmine; Karniadakis, George Em
2010-03-01
We combine multi-element polynomial chaos with analysis of variance (ANOVA) functional decomposition to enhance the convergence rate of polynomial chaos in high dimensions and in problems with low stochastic regularity. Specifically, we employ the multi-element probabilistic collocation method MEPCM and so we refer to the new method as MEPCM-A. We investigate the dependence of the convergence of MEPCM-A on two decomposition parameters, the polynomial order {mu} and the effective dimension {nu}, with {nu}<
An adaptive pseudospectral method for discontinuous problems
NASA Technical Reports Server (NTRS)
Augenbaum, Jeffrey M.
1988-01-01
The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given.
Image encoding with triangulation wavelets
NASA Astrophysics Data System (ADS)
Hebert, D. J.; Kim, HyungJun
1995-09-01
We demonstrate some wavelet-based image processing applications of a class of simplicial grids arising in finite element computations and computer graphics. The cells of a triangular grid form the set of leaves of a binary tree and the nodes of a directed graph consisting of a single cycle. The leaf cycle of a uniform grid forms a pattern for pixel image scanning and for coherent computation of coefficients of splines and wavelets. A simple form of image encoding is accomplished with a 1D quadrature mirror filter whose coefficients represent an expansion of the image in terms of 2D Haar wavelets with triangular support. A combination the leaf cycle and an inherent quadtree structure allow efficient neighbor finding, grid refinement, tree pruning and storage. Pruning of the simplex tree yields a partially compressed image which requires no decoding, but rather may be rendered as a shaded triangulation. This structure and its generalization to n-dimensions form a convenient setting for wavelet analysis and computations based on simplicial grids.
Wavelet/scalar quantization compression standard for fingerprint images
Brislawn, C.M.
1996-06-12
US Federal Bureau of Investigation (FBI) has recently formulated a national standard for digitization and compression of gray-scale fingerprint images. Fingerprints are scanned at a spatial resolution of 500 dots per inch, with 8 bits of gray-scale resolution. The compression algorithm for the resulting digital images is based on adaptive uniform scalar quantization of a discrete wavelet transform subband decomposition (wavelet/scalar quantization method). The FBI standard produces archival-quality images at compression ratios of around 15 to 1 and will allow the current database of paper fingerprint cards to be replaced by digital imagery. The compression standard specifies a class of potential encoders and a universal decoder with sufficient generality to reconstruct compressed images produced by any compliant encoder, allowing flexibility for future improvements in encoder technology. A compliance testing program is also being implemented to ensure high standards of image quality and interchangeability of data between different implementations.
Three-dimensional image compression with integer wavelet transforms.
Bilgin, A; Zweig, G; Marcellin, M W
2000-04-10
A three-dimensional (3-D) image-compression algorithm based on integer wavelet transforms and zerotree coding is presented. The embedded coding of zerotrees of wavelet coefficients (EZW) algorithm is extended to three dimensions, and context-based adaptive arithmetic coding is used to improve its performance. The resultant algorithm, 3-D CB-EZW, efficiently encodes 3-D image data by the exploitation of the dependencies in all dimensions, while enabling lossy and lossless decompression from the same bit stream. Compared with the best available two-dimensional lossless compression techniques, the 3-D CB-EZW algorithm produced averages of 22%, 25%, and 20% decreases in compressed file sizes for computed tomography, magnetic resonance, and Airborne Visible Infrared Imaging Spectrometer images, respectively. The progressive performance of the algorithm is also compared with other lossy progressive-coding algorithms.
Wavelet-based zerotree coding of aerospace images
NASA Astrophysics Data System (ADS)
Franques, Victoria T.; Jain, Vijay K.
1996-06-01
This paper presents a wavelet based image coding method achieving high levels of compression. A multi-resolution subband decomposition system is constructed using Quadrature Mirror Filters. Symmetric extension and windowing of the multi-scaled subbands are incorporated to minimize the boundary effects. Next, the Embedded Zerotree Wavelet coding algorithm is used for data compression method. Elimination of the isolated zero symbol, for certain subbands, leads to an improved EZW algorithm. Further compression is obtained with an adaptive arithmetic coder. We achieve a PSNR of 26.91 dB at a bit rate of 0.018, 35.59 dB at a bit rate of 0.149, and 43.05 dB at 0.892 bits/pixel for the aerospace image, Refuel.
Three-Dimensional Image Compression With Integer Wavelet Transforms
NASA Astrophysics Data System (ADS)
Bilgin, Ali; Zweig, George; Marcellin, Michael W.
2000-04-01
A three-dimensional (3-D) image-compression algorithm based on integer wavelet transforms and zerotree coding is presented. The embedded coding of zerotrees of wavelet coefficients (EZW) algorithm is extended to three dimensions, and context-based adaptive arithmetic coding is used to improve its performance. The resultant algorithm, 3-D CB-EZW, efficiently encodes 3-D image data by the exploitation of the dependencies in all dimensions, while enabling lossy and lossless decompression from the same bit stream. Compared with the best available two-dimensional lossless compression techniques, the 3-D CB-EZW algorithm produced averages of 22%, 25%, and 20% decreases in compressed file sizes for computed tomography, magnetic resonance, and Airborne Visible Infrared Imaging Spectrometer images, respectively. The progressive performance of the algorithm is also compared with other lossy progressive-coding algorithms.
Medical image compression algorithm based on wavelet transform
NASA Astrophysics Data System (ADS)
Chen, Minghong; Zhang, Guoping; Wan, Wei; Liu, Minmin
2005-02-01
With rapid development of electronic imaging and multimedia technology, the telemedicine is applied to modern medical servings in the hospital. Digital medical image is characterized by high resolution, high precision and vast data. The optimized compression algorithm can alleviate restriction in the transmission speed and data storage. This paper describes the characteristics of human vision system based on the physiology structure, and analyses the characteristics of medical image in the telemedicine, then it brings forward an optimized compression algorithm based on wavelet zerotree. After the image is smoothed, it is decomposed with the haar filters. Then the wavelet coefficients are quantified adaptively. Therefore, we can maximize efficiency of compression and achieve better subjective visual image. This algorithm can be applied to image transmission in the telemedicine. In the end, we examined the feasibility of this algorithm with an image transmission experiment in the network.
NASA Astrophysics Data System (ADS)
Stevens, D.; Power, H.; Meng, C. Y.; Howard, D.; Cliffe, K. A.
2013-12-01
This work proposes an alternative decomposition for local scalable meshless RBF collocation. The proposed method operates on a dataset of scattered nodes that are placed within the solution domain and on the solution boundary, forming a small RBF collocation system around each internal node. Unlike other meshless local RBF formulations that are based on a generalised finite difference (RBF-FD) principle, in the proposed "finite collocation" method the solution of the PDE is driven entirely by collocation of PDE governing and boundary operators within the local systems. A sparse global collocation system is obtained not by enforcing the PDE governing operator, but by assembling the value of the field variable in terms of the field value at neighbouring nodes. In analogy to full-domain RBF collocation systems, communication between stencils occurs only over the stencil periphery, allowing the PDE governing operator to be collocated in an uninterrupted manner within the stencil interior. The local collocation of the PDE governing operator allows the method to operate on centred stencils in the presence of strong convective fields; the reconstruction weights assigned to nodes in the stencils being automatically adjusted to represent the flow of information as dictated by the problem physics. This "implicit upwinding" effect mitigates the need for ad-hoc upwinding stencils in convective dominant problems. Boundary conditions are also enforced within the local collocation systems, allowing arbitrary boundary operators to be imposed naturally within the solution construction. The performance of the method is assessed using a large number of numerical examples with two steady PDEs; the convection-diffusion equation, and the Lamé-Navier equations for linear elasticity. The method exhibits high-order convergence in each case tested (greater than sixth order), and the use of centred stencils is demonstrated for convective-dominant problems. In the case of linear elasticity
NASA Astrophysics Data System (ADS)
Chai, Bing-Bing; Vass, Jozsef; Zhuang, Xinhua
1997-04-01
Recent success in wavelet coding is mainly attributed to the recognition of importance of data organization. There has been several very competitive wavelet codecs developed, namely, Shapiro's Embedded Zerotree Wavelets (EZW), Servetto et. al.'s Morphological Representation of Wavelet Data (MRWD), and Said and Pearlman's Set Partitioning in Hierarchical Trees (SPIHT). In this paper, we propose a new image compression algorithm called Significant-Linked Connected Component Analysis (SLCCA) of wavelet coefficients. SLCCA exploits both within-subband clustering of significant coefficients and cross-subband dependency in significant fields. A so-called significant link between connected components is designed to reduce the positional overhead of MRWD. In addition, the significant coefficients' magnitude are encoded in bit plane order to match the probability model of the adaptive arithmetic coder. Experiments show that SLCCA outperforms both EZW and MRWD, and is tied with SPIHT. Furthermore, it is observed that SLCCA generally has the best performance on images with large portion of texture. When applied to fingerprint image compression, it outperforms FBI's wavelet scalar quantization by about 1 dB.
Portal imaging: Performance improvement in noise reduction by means of wavelet processing.
González-López, Antonio; Morales-Sánchez, Juan; Larrey-Ruiz, Jorge; Bastida-Jumilla, María-Consuelo; Verdú-Monedero, Rafael
2016-01-01
This paper discusses the suitability, in terms of noise reduction, of various methods which can be applied to an image type often used in radiation therapy: the portal image. Among these methods, the analysis focuses on those operating in the wavelet domain. Wavelet-based methods tested on natural images--such as the thresholding of the wavelet coefficients, the minimization of the Stein unbiased risk estimator on a linear expansion of thresholds (SURE-LET), and the Bayes least-squares method using as a prior a Gaussian scale mixture (BLS-GSM method)--are compared with other methods that operate on the image domain--an adaptive Wiener filter and a nonlocal mean filter (NLM). For the assessment of the performance, the peak signal-to-noise ratio (PSNR), the structural similarity index (SSIM), the Pearson correlation coefficient, and the Spearman rank correlation (ρ) coefficient are used. The performance of the wavelet filters and the NLM method are similar, but wavelet filters outperform the Wiener filter in terms of portal image denoising. It is shown how BLS-GSM and NLM filters produce the smoothest image, while keeping soft-tissue and bone contrast. As for the computational cost, filters using a decimated wavelet transform (decimated thresholding and SURE-LET) turn out to be the most efficient, with calculation times around 1 s.
NASA Astrophysics Data System (ADS)
Ji, Yanju; Li, Dongsheng; Yuan, Guiyang; Lin, Jun; Du, Shangyu; Xie, Lijun; Wang, Yuan
2016-06-01
A denoising method based on wavelet analysis is presented for the removal of noise (background noise and random spike) from time domain electromagnetic (TEM) data. This method includes two signal processing technologies: wavelet threshold method and stationary wavelet transform. First, wavelet threshold method is used for the removal of background noise from TEM data. Then, the data are divided into a series of details and approximations by using stationary wavelet transform. The random spike in details is identified by zero reference data and adaptive energy detector. Next, the corresponding details are processed to suppress the random spike. The denoised TEM data are reconstructed via inverse stationary wavelet transform using the processed details at each level and the approximations at the highest level. The proposed method has been verified using a synthetic TEM data, the signal-to-noise ratio of synthetic TEM data is increased from 10.97 dB to 24.37 dB at last. This method is also applied to the noise suppression of the field data which were collected at Hengsha island, China. The section image results shown that the noise is suppressed effectively and the resolution of the deep anomaly is obviously improved.
Design Methodology of a New Wavelet Basis Function for Fetal Phonocardiographic Signals
Chourasia, Vijay S.; Tiwari, Anil Kumar
2013-01-01
Fetal phonocardiography (fPCG) based antenatal care system is economical and has a potential to use for long-term monitoring due to noninvasive nature of the system. The main limitation of this technique is that noise gets superimposed on the useful signal during its acquisition and transmission. Conventional filtering may result into loss of valuable diagnostic information from these signals. This calls for a robust, versatile, and adaptable denoising method applicable in different operative circumstances. In this work, a novel algorithm based on wavelet transform has been developed for denoising of fPCG signals. Successful implementation of wavelet theory in denoising is heavily dependent on selection of suitable wavelet basis function. This work introduces a new mother wavelet basis function for denoising of fPCG signals. The performance of newly developed wavelet is found to be better when compared with the existing wavelets. For this purpose, a two-channel filter bank, based on characteristics of fPCG signal, is designed. The resultant denoised fPCG signals retain the important diagnostic information contained in the original fPCG signal. PMID:23766693
Optical wavelet transform for fingerprint identification
NASA Astrophysics Data System (ADS)
MacDonald, Robert P.; Rogers, Steven K.; Burns, Thomas J.; Fielding, Kenneth H.; Warhola, Gregory T.; Ruck, Dennis W.
1994-03-01
The Federal Bureau of Investigation (FBI) has recently sanctioned a wavelet fingerprint image compression algorithm developed for reducing storage requirements of digitized fingerprints. This research implements an optical wavelet transform of a fingerprint image, as the first step in an optical fingerprint identification process. Wavelet filters are created from computer- generated holograms of biorthogonal wavelets, the same wavelets implemented in the FBI algorithm. Using a detour phase holographic technique, a complex binary filter mask is created with both symmetry and linear phase. The wavelet transform is implemented with continuous shift using an optical correlation between binarized fingerprints written on a Magneto-Optic Spatial Light Modulator and the biorthogonal wavelet filters. A telescopic lens combination scales the transformed fingerprint onto the filters, providing a means of adjusting the biorthogonal wavelet filter dilation continuously. The wavelet transformed fingerprint is then applied to an optical fingerprint identification process. Comparison between normal fingerprints and wavelet transformed fingerprints shows improvement in the optical identification process, in terms of rotational invariance.
A kurtosis-based wavelet algorithm for motion artifact correction of fNIRS data
Chiarelli, Antonio M.; Maclin, Edward L.; Fabiani, Monica; Gratton, Gabriele
2015-01-01
Movements are a major source of artifacts in functional Near-Infrared Spectroscopy (fNIRS). Several algorithms have been developed for motion artifact correction of fNIRS data, including Principal Component Analysis (PCA), targeted Principal Component Analysis (tPCA), Spline Interpolation (SI), and Wavelet Filtering (WF). WF is based on removing wavelets with coefficients deemed to be outliers based on their standardized scores, and it has proven to be effective on both synthetized and real data. However, when the SNR is high, it can lead to a reduction of signal amplitude. This may occur because standardized scores inherently adapt to the noise level, independently of the shape of the distribution of the wavelet coefficients. Higher-order moments of the wavelet coefficient distribution may provide a more diagnostic index of wavelet distribution abnormality than its variance. Here we introduce a new procedure that relies on eliminating wavelets that contribute to generate a large fourth-moment (i.e., kurtosis) of the coefficient distribution to define “outliers” wavelets (kurtosis-based Wavelet Filtering, kbWF). We tested kbWF by comparing it with other existing procedures, using simulated functional hemodynamic responses added to real resting-state fNIRS recordings. These simulations show that kbWF is highly effective in eliminating transient noise, yielding results with higher SNR than other existing methods over a wide range of signal and noise amplitudes. This is because: (1) the procedure is iterative; and (2) kurtosis is more diagnostic than variance in identifying outliers. However, kbWF does not eliminate slow components of artifacts whose duration is comparable to the total recording time. PMID:25747916
Optical Wavelet Signals Processing and Multiplexing
NASA Astrophysics Data System (ADS)
Cincotti, Gabriella; Moreolo, Michela Svaluto; Neri, Alessandro
2005-12-01
We present compact integrable architectures to perform the discrete wavelet transform (DWT) and the wavelet packet (WP) decomposition of an optical digital signal, and we show that the combined use of planar lightwave circuits (PLC) technology and multiresolution analysis (MRA) can add flexibility to current multiple access optical networks. We furnish the design guidelines to synthesize wavelet filters as two-port lattice-form planar devices, and we give some examples of optical signal denoising and compression/decompression techniques in the wavelet domain. Finally, we present a fully optical wavelet packet division multiplexing (WPDM) scheme where data signals are waveform-coded onto wavelet atom functions for transmission, and numerically evaluate its performances.
Wavelet analysis of internal gravity waves
NASA Astrophysics Data System (ADS)
Hawkins, J.; Warn-Varnas, A.; Chin-Bing, S.; King, D.; Smolarkiewicsz, P.
2005-05-01
A series of model studies of internal gravity waves (igw) have been conducted for several regions of interest. Dispersion relations from the results have been computed using wavelet analysis as described by Meyers (1993). The wavelet transform is repeatedly applied over time and the components are evaluated with respect to their amplitude and peak position (Torrence and Compo, 1998). In this sense we have been able to compute dispersion relations from model results and from measured data. Qualitative agreement has been obtained in some cases. The results from wavelet analysis must be carefully interpreted because the igw models are fully nonlinear and wavelet analysis is fundamentally a linear technique. Nevertheless, a great deal of information describing igw propagation can be obtained from the wavelet transform. We address the domains over which wavelet analysis techniques can be applied and discuss the limits of their applicability.
Sparse constrained wavelet-based double-difference seismic tomography method and its applications
NASA Astrophysics Data System (ADS)
Fang, H.; Zhang, H.
2013-12-01
Geophysical inverse problems are often ill-posed and we often need to impose a priori information on the solution to make the inversion stable. In travel time tomography, because the events and stations are not uniformly distributed, ray coverage is thus not even. The regular grid which is generally used to represent the model and the grid spacing is difficult to choose to be suitable for uneven ray coverage. Irregular grid nodes have thus been proposed to represent the model based on tetrahedral diagram (Zhang et al., 2006). That method is purely data adaptive and does not consider whether the model representation is suitable for the solution space. Here we present a method that takes advantage of the multi-resolution property of wavelet transform to overcome this limitation. For the general inverse system Gm=d, we can actually write it into a new form GW'Wm=d by using the orthogonal property of wavelet transform W, where G is the sensitivity matrix, m is the model, and d is the data vector. Therefore, instead of solving the model parameters directly in space, we solve the wavelet coefficients of model parameters by transforming the sensitivity matrix to the wavelet domain. In other words, the inverse problem is now recast as seeking wavelet coefficients of the model parameters. For regions with dense ray coverage, both the approximations and details of wavelet coefficients can be resolved. In comparison, regions with sparse sampling will only have larger wavelet coefficients of model parameters to be resolved. By doing this, the regions with dense ray coverage can have higher spatial resolution and more model details can be recovered. For most models, their representations in the wavelet domain are sparse. Therefore, we imposed the sparse constraint of wavelet coefficients of model parameters by using the iteratively reweight least square method. A generalized cross validation method was used to get the regularization parameter and the approximate model
2001-10-25
We evaluate a combined discrete wavelet transform (DWT) and wavelet packet algorithm to improve the homogeneity of magnetic resonance imaging when a...image and uses this information to normalize the image intensity variations. Estimation of the coil sensitivity profile based on the wavelet transform of
Wavelet Analysis of Soil Reflectance for the Characterization of Soil Properties
Technology Transfer Automated Retrieval System (TEKTRAN)
Wavelet analysis has proven to be effective in many fields including signal processing and digital image analysis. Recently, it has been adapted to spectroscopy, where the reflectance of various materials is measured with respect to wavelength (nm) or wave number (cm-1). Spectra can cover broad wave...
Wavelet transform of neural spike trains
NASA Astrophysics Data System (ADS)
Kim, Youngtae; Jung, Min Whan; Kim, Yunbok
2000-02-01
Wavelet transform of neural spike trains recorded with a tetrode in the rat primary somatosensory cortex is described. Continuous wavelet transform (CWT) of the spike train clearly shows singularities hidden in the noisy or chaotic spike trains. A multiresolution analysis of the spike train is also carried out using discrete wavelet transform (DWT) for denoising and approximating at different time scales. Results suggest that this multiscale shape analysis can be a useful tool for classifying the spike trains.
Application and Development of Wavelet Analysis
1992-08-15
found that optics is quite suitable to generate and display both the direct and the inverse wavelet transforms in parallel. Unlike the digital...toward identifying the suitability of using optics for the multichannel signal analysis. Both the Gabor and the wavelet transforms were studied in terms...inverse wavelet transforms . This is the case for processing both the one and two dimensional signals. A detail comparison of the space-bandwidth
Develop, Apply and Evaluate Wavelet Technology.
1992-10-20
Eddington (1928), A. S . The Nature of the Physical World, Cambridge: Cambridge University Press. [11] Einstein , A. (155), The Meaning of Relativity...Albequerque, NM, 1990. [9] R. A. Gopinath and C. S . Burrus, "Wavelet transforms and filter banks," pp. 603-654 in Wavelets: A Tutorial in Theory and...Resnikoff, "Multidimensional wavelet bases," Aware Technical Report, Aware, Inc., Cambridge, MA 1991. [25] S . G. Mallat, "A Theory for multiresolution
Wavelet analysis in two-dimensional tomography
NASA Astrophysics Data System (ADS)
Burkovets, Dimitry N.
2002-02-01
The diagnostic possibilities of wavelet-analysis of coherent images of connective tissue in its pathological changes diagnostics. The effectiveness of polarization selection in obtaining wavelet-coefficients' images is also shown. The wavelet structures, characterizing the process of skin psoriasis, bone-tissue osteoporosis have been analyzed. The histological sections of physiological normal and pathologically changed samples of connective tissue of human skin and spongy bone tissue have been analyzed.
Wavelet Features Based Fingerprint Verification
NASA Astrophysics Data System (ADS)
Bagadi, Shweta U.; Thalange, Asha V.; Jain, Giridhar P.
2010-11-01
In this work; we present a automatic fingerprint identification system based on Level 3 features. Systems based only on minutiae features do not perform well for poor quality images. In practice, we often encounter extremely dry, wet fingerprint images with cuts, warts, etc. Due to such fingerprints, minutiae based systems show poor performance for real time authentication applications. To alleviate the problem of poor quality fingerprints, and to improve overall performance of the system, this paper proposes fingerprint verification based on wavelet statistical features & co-occurrence matrix features. The features include mean, standard deviation, energy, entropy, contrast, local homogeneity, cluster shade, cluster prominence, Information measure of correlation. In this method, matching can be done between the input image and the stored template without exhaustive search using the extracted feature. The wavelet transform based approach is better than the existing minutiae based method and it takes less response time and hence suitable for on-line verification, with high accuracy.
Multidimensional signaling via wavelet packets
NASA Astrophysics Data System (ADS)
Lindsey, Alan R.
1995-04-01
This work presents a generalized signaling strategy for orthogonally multiplexed communication. Wavelet packet modulation (WPM) employs the basis functions from an arbitrary pruning of a full dyadic tree structured filter bank as orthogonal pulse shapes for conventional QAM symbols. The multi-scale modulation (MSM) and M-band wavelet modulation (MWM) schemes which have been recently introduced are handled as special cases, with the added benefit of an entire library of potentially superior sets of basis functions. The figures of merit are derived and it is shown that the power spectral density is equivalent to that for QAM (in fact, QAM is another special case) and hence directly applicable in existing systems employing this standard modulation. Two key advantages of this method are increased flexibility in time-frequency partitioning and an efficient all-digital filter bank implementation, making the WPM scheme more robust to a larger set of interferences (both temporal and sinusoidal) and computationally attractive as well.
A fully spectral collocation approximation for multi-dimensional fractional Schrödinger equations
NASA Astrophysics Data System (ADS)
Bhrawy, A. H.; Abdelkawy, M. A.
2015-08-01
A shifted Legendre collocation method in two consecutive steps is developed and analyzed to numerically solve one- and two-dimensional time fractional Schrödinger equations (TFSEs) subject to initial-boundary and non-local conditions. The first step depends mainly on shifted Legendre Gauss-Lobatto collocation (SL-GL-C) method for spatial discretization; an expansion in a series of shifted Legendre polynomials for the approximate solution and its spatial derivatives occurring in the TFSE is investigated. In addition, the Legendre-Gauss-Lobatto quadrature rule is established to treat the nonlocal conservation conditions. Thereby, the expansion coefficients are then determined by reducing the TFSE with its nonlocal conditions to a system of fractional differential equations (SFDEs) for these coefficients. The second step is to propose a shifted Legendre Gauss-Radau collocation (SL-GR-C) scheme, for temporal discretization, to reduce such system into a system of algebraic equations which is far easier to be solved. The proposed collocation scheme, both in temporal and spatial discretizations, is successfully extended to solve the two-dimensional TFSE. Numerical results are carried out to confirm the spectral accuracy and efficiency of the proposed algorithms. By selecting relatively limited Legendre Gauss-Lobatto and Gauss-Radau collocation nodes, we are able to get very accurate approximations, demonstrating the utility and high accuracy of the new approach over other numerical methods.
NASA Astrophysics Data System (ADS)
Bhrawy, A. H.
2016-01-01
This paper reports a new spectral collocation technique for solving time-space modified anomalous subdiffusion equation with a nonlinear source term subject to Dirichlet and Neumann boundary conditions. This model equation governs the evolution for the probability density function that describes anomalously diffusing particles. Anomalous diffusion is ubiquitous in physical and biological systems where trapping and binding of particles can occur. A space-time Jacobi collocation scheme is investigated for solving such problem. The main advantage of the proposed scheme is that, the shifted Jacobi Gauss-Lobatto collocation and shifted Jacobi Gauss-Radau collocation approximations are employed for spatial and temporal discretizations, respectively. Thereby, the problem is successfully reduced to a system of algebraic equations. The numerical results obtained by this algorithm have been compared with various numerical methods in order to demonstrate the high accuracy and efficiency of the proposed method. Indeed, for relatively limited number of Gauss-Lobatto and Gauss-Radau collocation nodes imposed, the absolute error in our numerical solutions is sufficiently small. The results have been compared with other techniques in order to demonstrate the high accuracy and efficiency of the proposed method.
Wavelet methods in data mining
NASA Astrophysics Data System (ADS)
Manchanda, P.
2012-07-01
Data mining (knowledge discovery in data base) is comparatively new interdisciplinary field developed by joint efforts of mathematicians, statisticians, computer scientists and engineers. There are twelve important ingredients of this field along with their applications in real world problems. In this chapter, we have reviewed application of wavelet methods to data mining, particularly denoising, dimension reduction, similarity search, feature extraction and prediction. Meteorological data of Saudi Arabia and Stock market data of India are considered for illustration.
Wavelets, signal processing and matrix computations
NASA Astrophysics Data System (ADS)
Suter, Bruce W.
1994-09-01
Key scientific results were found in the following four areas: (1) multidimensional Malvar wavelets; (2) time/spatial varying filter banks; (3) vector filter banks and vector-valued wavelets; and (4) multirate time-frequency. These results have opened the following new areas of research: nonseparable multidimensional Malvar wavelets, vector-valued wavelets and vector filter banks, and multirate time-frequency analysis. These results also provide fundamental tools in many Air Force and industrial applications, such as modeling of turbulence, compression of images/video images, etc.
Optical Aperture Synthesis Object's Information Extracting Based on Wavelet Denoising
NASA Astrophysics Data System (ADS)
Fan, W. J.; Lu, Y.
2006-10-01
Wavelet denoising is studied to improve OAS(optical aperture synthesis) object's Fourier information extracting. Translation invariance wavelet denoising based on Donoho wavelet soft threshold denoising is researched to remove Pseudo-Gibbs in wavelet soft threshold image. OAS object's information extracting based on translation invariance wavelet denoising is studied. The study shows that wavelet threshold denoising can improve the precision and the repetition of object's information extracting from interferogram, and the translation invariance wavelet denoising information extracting is better than soft threshold wavelet denoising information extracting.
LIDAR data compression using wavelets
NASA Astrophysics Data System (ADS)
Pradhan, B.; Mansor, Shattri; Ramli, Abdul Rahman; Mohamed Sharif, Abdul Rashid B.; Sandeep, K.
2005-10-01
The lifting scheme has been found to be a flexible method for constructing scalar wavelets with desirable properties. In this paper, it is extended to the LIDAR data compression. A newly developed data compression approach to approximate the LIDAR surface with a series of non-overlapping triangles has been presented. Generally a Triangulated Irregular Networks (TIN) are the most common form of digital surface model that consists of elevation values with x, y coordinates that make up triangles. But over the years the TIN data representation has become a case in point for many researchers due its large data size. Compression of TIN is needed for efficient management of large data and good surface visualization. This approach covers following steps: First, by using a Delaunay triangulation, an efficient algorithm is developed to generate TIN, which forms the terrain from an arbitrary set of data. A new interpolation wavelet filter for TIN has been applied in two steps, namely splitting and elevation. In the splitting step, a triangle has been divided into several sub-triangles and the elevation step has been used to 'modify' the point values (point coordinates for geometry) after the splitting. Then, this data set is compressed at the desired locations by using second generation wavelets. The quality of geographical surface representation after using proposed technique is compared with the original LIDAR data. The results show that this method can be used for significant reduction of data set.
JND measurements and wavelet-based image coding
NASA Astrophysics Data System (ADS)
Shen, Day-Fann; Yan, Loon-Shan
1998-06-01
Two major issues in image coding are the effective incorporation of human visual system (HVS) properties and the effective objective measure for evaluating image quality (OQM). In this paper, we treat the two issues in an integrated fashion. We build a JND model based on the measurements of the JND (Just Noticeable Difference) property of HVS. We found that JND does not only depend on the background intensity but also a function of both spatial frequency and patten direction. Wavelet transform, due to its excellent simultaneous Time (space)/frequency resolution, is the best choice to apply the JND model. We mathematically derive an OQM called JND_PSNR that is based on the JND property and wavelet decomposed subbands. JND_PSNR is more consistent with human perception and is recommended as an alternative to the PSNR or SNR. With the JND_PSNR in mind, we proceed to propose a wavelet and JND based codec called JZW. JZW quantizes coefficients in each subband with proper step size according to the subband's importance to human perception. Many characteristics of JZW are discussed, its performance evaluated and compared with other famous algorithms such as EZW, SPIHT and TCCVQ. Our algorithm has 1 - 1.5 dB gain over SPIHT even when we use simple Huffman coding rather than the more efficient adaptive arithmetic coding.
Wavelet-based pavement image compression and noise reduction
NASA Astrophysics Data System (ADS)
Zhou, Jian; Huang, Peisen S.; Chiang, Fu-Pen
2005-08-01
For any automated distress inspection system, typically a huge number of pavement images are collected. Use of an appropriate image compression algorithm can save disk space, reduce the saving time, increase the inspection distance, and increase the processing speed. In this research, a modified EZW (Embedded Zero-tree Wavelet) coding method, which is an improved version of the widely used EZW coding method, is proposed. This method, unlike the two-pass approach used in the original EZW method, uses only one pass to encode both the coordinates and magnitudes of wavelet coefficients. An adaptive arithmetic encoding method is also implemented to encode four symbols assigned by the modified EZW into binary bits. By applying a thresholding technique to terminate the coding process, the modified EZW coding method can compress the image and reduce noise simultaneously. The new method is much simpler and faster. Experimental results also show that the compression ratio was increased one and one-half times compared to the EZW coding method. The compressed and de-noised data can be used to reconstruct wavelet coefficients for off-line pavement image processing such as distress classification and quantification.
Miniaturized Multi-Band Antenna via Element Collocation
Martin, R P
2012-06-01
The resonant frequency of a microstrip patch antenna may be reduced through the addition of slots in the radiating element. Expanding upon this concept in favor of a significant reduction in the tuned width of the radiator, nearly 60% of the antenna metallization is removed, as seen in the top view of the antenna’s radiating element (shown in red, below, left). To facilitate an increase in the gain of the antenna, the radiator is suspended over the ground plane (green) by an air substrate at a height of 0.250" while being mechanically supported by 0.030" thick Rogers RO4003 laminate in the same profile as the element. Although the entire surface of the antenna (red) provides 2.45 GHz operation with insignificant negative effects on performance after material removal, the smaller square microstrip in the middle must be isolated from the additional aperture in order to afford higher frequency operation. A low insertion loss path centered at 2.45 GHz may simultaneously provide considerable attenuation at additional frequencies through the implementation of a series-parallel, resonant reactive path. However, an inductive reactance alone will not permit lower frequency energy to propagate across the intended discontinuity. To mitigate this, a capacitance is introduced in series with the inductor, generating a resonance at 2.45 GHz with minimum forward transmission loss. Four of these reactive pairs are placed between the coplanar elements as shown. Therefore, the aperture of the lower-frequency outer segment includes the smaller radiator while the higher frequency section is isolated from the additional material. In order to avoid cross-polarization losses due to the orientation of a transmitter or receiver in reference to the antenna, circular polarization is realized by a quadrature coupler for each collocated antenna as seen in the bottom view of the antenna (right). To generate electromagnetic radiation concentrically rotating about the direction of propagation
Shifted Jacobi spectral collocation method for solving two-sided fractional water wave models
NASA Astrophysics Data System (ADS)
Abdelkawy, M. A.; Alqahtani, Rubayyi T.
2017-01-01
This paper presents the spectral collocation technique to solve the two-sided fractional water wave models (TSF-WWMs). The shifted Jacobi-Gauss-Lobatto collocation (SJ-GL-C) and shifted Jacobi-Gauss-Radau collocation (SJ-GR-C) methods are developed to approximate the TSF-WWMs. The main idea in the novel algorithm is to reduce the TSF-WWM to a systems of algebraic equations. The applicability and accuracy of the present technique have been examined by the given numerical examples in this paper. By means of these numerical examples, we ensure that the present technique is a simple and very accurate numerical scheme for solving TSF-WWMs.
Fast Spectral Collocation Method for Surface Integral Equations of Potential Problems in a Spheroid
Xu, Zhenli; Cai, Wei
2009-01-01
This paper proposes a new technique to speed up the computation of the matrix of spectral collocation discretizations of surface single and double layer operators over a spheroid. The layer densities are approximated by a spectral expansion of spherical harmonics and the spectral collocation method is then used to solve surface integral equations of potential problems in a spheroid. With the proposed technique, the computation cost of collocation matrix entries is reduced from 𝒪(M2N4) to 𝒪(MN4), where N2 is the number of spherical harmonics (i.e., size of the matrix) and M is the number of one-dimensional integration quadrature points. Numerical results demonstrate the spectral accuracy of the method. PMID:20414359
Daubechies wavelets for linear scaling density functional theory.
Mohr, Stephan; Ratcliff, Laura E; Boulanger, Paul; Genovese, Luigi; Caliste, Damien; Deutsch, Thierry; Goedecker, Stefan
2014-05-28
We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10,000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.
Nondyadic decomposition algorithm with Meyer's wavelet packets: an application to EEG signal
NASA Astrophysics Data System (ADS)
Carre, Philippe; Richard, Noel; Fernandez-Maloigne, Christine; Paquereau, Joel
1999-10-01
In this paper, we propose an original decomposition scheme based on Meyer's wavelets. In opposition to a classical technique of wavelet packet analysis, the decomposition is an adaptative segmentation of the frequential axis which does not use a filters bank. This permits a higher flexibility in the band frequency definition. The decomposition computes all possible partitions from a sequential space: it does not only compute those that come from a dyadic decomposition. Our technique is applied on the electroencephalogram signal; here the purpose is to extract a best basis of frequential decomposition. This study is part of a multimodal functional cerebral imagery project.
Preconditioning cubic spline collocation method by FEM and FDM for elliptic equations
Kim, Sang Dong
1996-12-31
In this talk we discuss the finite element and finite difference technique for the cubic spline collocation method. For this purpose, we consider the uniformly elliptic operator A defined by Au := -{Delta}u + a{sub 1}u{sub x} + a{sub 2}u{sub y} + a{sub 0}u in {Omega} (the unit square) with Dirichlet or Neumann boundary conditions and its discretization based on Hermite cubic spline spaces and collocation at the Gauss points. Using an interpolatory basis with support on the Gauss points one obtains the matrix A{sub N} (h = 1/N).
A spectral collocation method for a rotating Bose-Einstein condensation in optical lattices
NASA Astrophysics Data System (ADS)
Li, Z.-C.; Chen, S.-Y.; Chien, C.-S.; Chen, H.-S.
2011-06-01
We extend the study of spectral collocation methods (SCM) in Li et al. (2009) [1] for semilinear elliptic eigenvalue problems to that for a rotating Bose-Einstein condensation (BEC) and a rotating BEC in optical lattices. We apply the Lagrange interpolants using the Legendre-Gauss-Lobatto points to derive error bounds for the SCM. The optimal error bounds are derived for both H-norm and L-norm. Extensive numerical experiments on a rotating Bose-Einstein condensation and a rotating BEC in optical lattices are reported. Our numerical results show that the convergence rate of the SCM is exponential, and is independent of the collocation points we choose.
2013-02-06
levels, the ratio saturates to an asymptotic value acceptably “close” to its optimum reff=1.0. Second, we focus on the 2D advection benchmark discussed in...112] D. Forsey and R.H. Bartels. Hierarchical B-spline refinement. Computer Graphics (SIGGRAPH ’88 Proceedings), 22(4):205–212, 1988. [113] R. Kraft
ERIC Educational Resources Information Center
Krummes, Cedric; Ensslin, Astrid
2015-01-01
Whereas there exists a plethora of research on collocations and formulaic language in English, this article contributes towards a somewhat less developed area: the understanding and teaching of formulaic language in German as a foreign language. It analyses formulaic sequences and collocations in German writing (corpus-driven) and provides modern…
ERIC Educational Resources Information Center
Ying, Yang
2015-01-01
This study aimed to seek an in-depth understanding about English collocation learning and the development of learner autonomy through investigating a group of English as a Second Language (ESL) learners' perspectives and practices in their learning of English collocations using an AWARE approach. A group of 20 PRC students learning English in…
ERIC Educational Resources Information Center
Chang, Yu-Chia; Chang, Jason S.; Chen, Hao-Jan; Liou, Hsien-Chin
2008-01-01
Previous work in the literature reveals that EFL learners were deficient in collocations that are a hallmark of near native fluency in learner's writing. Among different types of collocations, the verb-noun (V-N) one was found to be particularly difficult to master, and learners' first language was also found to heavily influence their collocation…
Optical Wavelet Transform for Fingerprint Identification
1993-12-15
requirements of digitized fingerprints. This research implements an optical wavelet transform of a fingerprint image, as the first step in an optical... wavelet transform is implemented with continuous shift using an optical correlation between binarized fingerprints written on a Magneto-Optic Spatial
Wavelet=Galerkin discretization of hyperbolic equations
Restrepo, J.M.; Leaf, G.K.
1994-12-31
The relative merits of the wavelet-Galerkin solution of hyperbolic partial differential equations, typical of geophysical problems, are quantitatively and qualitatively compared to traditional finite difference and Fourier-pseudo-spectral methods. The wavelet-Galerkin solution presented here is found to be a viable alternative to the two conventional techniques.
Improvements of embedded zerotree wavelet (EZW) coding
NASA Astrophysics Data System (ADS)
Li, Jin; Cheng, Po-Yuen; Kuo, C.-C. Jay
1995-04-01
In this research, we investigate several improvements of embedded zerotree wavelet (EZW) coding. Several topics addressed include: the choice of wavelet transforms and boundary conditions, the use of arithmetic coder and arithmetic context and the design of encoding order for effective embedding. The superior performance of our improvements is demonstrated with extensive experimental results.
Using wavelets to learn pattern templates
NASA Astrophysics Data System (ADS)
Scott, Clayton D.; Nowak, Robert D.
2002-07-01
Despite the success of wavelet decompositions in other areas of statistical signal and image processing, current wavelet-based image models are inadequate for modeling patterns in images, due to the presence of unknown transformations (e.g., translation, rotation, location of lighting source) inherent in most pattern observations. In this paper we introduce a hierarchical wavelet-based framework for modeling patterns in digital images. This framework takes advantage of the efficient image representations afforded by wavelets, while accounting for unknown translation and rotation. Given a trained model, we can use this framework to synthesize pattern observations. If the model parameters are unknown, we can infer them from labeled training data using TEMPLAR (Template Learning from Atomic Representations), a novel template learning algorithm with linear complexity. TEMPLAR employs minimum description length (MDL) complexity regularization to learn a template with a sparse representation in the wavelet domain. We discuss several applications, including template learning, pattern classification, and image registration.
Finite element wavelets with improved quantitative properties
NASA Astrophysics Data System (ADS)
Nguyen, Hoang; Stevenson, Rob
2009-08-01
In [W. Dahmen, R. Stevenson, Element-by-element construction of wavelets satisfying stability and moment conditions, SIAM J. Numer. Anal. 37 (1) (1999) 319-352 (electronic)], finite element wavelets were constructed on polygonal domains or Lipschitz manifolds that are piecewise parametrized by mappings with constant Jacobian determinants. The wavelets could be arranged to have any desired order of cancellation properties, and they generated stable bases for the Sobolev spaces Hs for (or s<=1 on manifolds). Unfortunately, it appears that the quantitative properties of these wavelets are rather disappointing. In this paper, we modify the construction from the above-mentioned work to obtain finite element wavelets which are much better conditioned.
Numerical solution of the Black-Scholes equation using cubic spline wavelets
NASA Astrophysics Data System (ADS)
Černá, Dana
2016-12-01
The Black-Scholes equation is used in financial mathematics for computation of market values of options at a given time. We use the θ-scheme for time discretization and an adaptive scheme based on wavelets for discretization on the given time level. Advantages of the proposed method are small number of degrees of freedom, high-order accuracy with respect to variables representing prices and relatively small number of iterations needed to resolve the problem with a desired accuracy. We use several cubic spline wavelet and multi-wavelet bases and discuss their advantages and disadvantages. We also compare an isotropic and anisotropic approach. Numerical experiments are presented for the two-dimensional Black-Scholes equation.
CW-THz image contrast enhancement using wavelet transform and Retinex
NASA Astrophysics Data System (ADS)
Chen, Lin; Zhang, Min; Hu, Qi-fan; Huang, Ying-Xue; Liang, Hua-Wei
2015-10-01
To enhance continuous wave terahertz (CW-THz) scanning images contrast and denoising, a method based on wavelet transform and Retinex theory was proposed. In this paper, the factors affecting the quality of CW-THz images were analysed. Second, an approach of combination of the discrete wavelet transform (DWT) and a designed nonlinear function in wavelet domain for the purpose of contrast enhancing was applied. Then, we combine the Retinex algorithm for further contrast enhancement. To evaluate the effectiveness of the proposed method in qualitative and quantitative, it was compared with the adaptive histogram equalization method, the homomorphic filtering method and the SSR(Single-Scale-Retinex) method. Experimental results demonstrated that the presented algorithm can effectively enhance the contrast of CW-THZ image and obtain better visual effect.
An Investigation of Wavelet Bases for Grid-Based Multi-Scale Simulations Final Report
Baty, R.S.; Burns, S.P.; Christon, M.A.; Roach, D.W.; Trucano, T.G.; Voth, T.E.; Weatherby, J.R.; Womble, D.E.
1998-11-01
The research summarized in this report is the result of a two-year effort that has focused on evaluating the viability of wavelet bases for the solution of partial differential equations. The primary objective for this work has been to establish a foundation for hierarchical/wavelet simulation methods based upon numerical performance, computational efficiency, and the ability to exploit the hierarchical adaptive nature of wavelets. This work has demonstrated that hierarchical bases can be effective for problems with a dominant elliptic character. However, the strict enforcement of orthogonality was found to be less desirable than weaker semi-orthogonality or bi-orthogonality for solving partial differential equations. This conclusion has led to the development of a multi-scale linear finite element based on a hierarchical change of basis. The reproducing kernel particle method has been found to yield extremely accurate phase characteristics for hyperbolic problems while providing a convenient framework for multi-scale analyses.
Inter-view wavelet compression of light fields with disparity-compensated lifting
NASA Astrophysics Data System (ADS)
Chang, Chuo-Ling; Zhu, Xiaoqing; Ramanathan, Prashant; Girod, Bernd
2003-06-01
We propose a novel approach that uses disparity-compensated lifting for wavelet compression of light fields. Disparity compensation is incorporated into the lifting structure for the transform across the views to solve the irreversibility limitation in previous wavelet coding schemes. With this approach, we obtain the benefits of wavelet coding, such as scalability in all dimensions, as well as superior compression performance. For light fields of an object, shape adaptation is adopted to improve the compression efficiency and visual quality of reconstructed images. In this work we extend the scheme to handle light fields with arbitrary camera arrangements. A view-sequencing algorithm is developed to encode the images. Experimental results show that the proposed scheme outperforms existing light field compression techniques in terms of compression efficiency and visual quality of the reconstructed views.
Seamless multiresolution isosurfaces using wavelets
Udeshi, T.; Hudson, R.; Papka, M. E.
2000-04-11
Data sets that are being produced by today's simulations, such as the ones generated by DOE's ASCI program, are too large for real-time exploration and visualization. Therefore, new methods of visualizing these data sets need to be investigated. The authors present a method that combines isosurface representations of different resolutions into a seamless solution, virtually free of cracks and overlaps. The solution combines existing isosurface generation algorithms and wavelet theory to produce a real-time solution to multiple-resolution isosurfaces.
Directional dual-tree complex wavelet packet transforms for processing quadrature signals.
Serbes, Gorkem; Gulcur, Halil Ozcan; Aydin, Nizamettin
2016-03-01
Quadrature signals containing in-phase and quadrature-phase components are used in many signal processing applications in every field of science and engineering. Specifically, Doppler ultrasound systems used to evaluate cardiovascular disorders noninvasively also result in quadrature format signals. In order to obtain directional blood flow information, the quadrature outputs have to be preprocessed using methods such as asymmetrical and symmetrical phasing filter techniques. These resultant directional signals can be employed in order to detect asymptomatic embolic signals caused by small emboli, which are indicators of a possible future stroke, in the cerebral circulation. Various transform-based methods such as Fourier and wavelet were frequently used in processing embolic signals. However, most of the times, the Fourier and discrete wavelet transforms are not appropriate for the analysis of embolic signals due to their non-stationary time-frequency behavior. Alternatively, discrete wavelet packet transform can perform an adaptive decomposition of the time-frequency axis. In this study, directional discrete wavelet packet transforms, which have the ability to map directional information while processing quadrature signals and have less computational complexity than the existing wavelet packet-based methods, are introduced. The performances of proposed methods are examined in detail by using single-frequency, synthetic narrow-band, and embolic quadrature signals.
Wavelet Neural Network Using Multiple Wavelet Functions in Target Threat Assessment
Guo, Lihong; Duan, Hong
2013-01-01
Target threat assessment is a key issue in the collaborative attack. To improve the accuracy and usefulness of target threat assessment in the aerial combat, we propose a variant of wavelet neural networks, MWFWNN network, to solve threat assessment. How to select the appropriate wavelet function is difficult when constructing wavelet neural network. This paper proposes a wavelet mother function selection algorithm with minimum mean squared error and then constructs MWFWNN network using the above algorithm. Firstly, it needs to establish wavelet function library; secondly, wavelet neural network is constructed with each wavelet mother function in the library and wavelet function parameters and the network weights are updated according to the relevant modifying formula. The constructed wavelet neural network is detected with training set, and then optimal wavelet function with minimum mean squared error is chosen to build MWFWNN network. Experimental results show that the mean squared error is 1.23 × 10−3, which is better than WNN, BP, and PSO_SVM. Target threat assessment model based on the MWFWNN has a good predictive ability, so it can quickly and accurately complete target threat assessment. PMID:23509436
Maximally Localized Radial Profiles for Tight Steerable Wavelet Frames.
Pad, Pedram; Uhlmann, Virginie; Unser, Michael
2016-03-22
A crucial component of steerable wavelets is the radial profile of the generating function in the frequency domain. In this work, we present an infinite-dimensional optimization scheme that helps us find the optimal profile for a given criterion over the space of tight frames. We consider two classes of criteria that measure the localization of the wavelet. The first class specifies the spatial localization of the wavelet profile, and the second that of the resulting wavelet coefficients. From these metrics and the proposed algorithm, we construct tight wavelet frames that are optimally localized and provide their analytical expression. In particular, one of the considered criterion helps us finding back the popular Simoncelli wavelet profile. Finally, the investigation of local orientation estimation, image reconstruction from detected contours in the wavelet domain, and denoising, indicate that optimizing wavelet localization improves the performance of steerable wavelets, since our new wavelets outperform the traditional ones.
Maximally Localized Radial Profiles for Tight Steerable Wavelet Frames.
Pad, Pedram; Uhlmann, Virginie; Unser, Michael
2016-05-01
A crucial component of steerable wavelets is the radial profile of the generating function in the frequency domain. In this paper, we present an infinite-dimensional optimization scheme that helps us find the optimal profile for a given criterion over the space of tight frames. We consider two classes of criteria that measure the localization of the wavelet. The first class specifies the spatial localization of the wavelet profile, and the second that of the resulting wavelet coefficients. From these metrics and the proposed algorithm, we construct tight wavelet frames that are optimally localized and provide their analytical expression. In particular, one of the considered criterion helps us finding back the popular Simoncelli wavelet profile. Finally, the investigation of local orientation estimation, image reconstruction from detected contours in the wavelet domain, and denoising indicate that optimizing wavelet localization improves the performance of steerable wavelets, since our new wavelets outperform the traditional ones.
ERIC Educational Resources Information Center
Reynolds, Barry Lee
2016-01-01
Lack of knowledge in the conventional usage of collocations in one's respective field of expertise cause Taiwanese students to produce academic writing that is markedly different than more competent writing. This is because Taiwanese students are first and foremost English as a Foreign language (EFL) readers and may have difficulties picking up on…
Your Participation Is "Greatly/Highly" Appreciated: Amplifier Collocations in L2 English
ERIC Educational Resources Information Center
Edmonds, Amanda; Gudmestad, Aarnes
2014-01-01
The current study sets out to investigate collocational knowledge for a set of 13 English amplifiers among native and nonnative speakers of English, by providing a partial replication of one of the projects reported on in Granger (1998). The project combines both phraseological and distributional approaches to research into formulaic language to…
Runge-Kutta collocation methods for differential-algebraic equations of indices 2 and 3
NASA Astrophysics Data System (ADS)
Skvortsov, L. M.
2012-10-01
Stiffly accurate Runge-Kutta collocation methods with explicit first stage are examined. The parameters of these methods are chosen so as to minimize the errors in the solutions to differential-algebraic equations of indices 2 and 3. This construction results in methods for solving such equations that are superior to the available Runge-Kutta methods.
Frequent Collocates and Major Senses of Two Prepositions in ESL and ENL Corpora
ERIC Educational Resources Information Center
Nkemleke, Daniel
2009-01-01
This contribution assesses in quantitative terms frequent collocates and major senses of "between" and "through" in the corpus of Cameroonian English (CCE), the corpus of East-African (Kenya and Tanzania) English which is part of the International Corpus of English (ICE) project (ICE-EA), and the London Oslo/Bergen (LOB) corpus…
Collocational Competence of Arabic Speaking Learners of English: A Study in Lexical Semantics.
ERIC Educational Resources Information Center
Zughoul, Muhammad Raji; Abdul-Fattah, Hussein S.
This study examined learners' productive competence in collocations and idioms by means of their performance on two interdependent tasks. Participants were two groups of English as a Foreign Language undergraduate and graduate students from the English department at Jordan's Yarmouk University. The two tasks included the following: a multiple…
Parameter estimation technique for boundary value problems by spline collocation method
NASA Technical Reports Server (NTRS)
Kojima, Fumio
1988-01-01
A parameter-estimation technique for boundary-integral equations of the second kind is developed. The output least-squares identification technique using the spline collocation method is considered. The convergence analysis for the numerical method is discussed. The results are applied to boundary parameter estimations for two-dimensional Laplace and Helmholtz equations.
ERIC Educational Resources Information Center
Gyllstad, Henrik; Wolter, Brent
2016-01-01
The present study investigates whether two types of word combinations (free combinations and collocations) differ in terms of processing by testing Howarth's Continuum Model based on word combination typologies from a phraseological tradition. A visual semantic judgment task was administered to advanced Swedish learners of English (n = 27) and…
ERIC Educational Resources Information Center
Chatpunnarangsee, Kwanjira
2013-01-01
The purpose of this study is to explore ways of incorporating web-based concordancers for the purpose of teaching English collocations. A mixed-methods design utilizing a case study strategy was employed to uncover four specific dimensions of corpus use by twenty-four students in two classroom sections of a writing course at a university in…
The Effect of Corpus-Based Activities on Verb-Noun Collocations in EFL Classes
ERIC Educational Resources Information Center
Ucar, Serpil; Yükselir, Ceyhun
2015-01-01
This current study sought to reveal the impacts of corpus-based activities on verb-noun collocation learning in EFL classes. This study was carried out on two groups--experimental and control groups- each of which consists of 15 students. The students were preparatory class students at School of Foreign Languages, Osmaniye Korkut Ata University.…
Strategies in Translating Collocations in Religious Texts from Arabic into English
ERIC Educational Resources Information Center
Dweik, Bader S.; Shakra, Mariam M. Abu
2010-01-01
The present study investigated the strategies adopted by students in translating specific lexical and semantic collocations in three religious texts namely, the Holy Quran, the Hadith and the Bible. For this purpose, the researchers selected a purposive sample of 35 MA translation students enrolled in three different public and private Jordanian…
Evaluating Remotely-Sensed Surface Soil Moisture Estimates Using Triple Collocation
Technology Transfer Automated Retrieval System (TEKTRAN)
Recent work has demonstrated the potential of enhancing remotely-sensed surface soil moisture validation activities through the application of triple collocation techniques which compare time series of three mutually independent geophysical variable estimates in order to acquire the root-mean-square...
Investigation of Native Speaker and Second Language Learner Intuition of Collocation Frequency
ERIC Educational Resources Information Center
Siyanova-Chanturia, Anna; Spina, Stefania
2015-01-01
Research into frequency intuition has focused primarily on native (L1) and, to a lesser degree, nonnative (L2) speaker intuitions about single word frequency. What remains a largely unexplored area is L1 and L2 intuitions about collocation (i.e., phrasal) frequency. To bridge this gap, the present study aimed to answer the following question: How…
The Role of Language for Thinking and Task Selection in EFL Learners' Oral Collocational Production
ERIC Educational Resources Information Center
Wang, Hung-Chun; Shih, Su-Chin
2011-01-01
This study investigated how English as a foreign language (EFL) learners' types of language for thinking and types of oral elicitation tasks influence their lexical collocational errors in speech. Data were collected from 42 English majors in Taiwan using two instruments: (1) 3 oral elicitation tasks and (2) an inner speech questionnaire. The…
Lexical Collocation and Topic Occurrence in Well-Written Editorials: A Study in Form.
ERIC Educational Resources Information Center
Addison, James C., Jr.
To explore the concept of lexical collocation, or relationships between words, a study was conducted based on three assumptions: (1) that a text structure for a unit of discourse was analogous to that existing at the level of the sentence, (2) that such a text form could be discovered if a large enough sample of generically similar texts was…
Image coding with geometric wavelets.
Alani, Dror; Averbuch, Amir; Dekel, Shai
2007-01-01
This paper describes a new and efficient method for low bit-rate image coding which is based on recent development in the theory of multivariate nonlinear piecewise polynomial approximation. It combines a binary space partition scheme with geometric wavelet (GW) tree approximation so as to efficiently capture curve singularities and provide a sparse representation of the image. The GW method successfully competes with state-of-the-art wavelet methods such as the EZW, SPIHT, and EBCOT algorithms. We report a gain of about 0.4 dB over the SPIHT and EBCOT algorithms at the bit-rate 0.0625 bits-per-pixels (bpp). It also outperforms other recent methods that are based on "sparse geometric representation." For example, we report a gain of 0.27 dB over the Bandelets algorithm at 0.1 bpp. Although the algorithm is computationally intensive, its time complexity can be significantely reduced by collecting a "global" GW n-term approximation to the image from a collection of GW trees, each constructed separately over tiles of the image.
Detecting the BAO using Discrete Wavelet Packets
NASA Astrophysics Data System (ADS)
Garcia, Noel Anthony; Wu, Yunyun; Kadowaki, Kevin; Pando, Jesus
2017-01-01
We use wavelet packets to investigate the clustering of matter on galactic scales in search of the Baryon Acoustic Oscillations. We do so in two ways. We develop a wavelet packet approach to measure the power spectrum and apply this method to the CMASS galaxy catalogue from the Sloan Digital Sky Survey (SDSS). We compare the resulting power spectrum to published BOSS results by measuring a parameter β that compares our wavelet detected oscillations to the results from the SDSS collaboration. We find that β=1 indicating that our wavelet packet methods are detecting the BAO at a similar level as traditional Fourier techniques. We then use wavelet packets to decompose, denoise, and then reconstruct the galaxy density field. Using this denoised field, we compute the standard two-point correlation function. We are able to successfully detect the BAO at r ≈ 105 h-1 Mpc in line with previous SDSS results. We conclude that wavelet packets do reproduce the results of the key clustering statistics computed by other means. The wavelet packets show distinct advantages in suppressing high frequency noise and in keeping information localized.
Improved collocation methods with application to six-degree-of-freedom trajectory optimization
NASA Astrophysics Data System (ADS)
Desai, Prasun N.
2005-11-01
An improved collocation method is developed for a class of problems that is intractable, or nearly so, by conventional collocation. These are problems in which there are two distinct timescales of the system states, that is, where a subset of the states have high-frequency variations while the remaining states vary comparatively slowly. In conventional collocation, the timescale for the discretization would be set by the need to capture the high-frequency dynamics. The problem then becomes very large and the solution of the corresponding nonlinear programming problem becomes geometrically more time consuming and difficult. A new two-timescale discretization method is developed for the solution of such problems using collocation. This improved collocation method allows the use of a larger time discretization for the low-frequency dynamics of the motion, and a second finer time discretization scheme for the higher-frequency dynamics of the motion. The accuracy of the new method is demonstrated first on an example problem, an optimal lunar ascent. The method is then applied to the type of challenging problem for which it is designed, the optimization of the approach to landing trajectory for a winged vehicle returning from space, the HL-20 lifting body vehicle. The converged solution shows a realistic landing profile and fully captures the higher-frequency rotational dynamics. A source code using the sparse optimizer SNOPT is developed for the use of this method which generates constraint equations, gradients, and the system Jacobian for problems of arbitrary size. This code constitutes a much-improved tool for aerospace vehicle design but has application to all two-timescale optimization problems.
Applications of a fast, continuous wavelet transform
Dress, W.B.
1997-02-01
A fast, continuous, wavelet transform, based on Shannon`s sampling theorem in frequency space, has been developed for use with continuous mother wavelets and sampled data sets. The method differs from the usual discrete-wavelet approach and the continuous-wavelet transform in that, here, the wavelet is sampled in the frequency domain. Since Shannon`s sampling theorem lets us view the Fourier transform of the data set as a continuous function in frequency space, the continuous nature of the functions is kept up to the point of sampling the scale-translation lattice, so the scale-translation grid used to represent the wavelet transform is independent of the time- domain sampling of the signal under analysis. Computational cost and nonorthogonality aside, the inherent flexibility and shift invariance of the frequency-space wavelets has advantages. The method has been applied to forensic audio reconstruction speaker recognition/identification, and the detection of micromotions of heavy vehicles associated with ballistocardiac impulses originating from occupants` heart beats. Audio reconstruction is aided by selection of desired regions in the 2-D representation of the magnitude of the transformed signal. The inverse transform is applied to ridges and selected regions to reconstruct areas of interest, unencumbered by noise interference lying outside these regions. To separate micromotions imparted to a mass-spring system (e.g., a vehicle) by an occupants beating heart from gross mechanical motions due to wind and traffic vibrations, a continuous frequency-space wavelet, modeled on the frequency content of a canonical ballistocardiogram, was used to analyze time series taken from geophone measurements of vehicle micromotions. By using a family of mother wavelets, such as a set of Gaussian derivatives of various orders, features such as the glottal closing rate and word and phrase segmentation may be extracted from voice data.
Electroencephalographic compression based on modulated filter banks and wavelet transform.
Bazán-Prieto, Carlos; Cárdenas-Barrera, Julián; Blanco-Velasco, Manuel; Cruz-Roldán, Fernando
2011-01-01
Due to the large volume of information generated in an electroencephalographic (EEG) study, compression is needed for storage, processing or transmission for analysis. In this paper we evaluate and compare two lossy compression techniques applied to EEG signals. It compares the performance of compression schemes with decomposition by filter banks or wavelet Packets transformation, seeking the best value for compression, best quality and more efficient real time implementation. Due to specific properties of EEG signals, we propose a quantization stage adapted to the dynamic range of each band, looking for higher quality. The results show that the compressor with filter bank performs better than transform methods. Quantization adapted to the dynamic range significantly enhances the quality.
Wavelet frames and admissibility in higher dimensions
NASA Astrophysics Data System (ADS)
Führ, Hartmut
1996-12-01
This paper is concerned with the relations between discrete and continuous wavelet transforms on k-dimensional Euclidean space. We start with the construction of continuous wavelet transforms with the help of square-integrable representations of certain semidirect products, thereby generalizing results of Bernier and Taylor. We then turn to frames of L2(Rk) and to the question, when the functions occurring in a given frame are admissible for a given continuous wavelet transform. For certain frames we give a characterization which generalizes a result of Daubechies to higher dimensions.
Wavelet Applications for Flight Flutter Testing
NASA Technical Reports Server (NTRS)
Lind, Rick; Brenner, Marty; Freudinger, Lawrence C.
1999-01-01
Wavelets present a method for signal processing that may be useful for analyzing responses of dynamical systems. This paper describes several wavelet-based tools that have been developed to improve the efficiency of flight flutter testing. One of the tools uses correlation filtering to identify properties of several modes throughout a flight test for envelope expansion. Another tool uses features in time-frequency representations of responses to characterize nonlinearities in the system dynamics. A third tool uses modulus and phase information from a wavelet transform to estimate modal parameters that can be used to update a linear model and reduce conservatism in robust stability margins.
Optical Planar Discrete Fourier and Wavelet Transforms
NASA Astrophysics Data System (ADS)
Cincotti, Gabriella; Moreolo, Michela Svaluto; Neri, Alessandro
2007-10-01
We present all-optical architectures to perform discrete wavelet transform (DWT), wavelet packet (WP) decomposition and discrete Fourier transform (DFT) using planar lightwave circuits (PLC) technology. Any compact-support wavelet filter can be implemented as an optical planar two-port lattice-form device, and different subband filtering schemes are possible to denoise, or multiplex optical signals. We consider both parallel and serial input cases. We design a multiport decoder/decoder that is able to generate/process optical codes simultaneously and a flexible logarithmic wavelength multiplexer, with flat top profile and reduced crosstalk.
Transionospheric signal detection with chirped wavelets
Doser, A.B.; Dunham, M.E.
1997-11-01
Chirped wavelets are utilized to detect dispersed signals in the joint time scale domain. Specifically, pulses that become dispersed by transmission through the ionosphere and are received by satellites as nonlinear chirps are investigated. Since the dispersion greatly lowers the signal to noise ratios, it is difficult to isolate the signals in the time domain. Satellite data are examined with discrete wavelet expansions. Detection is accomplished via a template matching threshold scheme. Quantitative experimental results demonstrate that the chirped wavelet detection scheme is successful in detecting the transionospheric pulses at very low signal to noise ratios.
Wavelet analysis of fusion plasma transients
Dose, V.; Venus, G.; Zohm, H.
1997-02-01
Analysis of transient signals in the diagnostic of fusion plasmas often requires the simultaneous consideration of their time and frequency information. The newly emerging technique of wavelet analysis contains both time and frequency domains. Therefore it can be a valuable tool for the analysis of transients. In this paper the basic method of wavelet analysis is described. As an example, wavelet analysis is applied to the well-known phenomena of mode locking and fishbone instability. The results quantify the current qualitative understanding of these events in terms of instantaneous frequencies and amplitudes and encourage applications of the method to other problems. {copyright} {ital 1997 American Institute of Physics.}
Sokolova, L V; Cherkasova, A S
2015-01-01
Texts or words/pseudowords are often used as stimuli for human verbal activity research. Our study pays attention to decoding processes of grammatical constructions consisted of two-three words--collocations. Russian and English collocation sets without any narrative were presented to Russian-speaking students with different English language skill. Stimulus material had two types of collocations: paradigmatic and syntagmatic. 30 students (average age--20.4 ± 0.22) took part in the study, they were divided into two equal groups depending on their English language skill (linguists/nonlinguists). During reading brain bioelectrical activity of cortex has been registered from 12 electrodes in alfa-, beta-, theta-bands. Coherent function reflecting cooperation of different cortical areas during reading collocations has been analyzed. Increase of interhemispheric and diagonal connections while reading collocations in different languages in the group of students with low knowledge of foreign language testifies of importance of functional cooperation between the hemispheres. It has been found out that brain bioelectrical activity of students with good foreign language knowledge during reading of all collocation types in Russian and English is characterized by economization of nervous substrate resources compared to nonlinguists. Selective activation of certain cortical areas has also been observed (depending on the grammatical construction type) in nonlinguists group that is probably related to special decoding system which processes presented stimuli. Reading Russian paradigmatic constructions by nonlinguists entailed increase between left cortical areas, reading of English syntagmatic collocations--between right ones.
Significance tests for the wavelet cross spectrum and wavelet linear coherence
NASA Astrophysics Data System (ADS)
Ge, Z.
2008-12-01
This work attempts to develop significance tests for the wavelet cross spectrum and the wavelet linear coherence as a follow-up study on Ge (2007). Conventional approaches that are used by Torrence and Compo (1998) based on stationary background noise time series were used here in estimating the sampling distributions of the wavelet cross spectrum and the wavelet linear coherence. The sampling distributions are then used for establishing significance levels for these two wavelet-based quantities. In addition to these two wavelet quantities, properties of the phase angle of the wavelet cross spectrum of, or the phase difference between, two Gaussian white noise series are discussed. It is found that the tangent of the principal part of the phase angle approximately has a standard Cauchy distribution and the phase angle is uniformly distributed, which makes it impossible to establish significance levels for the phase angle. The simulated signals clearly show that, when there is no linear relation between the two analysed signals, the phase angle disperses into the entire range of [-π,π] with fairly high probabilities for values close to ±π to occur. Conversely, when linear relations are present, the phase angle of the wavelet cross spectrum settles around an associated value with considerably reduced fluctuations. When two signals are linearly coupled, their wavelet linear coherence will attain values close to one. The significance test of the wavelet linear coherence can therefore be used to complement the inspection of the phase angle of the wavelet cross spectrum. The developed significance tests are also applied to actual data sets, simultaneously recorded wind speed and wave elevation series measured from a NOAA buoy on Lake Michigan. Significance levels of the wavelet cross spectrum and the wavelet linear coherence between the winds and the waves reasonably separated meaningful peaks from those generated by randomness in the data set. As with simulated
Abbaspour, Sara; Fallah, Ali; Lindén, Maria; Gholamhosseini, Hamid
2016-02-01
In recent years, the removal of electrocardiogram (ECG) interferences from electromyogram (EMG) signals has been given large consideration. Where the quality of EMG signal is of interest, it is important to remove ECG interferences from EMG signals. In this paper, an efficient method based on a combination of adaptive neuro-fuzzy inference system (ANFIS) and wavelet transform is proposed to effectively eliminate ECG interferences from surface EMG signals. The proposed approach is compared with other common methods such as high-pass filter, artificial neural network, adaptive noise canceller, wavelet transform, subtraction method and ANFIS. It is found that the performance of the proposed ANFIS-wavelet method is superior to the other methods with the signal to noise ratio and relative error of 14.97dB and 0.02 respectively and a significantly higher correlation coefficient (p<0.05).
Wavelet filtering for data recovery
NASA Astrophysics Data System (ADS)
Schmidt, W.
2013-09-01
In case of electrical wave measurements in space instruments, digital filtering and data compression on board can significantly enhance the signal and reduce the amount of data to be transferred to Earth. While often the instrument's transfer function is well known making the application of an optimized wavelet algorithm feasible the computational power requirements may be prohibitive as normally complex floating point operations are needed. This article presents a simplified possibility implemented in low-power 16-bit integer processors used for plasma wave measurements in the SPEDE instrument on SMART-1 and for the Permittivity Probe measurements of the SESAME/PP instrument in Rosetta's Philae Lander on its way to comet 67P/Churyumov-Gerasimenko.
Signal Approximation with a Wavelet Neural Network
1992-12-01
specialized electronic devices like the Intel Electronically Trainable Analog Neural Network (ETANN) chip. The WNN representation allows the...accurately approximated with a WNN trained with irregularly sampled data. Signal approximation, Wavelet neural network .
Discrete multiscale wavelet shrinkage and integrodifferential equations
NASA Astrophysics Data System (ADS)
Didas, S.; Steidl, G.; Weickert, J.
2008-04-01
We investigate the relation between discrete wavelet shrinkage and integrodifferential equations in the context of simplification and denoising of one-dimensional signals. In the continuous setting, strong connections between these two approaches were discovered in 6 (see references). The key observation is that the wavelet transform can be understood as derivative operator after the convolution with a smoothing kernel. In this paper, we extend these ideas to the practically relevant discrete setting with both orthogonal and biorthogonal wavelets. In the discrete case, the behaviour of the smoothing kernels for different scales requires additional investigation. The results of discrete multiscale wavelet shrinkage and related discrete versions of integrodifferential equations are compared with respect to their denoising quality by numerical experiments.
Digital transceiver implementation for wavelet packet modulation
NASA Astrophysics Data System (ADS)
Lindsey, Alan R.; Dill, Jeffrey C.
1998-03-01
Current transceiver designs for wavelet-based communication systems are typically reliant on analog waveform synthesis, however, digital processing is an important part of the eventual success of these techniques. In this paper, a transceiver implementation is introduced for the recently introduced wavelet packet modulation scheme which moves the analog processing as far as possible toward the antenna. The transceiver is based on the discrete wavelet packet transform which incorporates level and node parameters for generalized computation of wavelet packets. In this transform no particular structure is imposed on the filter bank save dyadic branching, and a maximum level which is specified a priori and dependent mainly on speed and/or cost considerations. The transmitter/receiver structure takes a binary sequence as input and, based on the desired time- frequency partitioning, processes the signal through demultiplexing, synthesis, analysis, multiplexing and data determination completely in the digital domain - with exception of conversion in and out of the analog domain for transmission.
Wavelet Analysis for Acoustic Phased Array
NASA Astrophysics Data System (ADS)
Kozlov, Inna; Zlotnick, Zvi
2003-03-01
Wavelet spectrum analysis is known to be one of the most powerful tools for exploring quasistationary signals. In this paper we use wavelet technique to develop a new Direction Finding (DF) Algorithm for the Acoustic Phased Array (APA) systems. Utilising multi-scale analysis of libraries of wavelets allows us to work with frequency bands instead of individual frequency of an acoustic source. These frequency bands could be regarded as features extracted from quasistationary signals emitted by a noisy object. For detection, tracing and identification of a sound source in a noisy environment we develop smart algorithm. The essential part of this algorithm is a special interacting procedure of the above-mentioned DF-algorithm and the wavelet-based Identification (ID) algorithm developed in [4]. Significant improvement of the basic properties of a receiving APA pattern is achieved.
Wavelet-based acoustic recognition of aircraft
Dress, W.B.; Kercel, S.W.
1994-09-01
We describe a wavelet-based technique for identifying aircraft from acoustic emissions during take-off and landing. Tests show that the sensor can be a single, inexpensive hearing-aid microphone placed close to the ground the paper describes data collection, analysis by various technique, methods of event classification, and extraction of certain physical parameters from wavelet subspace projections. The primary goal of this paper is to show that wavelet analysis can be used as a divide-and-conquer first step in signal processing, providing both simplification and noise filtering. The idea is to project the original signal onto the orthogonal wavelet subspaces, both details and approximations. Subsequent analysis, such as system identification, nonlinear systems analysis, and feature extraction, is then carried out on the various signal subspaces.
Applications of a fast continuous wavelet transform
NASA Astrophysics Data System (ADS)
Dress, William B.
1997-04-01
A fast, continuous, wavelet transform, justified by appealing to Shannon's sampling theorem in frequency space, has been developed for use with continuous mother wavelets and sampled data sets. The method differs from the usual discrete-wavelet approach and from the standard treatment of the continuous-wavelet transform in that, here, the wavelet is sampled in the frequency domain. Since Shannon's sampling theorem lets us view the Fourier transform of the data set as representing the continuous function in frequency space, the continuous nature of the functions is kept up to the point of sampling the scale-translation lattice, so the scale-translation grid used to represent the wavelet transform is independent of the time-domain sampling of the signal under analysis. Although more computationally costly and not represented by an orthogonal basis, the inherent flexibility and shift invariance of the frequency-space wavelets are advantageous for certain applications. The method has been applied to forensic audio reconstruction, speaker recognition/identification, and the detection of micromotions of heavy vehicles associated with ballistocardiac impulses originating from occupants' heart beats. Audio reconstruction is aided by selection of desired regions in the 2D representation of the magnitude of the transformed signals. The inverse transform is applied to ridges and selected regions to reconstruct areas of interest, unencumbered by noise interference lying outside these regions. To separate micromotions imparted to a mass- spring system by an occupant's beating heart from gross mechanical motions due to wind and traffic vibrations, a continuous frequency-space wavelet, modeled on the frequency content of a canonical ballistocardiogram, was used to analyze time series taken from geophone measurements of vehicle micromotions. By using a family of mother wavelets, such as a set of Gaussian derivatives of various orders, different features may be extracted from voice
Contour detection based on wavelet differentiation
NASA Astrophysics Data System (ADS)
Bezuglov, D.; Kuzin, A.; Voronin, V.
2016-05-01
This work proposes a novel algorithm for contour detection based on high-performance algorithm of wavelet analysis for multimedia applications. To solve the noise effect on the result of peaking in this paper we consider the direct and inverse wavelet differentiation. Extensive experimental evaluation on noisy images demonstrates that our contour detection method significantly outperform competing algorithms. The proposed algorithm provides a means of coupling our system to recognition application such as detection and identification of vehicle number plate.
EEG Multiresolution Analysis Using Wavelet Transform
2007-11-02
Wavelet transform (WT) is a new multiresolution time-frequency analysis method. WT possesses well localization feature both in tine and frequency...plays a key role in the diagnosing diseases and is useful for both physiological research and medical applications. Using the dyadic wavelet ... transform the EEG signals are successfully decomposed to the alpha rhythm (8-13Hz) beta rhythm (14-30Hz) theta rhythm (4-7Hz) and delta rhythm (0.3-3Hz) and
Wavelet Characterizations of Multi-Directional Regularity
NASA Astrophysics Data System (ADS)
Slimane, Mourad Ben
2011-05-01
The study of d dimensional traces of functions of m several variables leads to directional behaviors. The purpose of this paper is two-fold. Firstly, we extend the notion of one direction pointwise Hölder regularity introduced by Jaffard to multi-directions. Secondly, we characterize multi-directional pointwise regularity by Triebel anisotropic wavelet coefficients (resp. leaders), and also by Calderón anisotropic continuous wavelet transform.
A Wavelet Model for Vocalic Speech Coarticulation
1994-10-01
128 Figure 8. 1 Wavelet Transforms of the /d/ words: /did/, / dmd /, /d~d/, /dud/........................... 134 x Figure 8.2 Wavelet Transforms of... Kennedy (1967) used synthetic CVC syllables to demonstrate the influence of adjacent consonants on the perception of the vowel. A series of vowel sounds...34 The Journal of the Acoustical Society of America 35(11), pp. 1773-1781. 172 Lindblom, B.E.F. and Studdert- Kennedy , M. (1967). "On the Role of Formant
Optimal wavelet denoising for smart biomonitor systems
NASA Astrophysics Data System (ADS)
Messer, Sheila R.; Agzarian, John; Abbott, Derek
2001-03-01
Future smart-systems promise many benefits for biomedical diagnostics. The ideal is for simple portable systems that display and interpret information from smart integrated probes or MEMS-based devices. In this paper, we will discuss a step towards this vision with a heart bio-monitor case study. An electronic stethoscope is used to record heart sounds and the problem of extracting noise from the signal is addressed via the use of wavelets and averaging. In our example of heartbeat analysis, phonocardiograms (PCGs) have many advantages in that they may be replayed and analysed for spectral and frequency information. Many sources of noise may pollute a PCG including foetal breath sounds if the subject is pregnant, lung and breath sounds, environmental noise and noise from contact between the recording device and the skin. Wavelets can be employed to denoise the PCG. The signal is decomposed by a discrete wavelet transform. Due to the efficient decomposition of heart signals, their wavelet coefficients tend to be much larger than those due to noise. Thus, coefficients below a certain level are regarded as noise and are thresholded out. The signal can then be reconstructed without significant loss of information in the signal. The questions that this study attempts to answer are which wavelet families, levels of decomposition, and thresholding techniques best remove the noise in a PCG. The use of averaging in combination with wavelet denoising is also addressed. Possible applications of the Hilbert Transform to heart sound analysis are discussed.
Trabecular bone texture classification using wavelet leaders
NASA Astrophysics Data System (ADS)
Zou, Zilong; Yang, Jie; Megalooikonomou, Vasileios; Jennane, Rachid; Cheng, Erkang; Ling, Haibin
2016-03-01
In this paper we propose to use the Wavelet Leader (WL) transformation for studying trabecular bone patterns. Given an input image, its WL transformation is defined as the cross-channel-layer maximum pooling of an underlying wavelet transformation. WL inherits the advantage of the original wavelet transformation in capturing spatial-frequency statistics of texture images, while being more robust against scale and orientation thanks to the maximum pooling strategy. These properties make WL an attractive alternative to replace wavelet transformations which are used for trabecular analysis in previous studies. In particular, in this paper, after extracting wavelet leader descriptors from a trabecular texture patch, we feed them into two existing statistic texture characterization methods, namely the Gray Level Co-occurrence Matrix (GLCM) and the Gray Level Run Length Matrix (GLRLM). The most discriminative features, Energy of GLCM and Gray Level Non-Uniformity of GLRLM, are retained to distinguish two different populations between osteoporotic patients and control subjects. Receiver Operating Characteristics (ROC) curves are used to measure performance of classification. Experimental results on a recently released benchmark dataset show that WL significantly boosts the performance of baseline wavelet transformations by 5% in average.
Fast wavelet estimation of weak biosignals.
Causevic, Elvir; Morley, Robert E; Wickerhauser, M Victor; Jacquin, Arnaud E
2005-06-01
Wavelet-based signal processing has become commonplace in the signal processing community over the past decade and wavelet-based software tools and integrated circuits are now commercially available. One of the most important applications of wavelets is in removal of noise from signals, called denoising, accomplished by thresholding wavelet coefficients in order to separate signal from noise. Substantial work in this area was summarized by Donoho and colleagues at Stanford University, who developed a variety of algorithms for conventional denoising. However, conventional denoising fails for signals with low signal-to-noise ratio (SNR). Electrical signals acquired from the human body, called biosignals, commonly have below 0 dB SNR. Synchronous linear averaging of a large number of acquired data frames is universally used to increase the SNR of weak biosignals. A novel wavelet-based estimator is presented for fast estimation of such signals. The new estimation algorithm provides a faster rate of convergence to the underlying signal than linear averaging. The algorithm is implemented for processing of auditory brainstem response (ABR) and of auditory middle latency response (AMLR) signals. Experimental results with both simulated data and human subjects demonstrate that the novel wavelet estimator achieves superior performance to that of linear averaging.
Multisensensor Multitemporal Data Fusion Using Wavelet Transform
NASA Astrophysics Data System (ADS)
Ghannam, S.; Awadallah, M.; Abbott, A. L.; Wynne, R. H.
2014-11-01
Interest in data fusion, for remote-sensing applications, continues to grow due to the increasing importance of obtaining data in high resolution both spatially and temporally. Applications that will benefit from data fusion include ecosystem disturbance and recovery assessment, ecological forecasting, and others. This paper introduces a novel spatiotemporal fusion approach, the wavelet-based Spatiotemporal Adaptive Data Fusion Model (WSAD-FM). This new technique is motivated by the popular STARFM tool, which utilizes lower-resolution MODIS imagery to supplement Landsat scenes using a linear model. The novelty of WSAD-FM is twofold. First, unlike STARFM, this technique does not predict an entire new image in one linear step, but instead decomposes input images into separate "approximation" and "detail" parts. The different portions are fed into a prediction model that limits the effects of linear interpolation among images. Low-spatial-frequency components are predicted by a weighted mixture of MODIS images and low-spatial-frequency components of Landsat images that are neighbors in the temporal domain. Meanwhile, high-spatialfrequency components are predicted by a weighted average of high-spatial-frequency components of Landsat images alone. The second novelty is that the method has demonstrated good performance using only one input Landsat image and a pair of MODIS images. The technique has been tested using several Landsat and MODIS images for a study area from Central North Carolina (WRS-2 path/row 16/35 in Landsat and H/V11/5 in MODIS), acquired in 2001. NDVI images that were calculated from the study area were used as input to the algorithm. The technique was tested experimentally by predicting existing Landsat images, and we obtained R2 values in the range 0.70 to 0.92 for estimated Landsat images in the red band, and 0.62 to 0.89 for estimated NDVI images.
1982-08-18
The procedure for simulating quasireversible electron transfer systems for cyclic voltammetry experiments is presented, and the procedure applied to several systems. The technique is based on orthogonal collocation. (Author)
The convergence problem of collocation solutions in the framework of the stochastic interpretation
NASA Astrophysics Data System (ADS)
Sansò, F.; Venuti, G.
2011-01-01
The problem of the convergence of the collocation solution to the true gravity field was defined long ago (Tscherning in Boll Geod Sci Affini 39:221-252, 1978) and some results were derived, in particular by Krarup (Boll Geod Sci Affini 40:225-240, 1981). The problem is taken up again in the context of the stochastic interpretation of collocation theory and some new results are derived, showing that, when the potential T can be really continued down to a Bjerhammar sphere, we have a quite general convergence property in the noiseless case. When noise is present in data, still reasonable convergence results hold true. "Democrito che 'l mondo a caso pone" "Democritus who made the world stochastic" Dante Alighieri, La Divina Commedia, Inferno, IV - 136
A space-time spectral collocation algorithm for the variable order fractional wave equation.
Bhrawy, A H; Doha, E H; Alzaidy, J F; Abdelkawy, M A
2016-01-01
The variable order wave equation plays a major role in acoustics, electromagnetics, and fluid dynamics. In this paper, we consider the space-time variable order fractional wave equation with variable coefficients. We propose an effective numerical method for solving the aforementioned problem in a bounded domain. The shifted Jacobi polynomials are used as basis functions, and the variable-order fractional derivative is described in the Caputo sense. The proposed method is a combination of shifted Jacobi-Gauss-Lobatto collocation scheme for the spatial discretization and the shifted Jacobi-Gauss-Radau collocation scheme for temporal discretization. The aforementioned problem is then reduced to a problem consists of a system of easily solvable algebraic equations. Finally, numerical examples are presented to show the effectiveness of the proposed numerical method.
NASA Astrophysics Data System (ADS)
Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohammed A.
2014-09-01
In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach
Avila, Gustavo Carrington, Tucker
2015-12-07
In this paper, we improve the collocation method for computing vibrational spectra that was presented in Avila and Carrington, Jr. [J. Chem. Phys. 139, 134114 (2013)]. Using an iterative eigensolver, energy levels and wavefunctions are determined from values of the potential on a Smolyak grid. The kinetic energy matrix-vector product is evaluated by transforming a vector labelled with (nondirect product) grid indices to a vector labelled by (nondirect product) basis indices. Both the transformation and application of the kinetic energy operator (KEO) scale favorably. Collocation facilitates dealing with complicated KEOs because it obviates the need to calculate integrals of coordinate dependent coefficients of differential operators. The ideas are tested by computing energy levels of HONO using a KEO in bond coordinates.
Domain decomposition methods for systems of conservation laws: Spectral collocation approximations
NASA Technical Reports Server (NTRS)
Quarteroni, Alfio
1989-01-01
Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.
NASA Technical Reports Server (NTRS)
Goldsmith, J. E. M.; Bisson, Scott E.; Ferrare, Richard A.; Evans, Keith D.; Whiteman, David N.; Melfi, S. H.
1994-01-01
Raman lidar is a leading candidate for providing the detailed space- and time-resolved measurements of water vapor needed by a variety of atmospheric studies. Simultaneous measurements of atmospheric water vapor are described using two collocated Raman lidar systems. These lidar systems, developed at the NASA/Goddard Space Flight Center and Sandia National Laboratories, acquired approximately 12 hours of simultaneous water vapor data during three nights in November 1992 while the systems were collocated at the Goddard Space Flight Center. Although these lidar systems differ substantially in their design, measured water vapor profiles agreeed within 0.15 g/kg between altitudes of 1 and 5 km. Comparisons with coincident radiosondes showed all instruments agreed within 0.2 g/kg in this same altitude range. Both lidars also clearly showed the advection of water vapor in the middle troposphere and the pronounced increase in water vapor in the nocturnal boundary layer that occurred during one night.
The Benard problem: A comparison of finite difference and spectral collocation eigen value solutions
NASA Technical Reports Server (NTRS)
Skarda, J. Raymond Lee; Mccaughan, Frances E.; Fitzmaurice, Nessan
1995-01-01
The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.
NASA Astrophysics Data System (ADS)
Sweilam, N. H.; Abou Hasan, M. M.
2016-08-01
This paper reports a new spectral algorithm for obtaining an approximate solution for the Lévy-Feller diffusion equation depending on Legendre polynomials and Chebyshev collocation points. The Lévy-Feller diffusion equation is obtained from the standard diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative. A new formula expressing explicitly any fractional-order derivatives, in the sense of Riesz-Feller operator, of Legendre polynomials of any degree in terms of Jacobi polynomials is proved. Moreover, the Chebyshev-Legendre collocation method together with the implicit Euler method are used to reduce these types of differential equations to a system of algebraic equations which can be solved numerically. Numerical results with comparisons are given to confirm the reliability of the proposed method for the Lévy-Feller diffusion equation.
Global collocation methods for approximation and the solution of partial differential equations
NASA Technical Reports Server (NTRS)
Solomonoff, A.; Turkel, E.
1986-01-01
Polynomial interpolation methods are applied both to the approximation of functions and to the numerical solutions of hyperbolic and elliptic partial differential equations. The derivative matrix for a general sequence of the collocation points is constructed. The approximate derivative is then found by a matrix times vector multiply. The effects of several factors on the performance of these methods including the effect of different collocation points are then explored. The resolution of the schemes for both smooth functions and functions with steep gradients or discontinuities in some derivative are also studied. The accuracy when the gradients occur both near the center of the region and in the vicinity of the boundary is investigated. The importance of the aliasing limit on the resolution of the approximation is investigated in detail. Also examined is the effect of boundary treatment on the stability and accuracy of the scheme.
Compression of multispectral Landsat imagery using the Embedded Zerotree Wavelet (EZW) algorithm
NASA Technical Reports Server (NTRS)
Shapiro, Jerome M.; Martucci, Stephen A.; Czigler, Martin
1994-01-01
The Embedded Zerotree Wavelet (EZW) algorithm has proven to be an extremely efficient and flexible compression algorithm for low bit rate image coding. The embedding algorithm attempts to order the bits in the bit stream in numerical importance and thus a given code contains all lower rate encodings of the same algorithm. Therefore, precise bit rate control is achievable and a target rate or distortion metric can be met exactly. Furthermore, the technique is fully image adaptive. An algorithm for multispectral image compression which combines the spectral redundancy removal properties of the image-dependent Karhunen-Loeve Transform (KLT) with the efficiency, controllability, and adaptivity of the embedded zerotree wavelet algorithm is presented. Results are shown which illustrate the advantage of jointly encoding spectral components using the KLT and EZW.
NASA Astrophysics Data System (ADS)
Parand, K.; Khaleqi, S.
2016-02-01
The Lane-Emden equation has been used to model several phenomena in theoretical physics, mathematical physics and astrophysics such as the theory of stellar structure. This study is an attempt to utilize the collocation method with the rational Chebyshev function of Second kind (RCS) to solve the Lane-Emden equation over the semi-infinite interval [0,+∞[ . According to well-known results and comparing with previous methods, it can be said that this method is efficient and applicable.
Parallel Implementation of a High Order Implicit Collocation Method for the Heat Equation
NASA Technical Reports Server (NTRS)
Kouatchou, Jules; Halem, Milton (Technical Monitor)
2000-01-01
We combine a high order compact finite difference approximation and collocation techniques to numerically solve the two dimensional heat equation. The resulting method is implicit arid can be parallelized with a strategy that allows parallelization across both time and space. We compare the parallel implementation of the new method with a classical implicit method, namely the Crank-Nicolson method, where the parallelization is done across space only. Numerical experiments are carried out on the SGI Origin 2000.
Design and Application of a Collocated Capacitance Sensor for Magnetic Bearing Spindle
NASA Technical Reports Server (NTRS)
Shin, Dongwon; Liu, Seon-Jung; Kim, Jongwon
1996-01-01
This paper presents a collocated capacitance sensor for magnetic bearings. The main feature of the sensor is that it is made of a specific compact printed circuit board (PCB). The signal processing unit has been also developed. The results of the experimental performance evaluation on the sensitivity, resolution and frequency response of the sensor are presented. Finally, an application example of the sensor to the active control of a magnetic bearing is described.
Verdu, G.; Capilla, M.; Talavera, C. F.; Ginestar, D.
2012-07-01
PL equations are classical high order approximations to the transport equations which are based on the expansion of the angular dependence of the angular neutron flux and the nuclear cross sections in terms of spherical harmonics. A nodal collocation method is used to discretize the PL equations associated with a neutron source transport problem. The performance of the method is tested solving two 1D problems with analytical solution for the transport equation and a classical 2D problem. (authors)
Orthogonal cubic spline collocation method for the extended Fisher-Kolmogorov equation
NASA Astrophysics Data System (ADS)
Danumjaya, P.; Pani, Amiya K.
2005-02-01
A second-order splitting combined with orthogonal cubic spline collocation method is formulated and analysed for the extended Fisher-Kolmogorov equation. With the help of Lyapunov functional, a bound in maximum norm is derived for the semidiscrete solution. Optimal error estimates are established for the semidiscrete case. Finally, using the monomial basis functions we present the numerical results in which the integration in time is performed using RADAU 5 software library.
Optimal control of a satellite-robot system using direct collocation with non-linear programming
NASA Astrophysics Data System (ADS)
Coverstone-Carroll, V. L.; Wilkey, N. M.
1995-08-01
The non-holonomic behavior of a satellite-robot system is used to develop the system's equations of motion. The resulting non-linear differential equations are transformed into a non-linear programming problem using direct collocation. The link rates of the robot are minimized along optimal reorientations. Optimal solutions to several maneuvers are obtained and the results are interpreted to gain an understanding of the satellite-robot dynamics.
Single-grid spectral collocation for the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Bernardi, Christine; Canuto, Claudio; Maday, Yvon; Metivet, Brigitte
1988-01-01
The aim of the paper is to study a collocation spectral method to approximate the Navier-Stokes equations: only one grid is used, which is built from the nodes of a Gauss-Lobatto quadrature formula, either of Legendre or of Chebyshev type. The convergence is proven for the Stokes problem provided with inhomogeneous Dirichlet conditions, then thoroughly analyzed for the Navier-Stokes equations. The practical implementation algorithm is presented, together with numerical results.
3-D wavelet compression and progressive inverse wavelet synthesis rendering of concentric mosaic.
Luo, Lin; Wu, Yunnan; Li, Jin; Zhang, Ya-Qin
2002-01-01
Using an array of photo shots, the concentric mosaic offers a quick way to capture and model a realistic three-dimensional (3-D) environment. We compress the concentric mosaic image array with a 3-D wavelet transform and coding scheme. Our compression algorithm and bitstream syntax are designed to ensure that a local view rendering of the environment requires only a partial bitstream, thereby eliminating the need to decompress the entire compressed bitstream before rendering. By exploiting the ladder-like structure of the wavelet lifting scheme, the progressive inverse wavelet synthesis (PIWS) algorithm is proposed to maximally reduce the computational cost of selective data accesses on such wavelet compressed datasets. Experimental results show that the 3-D wavelet coder achieves high-compression performance. With the PIWS algorithm, a 3-D environment can be rendered in real time from a compressed dataset.
NASA Technical Reports Server (NTRS)
Robbins, J. W.
1985-01-01
An autonomous spaceborne gravity gradiometer mission is being considered as a post Geopotential Research Mission project. The introduction of satellite diometry data to geodesy is expected to improve solid earth gravity models. The possibility of utilizing gradiometer data for the determination of pertinent gravimetric quantities on a local basis is explored. The analytical technique of least squares collocation is investigated for its usefulness in local solutions of this type. It is assumed, in the error analysis, that the vertical gravity gradient component of the gradient tensor is used as the raw data signal from which the corresponding reference gradients are removed to create the centered observations required in the collocation solution. The reference gradients are computed from a high degree and order geopotential model. The solution can be made in terms of mean or point gravity anomalies, height anomalies, or other useful gravimetric quantities depending on the choice of covariance types. Selected for this study were 30 x 30 foot mean gravity and height anomalies. Existing software and new software are utilized to implement the collocation technique. It was determined that satellite gradiometry data at an altitude of 200 km can be used successfully for the determination of 30 x 30 foot mean gravity anomalies to an accuracy of 9.2 mgal from this algorithm. It is shown that the resulting accuracy estimates are sensitive to gravity model coefficient uncertainties, data reduction assumptions and satellite mission parameters.
NASA Astrophysics Data System (ADS)
Fascetti, F.; Pierdicca, N.; Pulvirenti, L.; Crapolicchio, R.
2016-10-01
In this work, a comparison between soil moisture products derived from satellite and land model data was performed; in particular, the soil moisture retrievals of SMOS and ASCAT were compared with those of the ERA-Interim/Land model, produced by the ECMWF in a timeframe of 3 years. Subsequently, for a limited period of time, the product from the SMAP radiometer was joined to SMOS, ASCAT and ERA-Interim model data as a fourth dataset. In both cases, the whole H-SAF region of interest, which includes Northern Africa and Europe, was analysed. In order to validate the products, the Triple Collocation technique was applied to estimate the independent error standard deviation of three systems that observe the same target parameter. When more than three datasets were available, the Quadruple Collocation technique was used to jointly estimate the error standard deviation of four sources. Moreover, when the SMOS and SMAP radiometer products were considered, the Extended Collocation was adopted in order to evaluate the error variances of the systems, taking into account the possible presence of an error cross-correlation between the radiometer retrievals.
A novel stochastic collocation method for uncertainty propagation in complex mechanical systems
NASA Astrophysics Data System (ADS)
Qi, WuChao; Tian, SuMei; Qiu, ZhiPing
2015-02-01
This paper presents a novel stochastic collocation method based on the equivalent weak form of multivariate function integral to quantify and manage uncertainties in complex mechanical systems. The proposed method, which combines the advantages of the response surface method and the traditional stochastic collocation method, only sets integral points at the guide lines of the response surface. The statistics, in an engineering problem with many uncertain parameters, are then transformed into a linear combination of simple functions' statistics. Furthermore, the issue of determining a simple method to solve the weight-factor sets is discussed in detail. The weight-factor sets of two commonly used probabilistic distribution types are given in table form. Studies on the computational accuracy and efforts show that a good balance in computer capacity is achieved at present. It should be noted that it's a non-gradient and non-intrusive algorithm with strong portability. For the sake of validating the procedure, three numerical examples concerning a mathematical function with analytical expression, structural design of a straight wing, and flutter analysis of a composite wing are used to show the effectiveness of the guided stochastic collocation method.
Background Subtraction Based on Three-Dimensional Discrete Wavelet Transform.
Han, Guang; Wang, Jinkuan; Cai, Xi
2016-03-30
Background subtraction without a separate training phase has become a critical task, because a sufficiently long and clean training sequence is usually unavailable, and people generally thirst for immediate detection results from the first frame of a video. Without a training phase, we propose a background subtraction method based on three-dimensional (3D) discrete wavelet transform (DWT). Static backgrounds with few variations along the time axis are characterized by intensity temporal consistency in the 3D space-time domain and, hence, correspond to low-frequency components in the 3D frequency domain. Enlightened by this, we eliminate low-frequency components that correspond to static backgrounds using the 3D DWT in order to extract moving objects. Owing to the multiscale analysis property of the 3D DWT, the elimination of low-frequency components in sub-bands of the 3D DWT is equivalent to performing a pyramidal 3D filter. This 3D filter brings advantages to our method in reserving the inner parts of detected objects and reducing the ringing around object boundaries. Moreover, we make use of wavelet shrinkage to remove disturbance of intensity temporal consistency and introduce an adaptive threshold based on the entropy of the histogram to obtain optimal detection results. Experimental results show that our method works effectively in situations lacking training opportunities and outperforms several popular techniques.
Wavelet transforms for electroencephalographic spike and seizure detection
NASA Astrophysics Data System (ADS)
Schiff, Steven J.; Milton, John G.
1993-11-01
The application of wavelet transforms (WT) to experimental data from the nervous system has been hindered by the lack of a straightforward method to handle noise. A noise reduction technique, developed recently for use in wavelet cluster analysis in cosmology and astronomy, is here adapted for electroencephalographic (EEG) time-series data. Noise is filtered using control surrogate data sets generated from randomized aspects of the original time-series. In this study, WT were applied to EEG data from human patients undergoing brain mapping with implanted subdural electrodes for the localization of epileptic seizure foci. EEG data in 1D were analyzed from individual electrodes, and 2D data from electrode grids. These techniques are a powerful means to identify epileptic spikes in such data, and offer a method to identity the onset and spatial extent of epileptic seizure foci. The method is readily applied to the detection of structure in stationary and non-stationary time-series from a variety of physical systems.
Background Subtraction Based on Three-Dimensional Discrete Wavelet Transform
Han, Guang; Wang, Jinkuan; Cai, Xi
2016-01-01
Background subtraction without a separate training phase has become a critical task, because a sufficiently long and clean training sequence is usually unavailable, and people generally thirst for immediate detection results from the first frame of a video. Without a training phase, we propose a background subtraction method based on three-dimensional (3D) discrete wavelet transform (DWT). Static backgrounds with few variations along the time axis are characterized by intensity temporal consistency in the 3D space-time domain and, hence, correspond to low-frequency components in the 3D frequency domain. Enlightened by this, we eliminate low-frequency components that correspond to static backgrounds using the 3D DWT in order to extract moving objects. Owing to the multiscale analysis property of the 3D DWT, the elimination of low-frequency components in sub-bands of the 3D DWT is equivalent to performing a pyramidal 3D filter. This 3D filter brings advantages to our method in reserving the inner parts of detected objects and reducing the ringing around object boundaries. Moreover, we make use of wavelet shrinkage to remove disturbance of intensity temporal consistency and introduce an adaptive threshold based on the entropy of the histogram to obtain optimal detection results. Experimental results show that our method works effectively in situations lacking training opportunities and outperforms several popular techniques. PMID:27043570
Improved successive refinement for wavelet-based embedded image compression
NASA Astrophysics Data System (ADS)
Creusere, Charles D.
1999-10-01
In this paper we consider a new form of successive coefficient refinement which can be used in conjunction with embedded compression algorithms like Shapiro's EZW (Embedded Zerotree Wavelet) and Said & Pearlman's SPIHT (Set Partitioning in Hierarchical Trees). Using the conventional refinement process, the approximation of a coefficient that was earlier determined to be significantly is refined by transmitting one of two symbols--an `up' symbol if the actual coefficient value is in the top half of the current uncertainty interval or a `down' symbol if it is the bottom half. In the modified scheme developed here, we transmit one of 3 symbols instead--`up', `down', or `exact'. The new `exact' symbol tells the decoder that its current approximation of a wavelet coefficient is `exact' to the level of precision desired. By applying this scheme in earlier work to lossless embedded compression (also called lossy/lossless compression), we achieved significant reductions in encoder and decoder execution times with no adverse impact on compression efficiency. These excellent results for lossless systems have inspired us to adapt this refinement approach to lossy embedded compression. Unfortunately, the results we have achieved thus far for lossy compression are not as good.
Wavelet-aided pavement distress image processing
NASA Astrophysics Data System (ADS)
Zhou, Jian; Huang, Peisen S.; Chiang, Fu-Pen
2003-11-01
A wavelet-based pavement distress detection and evaluation method is proposed. This method consists of two main parts, real-time processing for distress detection and offline processing for distress evaluation. The real-time processing part includes wavelet transform, distress detection and isolation, and image compression and noise reduction. When a pavement image is decomposed into different frequency subbands by wavelet transform, the distresses, which are usually irregular in shape, appear as high-amplitude wavelet coefficients in the high-frequency details subbands, while the background appears in the low-frequency approximation subband. Two statistical parameters, high-amplitude wavelet coefficient percentage (HAWCP) and high-frequency energy percentage (HFEP), are established and used as criteria for real-time distress detection and distress image isolation. For compression of isolated distress images, a modified EZW (Embedded Zerotrees of Wavelet coding) is developed, which can simultaneously compress the images and reduce the noise. The compressed data are saved to the hard drive for further analysis and evaluation. The offline processing includes distress classification, distress quantification, and reconstruction of the original image for distress segmentation, distress mapping, and maintenance decision-making. The compressed data are first loaded and decoded to obtain wavelet coefficients. Then Radon transform is then applied and the parameters related to the peaks in the Radon domain are used for distress classification. For distress quantification, a norm is defined that can be used as an index for evaluating the severity and extent of the distress. Compared to visual or manual inspection, the proposed method has the advantages of being objective, high-speed, safe, automated, and applicable to different types of pavements and distresses.
Wavelet transforms as solutions of partial differential equations
Zweig, G.
1997-10-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). Wavelet transforms are useful in representing transients whose time and frequency structure reflect the dynamics of an underlying physical system. Speech sound, pressure in turbulent fluid flow, or engine sound in automobiles are excellent candidates for wavelet analysis. This project focused on (1) methods for choosing the parent wavelet for a continuous wavelet transform in pattern recognition applications and (2) the more efficient computation of continuous wavelet transforms by understanding the relationship between discrete wavelet transforms and discretized continuous wavelet transforms. The most interesting result of this research is the finding that the generalized wave equation, on which the continuous wavelet transform is based, can be used to understand phenomena that relate to the process of hearing.
Application of Hermitian wavelet to crack fault detection in gearbox
NASA Astrophysics Data System (ADS)
Li, Hui; Zhang, Yuping; Zheng, Haiqi
2011-05-01
The continuous wavelet transform enables one to look at the evolution in the time scale joint representation plane. This advantage makes it very suitable for the detection of singularity generated by localized defects in the mechanical system. However, most of the applications of the continuous wavelet transform have widely focused on the use of Morlet wavelet transform. The complex Hermitian wavelet is constructed based on the first and the second derivatives of the Gaussian function to detect signal singularities. The Fourier spectrum of Hermitian wavelet is real; therefore, Hermitian wavelet does not affect the phase of a signal in the complex domain. This gives a desirable ability to extract the singularity characteristic of a signal precisely. In this study, Hermitian wavelet is used to diagnose the gear localized crack fault. The simulative and experimental results show that Hermitian wavelet can extract the transients from strong noise signals and can effectively diagnose the localized gear fault.
Wavelet analysis deformation monitoring data of high-speed railway bridge
NASA Astrophysics Data System (ADS)
Tang, ShiHua; Huang, Qing; Zhou, Conglin; Xu, HongWei; Liu, YinTao; Li, FeiDa
2015-12-01
Deformation monitoring data of high-speed railway bridges will inevitably be affected because of noise pollution, A deformation monitoring point of high-speed railway bridge was measurd by using sokkia SDL30 electronic level for a long time,which got a large number of deformation monitoring data. Based on the characteristics of the deformation monitoring data of high-speed railway bridge, which contain lots of noise. Based on the MATLAB software platform, 120 groups of deformation monitoring data were applied to analysis of wavelet denoising.sym6,db6 wavelet basis function were selected to analyze and remove the noise.The original signal was broken into three layers wavelet,which contain high frequency coefficients and low frequency coefficients.However, high frequency coefficient have plenty of noise.Adaptive method of soft and hard threshold were used to handle in the high frequency coefficient.Then,high frequency coefficient that was removed much of noise combined with low frequency coefficient to reconstitute and obtain reconstruction wavelet signal.Root Mean Square Error (RMSE) and Signal-To-Noise Ratio (SNR) were regarded as evaluation index of denoising,The smaller the root mean square error and the greater signal-to-noise ratio indicate that them have a good effect in denoising. We can surely draw some conclusions in the experimental analysis:the db6 wavelet basis function has a good effect in wavelet denoising by using a adaptive soft threshold method,which root mean square error is minimum and signal-to-noise ratio is maximum.Moreover,the reconstructed image are more smooth than original signal denoising after wavelet denoising, which removed noise and useful signal are obtained in the original signal.Compared to the other three methods, this method has a good effect in denoising, which not only retain useful signal in the original signal, but aiso reach the goal of removing noise. So, it has a strong practical value in a actual deformation monitoring
Harris, Arief R; Schwerdtfeger, Karsten; Strauss, Daniel J
2008-01-01
Local discriminant bases (LDB) have a major disadvantage in their representation which is sensitive to signal translations. The discriminant features will be not consistent when the same but shifted signal is applied. Thus, to overcome this problem, an approximate shift-invariant features extraction based on local discriminant bases is introduced. This technique is based on approximate shift-invariant wavelet packed decomposition which integrate a cost function for decimation decision in each sub-band expansion. This technique gives a consistent best tree selection both in top-down and bottom-up search method. It also provides a consistent wavelet shape in a shape-adapted wavelet method to determine the best wavelet library for a particular signal. This method has an advantage especially in electroencephalographic (EEG) measurement in which there is an inter-individual shift in time for the signals. An application of this method is provided by the discrimination between signals with transcranial magnetic stimulation (TMS) and acoustic-somatosensory stimulation (ASS).
Novel detection of local tooth damage in gears by the wavelet bicoherence
NASA Astrophysics Data System (ADS)
Combet, F.; Gelman, L.; LaPayne, G.
2012-01-01
A new technique, the instantaneous wavelet bicoherence (WB) is proposed and investigated. The use of the instantaneous and locally averaged WB from vibration measurements for local damage detection in gears is investigated for the first time; these bicoherences are better adapted than the classical Fourier bicoherence to the case of non-stationary signals. A new diagnostic feature based on the integrated modulus of the WB in a specific frequency range and a methodology for feature estimation are proposed. The WB techniques are applied to detection of a multiple "like natural" pitting on a back-to-back industrial spur gearbox system and natural pitting on a gear at test rig and show the possibility of early detection of local tooth faults. The detection effectiveness is evaluated by a local Fisher criterion estimated at each angular position of gear for the unpitted and pitted cases. The proposed WB-based diagnostic feature demonstrates robust experimental performance and superior detection capabilities (i.e., effective early damage detection differentially for teeth of the gear wheel) over the conventional detection methods based on the wavelet transform. The reason for this superior effectiveness is that the WB exploits the phase couplings of the wavelet transform at different frequencies, which contain useful additional information for detection of non-linear phenomena induced by local faults. The proposed approaches are compared with the two conventional approaches based on the wavelet transform.
Image wavelet decomposition and applications
NASA Technical Reports Server (NTRS)
Treil, N.; Mallat, S.; Bajcsy, R.
1989-01-01
The general problem of computer vision has been investigated for more that 20 years and is still one of the most challenging fields in artificial intelligence. Indeed, taking a look at the human visual system can give us an idea of the complexity of any solution to the problem of visual recognition. This general task can be decomposed into a whole hierarchy of problems ranging from pixel processing to high level segmentation and complex objects recognition. Contrasting an image at different representations provides useful information such as edges. An example of low level signal and image processing using the theory of wavelets is introduced which provides the basis for multiresolution representation. Like the human brain, we use a multiorientation process which detects features independently in different orientation sectors. So, images of the same orientation but of different resolutions are contrasted to gather information about an image. An interesting image representation using energy zero crossings is developed. This representation is shown to be experimentally complete and leads to some higher level applications such as edge and corner finding, which in turn provides two basic steps to image segmentation. The possibilities of feedback between different levels of processing are also discussed.
Functional calculus using wavelet transforms
NASA Astrophysics Data System (ADS)
Holschneider, Matthias
1994-07-01
It is shown how the wavelet transform may be used to compute for a function s the symbol s(A) for any (not necessarily) self-adjoint operator A whose spectrum is contained in the upper half plane. For self-adjoint operators it is shown that this functional calculus coincides with the usual one. In particular it is shown how the exponential eitA can be written in terms of the resolvent Rz=(A-z)-1 of A as follows: eitA=(1/c) ∫0∞da an-2∫-∞+∞ dbĝ¯ (at)eitbRb-ian(A), with c=-2iπ×∫0∞(dω/ω) (-iω)n-1ĝ¯(ω)e-ω, and n∈N, and the integral is understood as the Cesaro limit. This shows explicitly how the behavior for large t is determined by the behavior of Rz at Iz ≂1/t.
Generalizing Lifted Tensor-Product Wavelets to Irregular Polygonal Domains
Bertram, M.; Duchaineau, M.A.; Hamann, B.; Joy, K.I.
2002-04-11
We present a new construction approach for symmetric lifted B-spline wavelets on irregular polygonal control meshes defining two-manifold topologies. Polygonal control meshes are recursively refined by stationary subdivision rules and converge to piecewise polynomial limit surfaces. At every subdivision level, our wavelet transforms provide an efficient way to add geometric details that are expanded from wavelet coefficients. Both wavelet decomposition and reconstruction operations are based on local lifting steps and have linear-time complexity.
Wavelet Based Feature Extraction for Target Recognition and Minefield Detection
2007-11-02
with Ron Gross (NSWC); presentation of course "Wavelets and Filter Banks " to NSWC personnel; application of simulated annealing to optimize RF absorption...characteristics of multilayer surfaces; generalization of wavelet transform to M-band wavelets; algorithm to generate a wavelet filter bank using any...filter whatsoever as the analysis filter; implementation of an algorithm to parameterize all M-band paraunitary filter banks .
Multiresolution Stochastic Models, Data Fusion, and Wavelet Transforms
1992-05-01
based on the wavelet transform . The statistical structure of these models is Markovian in scale, and in addition the eigenstructure of these models is...given by the wavelet transform . The implication of this is that by using the wavelet transform we can convert the apparently complicated problem of...plays the role of the time-like variable. In addition we show how the wavelet transform , which is defined for signals that extend from -infinity to
Undecimated Wavelet Transforms for Image De-noising
Gyaourova, A; Kamath, C; Fodor, I K
2002-11-19
A few different approaches exist for computing undecimated wavelet transform. In this work we construct three undecimated schemes and evaluate their performance for image noise reduction. We use standard wavelet based de-noising techniques and compare the performance of our algorithms with the original undecimated wavelet transform, as well as with the decimated wavelet transform. The experiments we have made show that our algorithms have better noise removal/blurring ratio.
Wavelet applied to computer vision in astrophysics
NASA Astrophysics Data System (ADS)
Bijaoui, Albert; Slezak, Eric; Traina, Myriam
2004-02-01
Multiscale analyses can be provided by application wavelet transforms. For image processing purposes, we applied algorithms which imply a quasi isotropic vision. For a uniform noisy image, a wavelet coefficient W has a probability density function (PDF) p(W) which depends on the noise statistic. The PDF was determined for many statistical noises: Gauss, Poission, Rayleigh, exponential. For CCD observations, the Anscombe transform was generalized to a mixed Gasus+Poisson noise. From the discrete wavelet transform a set of significant wavelet coefficients (SSWC)is obtained. Many applications have been derived like denoising and deconvolution. Our main application is the decomposition of the image into objects, i.e the vision. At each scale an image labelling is performed in the SSWC. An interscale graph linking the fields of significant pixels is then obtained. The objects are identified using this graph. The wavelet coefficients of the tree related to a given object allow one to reconstruct its image by a classical inverse method. This vision model has been applied to astronomical images, improving the analysis of complex structures.
Embedded wavelet video coding with error concealment
NASA Astrophysics Data System (ADS)
Chang, Pao-Chi; Chen, Hsiao-Ching; Lu, Ta-Te
2000-04-01
We present an error-concealed embedded wavelet (ECEW) video coding system for transmission over Internet or wireless networks. This system consists of two types of frames: intra (I) frames and inter, or predicted (P), frames. Inter frames are constructed by the residual frames formed by variable block-size multiresolution motion estimation (MRME). Motion vectors are compressed by arithmetic coding. The image data of intra frames and residual frames are coded by error-resilient embedded zerotree wavelet (ER-EZW) coding. The ER-EZW coding partitions the wavelet coefficients into several groups and each group is coded independently. Therefore, the error propagation effect resulting from an error is only confined in a group. In EZW coding any single error may result in a totally undecodable bitstream. To further reduce the error damage, we use the error concealment at the decoding end. In intra frames, the erroneous wavelet coefficients are replaced by neighbors. In inter frames, erroneous blocks of wavelet coefficients are replaced by data from the previous frame. Simulations show that the performance of ECEW is superior to ECEW without error concealment by 7 to approximately 8 dB at the error-rate of 10-3 in intra frames. The improvement still has 2 to approximately 3 dB at a higher error-rate of 10-2 in inter frames.
An Adaptive Inpainting Algorithm Based on DCT Induced Wavelet Regularization
2013-01-01
differentiable and its gradient is Lipschitz continuous. This property is particularly important in developing a fast and efficient numerical algorithm for...with Lipschitz continuous gra- dient L(ψ), i.e., ∥∇ψ(f1) − ∇ψ(f2)∥2 ≤ L(ψ)∥f1 − f2∥2 for every f1, f2 ∈ Rn. The corresponding APG algorithm proposed in...entries are uniformly distributed on the interval [0, 255]; 2) Take u1 = f0 and L = L(ψ) as a Lipschitz constant of ∇ψ; 3) For k = 1, 2, . . ., compute a
Higher-density dyadic wavelet transform and its application
NASA Astrophysics Data System (ADS)
Qin, Yi; Tang, Baoping; Wang, Jiaxu
2010-04-01
This paper proposes a higher-density dyadic wavelet transform with two generators, whose corresponding wavelet filters are band-pass and high-pass. The wavelet coefficients at each scale in this case have the same length as the signal. This leads to a new redundant dyadic wavelet transform, which is strictly shift invariant and further increases the sampling in the time dimension. We describe the definition of higher-density dyadic wavelet transform, and discuss the condition of perfect reconstruction of the signal from its wavelet coefficients. The fast implementation algorithm for the proposed transform is given as well. Compared with the higher-density discrete wavelet transform, the proposed transform is shift invariant. Applications into signal denoising indicate that the proposed wavelet transform has better denoising performance than other commonly used wavelet transforms. In the end, various typical wavelet transforms are applied to analyze the vibration signals of two faulty roller bearings, the results show that the proposed wavelet transform can more effectively extract the fault characteristics of the roller bearings than the other wavelet transforms.
The Discrete, Orthogonal Wavelet Transform, A Protective Approach.
1995-09-01
completely determined by the collection of functions onto which it projects. The wavelet transform projects onto a set of functions which satisfy a...simple linear relationship between different levels of dilation. The properties of the wavelet transform are determined by the coefficients of this linear...relationship. This thesis examines the connections between the wavelet transform properties and the linear relationship coefficients. (AN)
[Wavelet entropy analysis of spontaneous EEG signals in Alzheimer's disease].
Zhang, Meiyun; Zhang, Benshu; Chen, Ying
2014-08-01
Wavelet entropy is a quantitative index to describe the complexity of signals. Continuous wavelet transform method was employed to analyze the spontaneous electroencephalogram (EEG) signals of mild, moderate and severe Alzheimer's disease (AD) patients and normal elderly control people in this study. Wavelet power spectrums of EEG signals were calculated based on wavelet coefficients. Wavelet entropies of mild, moderate and severe AD patients were compared with those of normal controls. The correlation analysis between wavelet entropy and MMSE score was carried out. There existed significant difference on wavelet entropy among mild, moderate, severe AD patients and normal controls (P<0.01). Group comparisons showed that wavelet entropy for mild, moderate, severe AD patients was significantly lower than that for normal controls, which was related to the narrow distribution of their wavelet power spectrums. The statistical difference was significant (P<0.05). Further studies showed that the wavelet entropy of EEG and the MMSE score were significantly correlated (r= 0. 601-0. 799, P<0.01). Wavelet entropy is a quantitative indicator describing the complexity of EEG signals. Wavelet entropy is likely to be an electrophysiological index for AD diagnosis and severity assessment.
Time Difference of Arrival (TDOA) Estimation Using Wavelet Based Denoising
1999-03-01
NAVAL POSTGRADUATE SCHOOL Monterey, California THESIS TIME DIFFERENCE OF ARRIVAL (TDOA) ESTIMATION USING WAVELET BASED DENOISING by Unal Aktas...4. TITLE AND SUBTITLE TIME DIFFERENCE OF ARRIVAL (TDOA) ESTIMATION USING WAVELET BASED DENOISING 6. AUTHOR(S) Unal Aktas 7...difference of arrival (TDOA) method. The wavelet transform is used to increase the accuracy of TDOA estimation. Several denoising techniques based on
Brain electrical activity analysis using wavelet-based informational tools
NASA Astrophysics Data System (ADS)
Rosso, O. A.; Martin, M. T.; Plastino, A.
2002-10-01
The traditional way of analyzing brain electrical activity, on the basis of Electroencephalography (EEG) records, relies mainly on visual inspection and years of training. Although it is quite useful, of course, one has to acknowledge its subjective nature that hardly allows for a systematic protocol. In order to overcome this undesirable feature, a quantitative EEG analysis has been developed over the years that introduces objective measures, reflecting not only the characteristics of the brain activity itself but also giving clues concerning the underlying associated neural dynamics. The processing of information by the brain is reflected in dynamical changes of the electrical activity in (i) time, (ii) frequency, and (iii) space. Therefore, the concomitant studies require methods capable of describing the qualitative variation of the signal in both time and frequency. In the present work we introduce new information tools based on the wavelet transform for the assessment of EEG data as adapted to a non-extensive scenario.
Optimization of integer wavelet transforms based on difference correlation structures.
Li, Hongliang; Liu, Guizhong; Zhang, Zhongwei
2005-11-01
In this paper, a novel lifting integer wavelet transform based on difference correlation structure (DCCS-LIWT) is proposed. First, we establish a relationship between the performance of a linear predictor and the difference correlations of an image. The obtained results provide a theoretical foundation for the following construction of the optimal lifting filters. Then, the optimal prediction lifting coefficients in the sense of least-square prediction error are derived. DCCS-LIWT puts heavy emphasis on image inherent dependence. A distinct feature of this method is the use of the variance-normalized autocorrelation function of the difference image to construct a linear predictor and adapt the predictor to varying image sources. The proposed scheme also allows respective calculations of the lifting filters for the horizontal and vertical orientations. Experimental evaluation shows that the proposed method produces better results than the other well-known integer transforms for the lossless image compression.
Obtaining single stimulus evoked potentials with wavelet denoising
NASA Astrophysics Data System (ADS)
Quian Quiroga, R.
2000-11-01
We present a method for the analysis of electroencephalograms (EEG). In particular, small signals due to stimulation, so-called evoked potentials (EPs), have to be detected in the background EEG. This is achieved by using a denoising implementation based on the wavelet decomposition. One recording of visual evoked potentials, and recordings of auditory evoked potentials from four subjects corresponding to different age groups are analyzed. We find higher variability in older individuals. Moreover, since the EPs are identified at the single stimulus level (without need of ensemble averaging), this will allow the calculation of better resolved averages. Since the method is parameter free (i.e. it does not need to be adapted to the particular characteristics of each recording), implementations in clinical settings are imaginable.
Significance tests for the wavelet power and the wavelet power spectrum
NASA Astrophysics Data System (ADS)
Ge, Z.
2007-11-01
Significance tests usually address the issue how to distinguish statistically significant results from those due to pure randomness when only one sample of the population is studied. This issue is also important when the results obtained using the wavelet analysis are to be interpreted. Torrence and Compo (1998) is one of the earliest works that has systematically discussed this problem. Their results, however, were based on Monte Carlo simulations, and hence, failed to unveil many interesting and important properties of the wavelet analysis. In the present work, the sampling distributions of the wavelet power and power spectrum of a Gaussian White Noise (GWN) were derived in a rigorous statistical framework, through which the significance tests for these two fundamental quantities in the wavelet analysis were established. It was found that the results given by Torrence and Compo (1998) are numerically accurate when adjusted by a factor of the sampling period, while some of their statements require reassessment. More importantly, the sampling distribution of the wavelet power spectrum of a GWN was found to be highly dependent on the local covariance structure of the wavelets, a fact that makes the significance levels intimately related to the specific wavelet family. In addition to simulated signals, the significance tests developed in this work were demonstrated on an actual wave elevation time series observed from a buoy on Lake Michigan. In this simple application in geophysics, we showed how proper significance tests helped to sort out physically meaningful peaks from those created by random noise. The derivations in the present work can be readily extended to other wavelet-based quantities or analyses using other wavelet families.
Novel wavelet coder for color image compression
NASA Astrophysics Data System (ADS)
Wang, Houng-Jyh M.; Kuo, C.-C. Jay
1997-10-01
A new still image compression algorithm based on the multi-threshold wavelet coding (MTWC) technique is proposed in this work. It is an embedded wavelet coder in the sense that its compression ratio can be controlled depending on the bandwidth requirement of image transmission. At low bite rates, MTWC can avoid the blocking artifact from JPEG to result in a better reconstructed image quality. An subband decision scheme is developed based on the rate-distortion theory to enhance the image fidelity. Moreover, a new quantization sequence order is introduced based on our analysis of error energy reduction in significant and refinement maps. Experimental results are given to demonstrate the superior performance of the proposed new algorithm in its high reconstructed quality for color and gray level image compression and low computational complexity. Generally speaking, it gives a better rate- distortion tradeoff and performs faster than most existing state-of-the-art wavelet coders.
Analysis of acceleration signals using wavelet transform.
Sekine, M; Tamura, T; Akay, M; Togawa, T; Fukui, Y
2000-06-01
In this study, we attempted to discriminate the acceleration signal for horizontal level and stairway walking using wavelet-based fractal analysis method. The acceleration signal was measured close to the center of gravity of the body, while the subjects walked continuously in the corridor and up and down the stairs. We used the wavelet-based fractal analysis method to discriminate walking pattern. The parameter H which is related directly to the fractal dimension was estimated by the wavelet coefficient and was changed into low value during walking upstairs. By manually setting the threshold level for individual, it was possible to discriminate walking upstairs from the other walking type. However, the common feature among subjects was not shown between level walking and walking downstairs.
Applicability analysis of wavelet-transform profilometry.
Zhang, Zibang; Zhong, Jingang
2013-08-12
The applicability of the wavelet-transform profilometry is examined in detail. The wavelet-ridge-based phase demodulation is an integral operation of the fringe signal in the spatial domain. The accuracy of the phase demodulation is related to the local linearity of the phase modulated by the object surface. We present a more robust applicability condition which is based on the evaluation of the local linearity. Since high carrier frequency leads to the phase demodulation integral in a narrow interval and the narrow interval results in the high local linearity of modulated phase, we propose to increase the carrier fringe frequency to improve the applicability of the wavelet-transform profilometry and the measurement accuracy. The numerical simulations and the experiment are presented.
Wavelet Analysis for Wind Fields Estimation
Leite, Gladeston C.; Ushizima, Daniela M.; Medeiros, Fátima N. S.; de Lima, Gilson G.
2010-01-01
Wind field analysis from synthetic aperture radar images allows the estimation of wind direction and speed based on image descriptors. In this paper, we propose a framework to automate wind direction retrieval based on wavelet decomposition associated with spectral processing. We extend existing undecimated wavelet transform approaches, by including à trous with B3 spline scaling function, in addition to other wavelet bases as Gabor and Mexican-hat. The purpose is to extract more reliable directional information, when wind speed values range from 5 to 10 ms−1. Using C-band empirical models, associated with the estimated directional information, we calculate local wind speed values and compare our results with QuikSCAT scatterometer data. The proposed approach has potential application in the evaluation of oil spills and wind farms. PMID:22219699
Wavelet analysis for wind fields estimation.
Leite, Gladeston C; Ushizima, Daniela M; Medeiros, Fátima N S; de Lima, Gilson G
2010-01-01
Wind field analysis from synthetic aperture radar images allows the estimation of wind direction and speed based on image descriptors. In this paper, we propose a framework to automate wind direction retrieval based on wavelet decomposition associated with spectral processing. We extend existing undecimated wavelet transform approaches, by including à trous with B(3) spline scaling function, in addition to other wavelet bases as Gabor and Mexican-hat. The purpose is to extract more reliable directional information, when wind speed values range from 5 to 10 ms(-1). Using C-band empirical models, associated with the estimated directional information, we calculate local wind speed values and compare our results with QuikSCAT scatterometer data. The proposed approach has potential application in the evaluation of oil spills and wind farms.
New trends in despeckling: undecimated-wavelet shrinkage and fuzzy matching-pursuits estimation
NASA Astrophysics Data System (ADS)
Aiazzi, Bruno; Alparone, Luciano; Argenti, Fabrizio; Baronti, Stefano
2002-02-01
This paper presents two novel approaches to speckle reduction in SAR images. The former relies on the multiplicative speckle model as an MMSE filtering performed in the wavelet domain by means of an adaptive shrinkage of the detail coefficients of an undecimated decomposition. Each coefficient is shrunk by the variance ratio of the noise-free coefficient to the noisy one. All the above quantities are analytically calculated from the speckled image, the noise variance, and the wavelet filters only, without resorting to any model to describe the underlying backscatter. Estimation of the local statistics driving the filter is expedited and layered processing allows to extend adaptivity also across the spatial scale. The latter is not model-based and provides a blind estimation of the backscatter underlying the speckled image stated as a problem of matching pursuits. The local adaptive MMSE estimator is obtained as an expansion in series of a finite number of prototype estimators, fitting the spatial features of the different statistical classes encountered, e.g., edges and textures. Such estimators are calculated in a fuzzy fashion through an automatic training procedure. The space-varying coefficients of the expansion are stated as degrees of fuzzy membership of a pixel to each of the estimators. A thorough performance comparison is carried out with the Gamma-MAP filter and with the Rational Laplacian Pyramid (RLP) filter, recently introduced by three of the authors. On simulated speckled images both the proposed filters gain almost 3 dB SNR with respect to conventional local-statistics (Lee/Kuan) filtering. Experiments carried out on widespread test SAR images and on a speckled mosaic image, comprising synthetic shapes, textures, and details from true SAR images, demonstrate that the visual quality of the results is excellent in terms of both background smoothing and preservation of edge sharpness, textures, and point targets. The absence of decimation in the
Chitchian, Shahab; Mayer, Markus A; Boretsky, Adam R; van Kuijk, Frederik J; Motamedi, Massoud
2012-11-01
ABSTRACT. Image enhancement of retinal structures, in optical coherence tomography (OCT) scans through denoising, has the potential to aid in the diagnosis of several eye diseases. In this paper, a locally adaptive denoising algorithm using double-density dual-tree complex wavelet transform, a combination of the double-density wavelet transform and the dual-tree complex wavelet transform, is applied to reduce speckle noise in OCT images of the retina. The algorithm overcomes the limitations of commonly used multiple frame averaging technique, namely the limited number of frames that can be recorded due to eye movements, by providing a comparable image quality in significantly less acquisition time equal to an order of magnitude less time compared to the averaging method. In addition, improvements of image quality metrics and 5 dB increase in the signal-to-noise ratio are attained.
Mayer, Markus A.; Boretsky, Adam R.; van Kuijk, Frederik J.; Motamedi, Massoud
2012-01-01
Abstract. Image enhancement of retinal structures, in optical coherence tomography (OCT) scans through denoising, has the potential to aid in the diagnosis of several eye diseases. In this paper, a locally adaptive denoising algorithm using double-density dual-tree complex wavelet transform, a combination of the double-density wavelet transform and the dual-tree complex wavelet transform, is applied to reduce speckle noise in OCT images of the retina. The algorithm overcomes the limitations of commonly used multiple frame averaging technique, namely the limited number of frames that can be recorded due to eye movements, by providing a comparable image quality in significantly less acquisition time equal to an order of magnitude less time compared to the averaging method. In addition, improvements of image quality metrics and 5 dB increase in the signal-to-noise ratio are attained. PMID:23117804
Wavelet Multiscale Edge Detection Using An ADALINE Neural Network To Match Up Edge Indicators
2001-12-14
the WMED is modified to use an ADALINE (ADAptive LInear NEuron) neural network that adapts to match up edge indicators across multiple wavelet levels...The ADALINE uses the least mean squared (LMS) learning rule to minimize the mean square error. The LMS algorithm is able to optimize the decision...boundaries of the network. This makes the boundaries more effective in the presence of noise. This paper will test the capability of the ADALINE to match up the edge indicators in noisy two-dimensional sidescan imagery.
Signal extrapolation based on wavelet representation
NASA Astrophysics Data System (ADS)
Xia, Xiang-Gen; Kuo, C.-C. Jay; Zhang, Zhen
1993-11-01
The Papoulis-Gerchberg (PG) algorithm is well known for band-limited signal extrapolation. We consider the generalization of the PG algorithm to signals in the wavelet subspaces in this research. The uniqueness of the extrapolation for continuous-time signals is examined, and sufficient conditions on signals and wavelet bases for the generalized PG (GPG) algorithm to converge are given. We also propose a discrete GPG algorithm for discrete-time signal extrapolation, and investigate its convergence. Numerical examples are given to illustrate the performance of the discrete GPG algorithm.
Numerical Algorithms Based on Biorthogonal Wavelets
NASA Technical Reports Server (NTRS)
Ponenti, Pj.; Liandrat, J.
1996-01-01
Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the corresponding numerical problems. Detailed algorithms are provided as well as the results of numerical tests on partial differential equations defined on the bidimensional torus.
Turbulence dynamics in the wavelet representation
NASA Technical Reports Server (NTRS)
Meneveau, C.
1990-01-01
The phenomenon of small-scale intermittency is shown to motivate the decomposition of the velocity fields into modes that exhibit both localization in wavenumber and physical space. We review some basic properties of such a decomposition, called the wavelet transform. The wavelet-transformed Navier-Stokes equations are derived, and we define a new quantity Pi(r, vector-x, t), which is the flux of kinetic energy to scales smaller than r at position vector-x (at time t). The main goals of this research are also summarized.
Analysis of wavelet technology for NASA applications
NASA Technical Reports Server (NTRS)
Wells, R. O., Jr.
1994-01-01
The purpose of this grant was to introduce a broad group of NASA researchers and administrators to wavelet technology and to determine its future role in research and development at NASA JSC. The activities of several briefings held between NASA JSC scientists and Rice University researchers are discussed. An attached paper, 'Recent Advances in Wavelet Technology', summarizes some aspects of these briefings. Two proposals submitted to NASA reflect the primary areas of common interest. They are image analysis and numerical solutions of partial differential equations arising in computational fluid dynamics and structural mechanics.
a Wavelet Model for Vocalic Speech Coarticulation
NASA Astrophysics Data System (ADS)
Lange, Robert Charles
A known aspect of human speech is that a vowel produced in isolation (for example, "ee") is acoustically different from a production of the same vowel in the company of two consonants ("deed"). This phenomenon, natural to the speech of any language, is known as consonant-vowel -consonant coarticulation. The effect of coarticulation results when a speech segment ("d") dynamically influences the articulation of an adjacent segment ("ee" within "deed"). A recent development in the theory of wavelet signal processing is wavelet system characterization. In wavelet system theory, the wavelet transform is used to describe the time-frequency behavior of a transmission channel, by virtue of its ability to describe the time -frequency content of the system's input and output signals. The present research proposes a wavelet-system model for speech coarticulation; wherein, the system is the process of transformation from a control speech state (input) to an effected speech state (output). Specifically, a vowel produced in isolation is transformed into an effected version of the same vowel produced in consonant-vowel-consonant, via the "coarticulation channel". Quantitatively, the channel is determined by the wavelet transform of the effected vowel's signal, using the control vowel's signal as the mother wavelet. A practical experiment is conducted to evaluate the coarticulation channel using samples of real speech. The results show that the model is capable of depicting coarticulation effects associated with certain vowel-consonant combinations. They suggest that elements of the vowel's acoustic composition are continuously present, in a modified form, throughout the consonant-vowel transition. For other phonetic combinations, however, the model does not respond to instances of segmental transition in a characteristic way. The conclusions drawn from the study are that the wavelet techniques employed here are effective tools for the general analysis of speech sounds, and can
Scalable still image coding based on wavelet
NASA Astrophysics Data System (ADS)
Yan, Yang; Zhang, Zhengbing
2005-02-01
The scalable image coding is an important objective of the future image coding technologies. In this paper, we present a kind of scalable image coding scheme based on wavelet transform. This method uses the famous EZW (Embedded Zero tree Wavelet) algorithm; we give a high-quality encoding to the ROI (region of interest) of the original image and a rough encoding to the rest. This method is applied well in limited memory space condition, and we encode the region of background according to the memory capacity. In this way, we can store the encoded image in limited memory space easily without losing its main information. Simulation results show it is effective.
Wavelet encoding and variable resolution progressive transmission
NASA Technical Reports Server (NTRS)
Blanford, Ronald P.
1993-01-01
Progressive transmission is a method of transmitting and displaying imagery in stages of successively improving quality. The subsampled lowpass image representations generated by a wavelet transformation suit this purpose well, but for best results the order of presentation is critical. Candidate data for transmission are best selected using dynamic prioritization criteria generated from image contents and viewer guidance. We show that wavelets are not only suitable but superior when used to encode data for progressive transmission at non-uniform resolutions. This application does not preclude additional compression using quantization of highpass coefficients, which to the contrary results in superior image approximations at low data rates.
Wavelet analysis applied to the IRAS cirrus
NASA Technical Reports Server (NTRS)
Langer, William D.; Wilson, Robert W.; Anderson, Charles H.
1994-01-01
The structure of infrared cirrus clouds is analyzed with Laplacian pyramid transforms, a form of non-orthogonal wavelets. Pyramid and wavelet transforms provide a means to decompose images into their spatial frequency components such that all spatial scales are treated in an equivalent manner. The multiscale transform analysis is applied to IRAS 100 micrometer maps of cirrus emission in the north Galactic pole region to extract features on different scales. In the maps we identify filaments, fragments and clumps by separating all connected regions. These structures are analyzed with respect to their Hausdorff dimension for evidence of the scaling relationships in the cirrus clouds.
[Application of wavelet transform to infrared analysis].
Li, Dan-ting; Zhang, Chang-jiang; Wang, Jin; Cheng, Cun-gui
2006-11-01
In the present article the FTIR spectra of the xylems of Smilax glabra Roxb. and its three kinds of counterfeits were obtained by Fourier transform infrared spectroscopy (FTIR) with OMNI-sampler directly, fast and accurately. By adopting wavelet transform analytical method the samples were studied in detail. The results showed that wavelet transform could remove the noises and condense variable, and have the advantages of fast operating speed, high degree of accuracy, and no noise disposal. It will have a good application prospect in infrared spectroscopic analysis.
NASA Astrophysics Data System (ADS)
He, Wangpeng; Zi, Yanyang; Chen, Binqiang; Wu, Feng; He, Zhengjia
2015-03-01
Mechanical anomaly is a major failure type of induction motor. It is of great value to detect the resulting fault feature automatically. In this paper, an ensemble super-wavelet transform (ESW) is proposed for investigating vibration features of motor bearing faults. The ESW is put forward based on the combination of tunable Q-factor wavelet transform (TQWT) and Hilbert transform such that fault feature adaptability is enabled. Within ESW, a parametric optimization is performed on the measured signal to obtain a quality TQWT basis that best demonstrate the hidden fault feature. TQWT is introduced as it provides a vast wavelet dictionary with time-frequency localization ability. The parametric optimization is guided according to the maximization of fault feature ratio, which is a new quantitative measure of periodic fault signatures. The fault feature ratio is derived from the digital Hilbert demodulation analysis with an insightful quantitative interpretation. The output of ESW on the measured signal is a selected wavelet scale with indicated fault features. It is verified via numerical simulations that ESW can match the oscillatory behavior of signals without artificially specified. The proposed method is applied to two engineering cases, signals of which were collected from wind turbine and steel temper mill, to verify its effectiveness. The processed results demonstrate that the proposed method is more effective in extracting weak fault features of induction motor bearings compared with Fourier transform, direct Hilbert envelope spectrum, different wavelet transforms and spectral kurtosis.
Parallel object-oriented, denoising system using wavelet multiresolution analysis
Kamath, Chandrika; Baldwin, Chuck H.; Fodor, Imola K.; Tang, Nu A.
2005-04-12
The present invention provides a data de-noising system utilizing processors and wavelet denoising techniques. Data is read and displayed in different formats. The data is partitioned into regions and the regions are distributed onto the processors. Communication requirements are determined among the processors according to the wavelet denoising technique and the partitioning of the data. The data is transforming onto different multiresolution levels with the wavelet transform according to the wavelet denoising technique, the communication requirements, and the transformed data containing wavelet coefficients. The denoised data is then transformed into its original reading and displaying data format.
Mass spectrometry cancer data classification using wavelets and genetic algorithm.
Nguyen, Thanh; Nahavandi, Saeid; Creighton, Douglas; Khosravi, Abbas
2015-12-21
This paper introduces a hybrid feature extraction method applied to mass spectrometry (MS) data for cancer classification. Haar wavelets are employed to transform MS data into orthogonal wavelet coefficients. The most prominent discriminant wavelets are then selected by genetic algorithm (GA) to form feature sets. The combination of wavelets and GA yields highly distinct feature sets that serve as inputs to classification algorithms. Experimental results show the robustness and significant dominance of the wavelet-GA against competitive methods. The proposed method therefore can be applied to cancer classification models that are useful as real clinical decision support systems for medical practitioners.
Unbalanced multiple description wavelet coding for scalable video transmission
NASA Astrophysics Data System (ADS)
Choupani, Roya; Wong, Stephan; Tolun, Mehmet
2012-10-01
Scalable video coding and multiple description coding are the two different adaptation schemes for video transmission over heterogeneous and best-effort networks such as the Internet. We propose a new method to encode video for unreliable networks with rate adaptation capability. Our proposed method groups three dimensional discrete wavelet transform coefficients in different descriptions and applies a modified embedded zero tree data for rate adaptation. The proposed method optimizes the bit-rates of the descriptions with respect to the channel bit rates and the maximum acceptable distortion. The experimental results in the presence of one description loss indicate that on average the videos at the rate of 1000 Kbit/s are reconstructed with Y-component of peak signal to noise ratio (Y-PSNR) value of 36.2 dB. The dynamic allocation of descriptions to the network channels is optimized for rate distortion minimization. The improvement in term of Y-PSNR achieved by rate distortion optimization has been between 0.7 and 5.3 dB in different bit rates.
Study on the FOG's signal based on wavelet
NASA Astrophysics Data System (ADS)
Tang, Ji-qiang; Fang, Jian-cheng; Zhang, Yan-shun
2006-11-01
In order to study on the fiber optical gyro (abbreviated as FOG) signal based on wavelet, this paper researches the FOG signal drift model and the properties of wavelet analyzed noise, introduces the wavelet filtering method, wavelet base selection, soft and hard threshold value de-noising algorithm and compulsive filtering based on The Haar wavelet. These threshold value filtering results of both of the soft and of the hard threshold value for the same wavelet base of db4 with the same Donoho threshold values and these results of compulsive filtering based on The Haar wavelet and db4 wavelet are presented also in this paper and then these main conclusions based on foregoing analysis are reached: Larger the resolving scale is, the filtering effect is more perfect. The soft threshold value filtering effect is better than that of the hard threshold value filtering at the cost of calculation when the threshold value is same. The zero shift of the compulsive filtering is least when both the wavelet and the resolving scale are same for these filtering methods. For the compulsive filtering with same wavelets, the filtering effect of Harr is better than that of db4 and the calculation of the former is fewer. Finally the author point out that applying the compulsive filtering with the Harr wavelet base and suitable resolving scale to the signal processing of FOG be helpful for the FOG's design and manufacturing.
NASA Astrophysics Data System (ADS)
Stevens, D.; Power, H.
2015-10-01
We propose a node-based local meshless method for advective transport problems that is capable of operating on centrally defined stencils and is suitable for shock-capturing purposes. High spatial convergence rates can be achieved; in excess of eighth-order in some cases. Strongly-varying smooth profiles may be captured at infinite Péclet number without instability, and for discontinuous profiles the solution exhibits neutrally stable oscillations that can be damped by introducing a small artificial diffusion parameter, allowing a good approximation to the shock-front to be maintained for long travel times without introducing spurious oscillations. The proposed method is based on local collocation with radial basis functions (RBFs) in a "finite collocation" configuration. In this approach the PDE governing and boundary equations are enforced directly within the local RBF collocation systems, rather than being reconstructed from fixed interpolating functions as is typical of finite difference, finite volume or finite element methods. In this way the interpolating basis functions naturally incorporate information from the governing PDE, including the strength and direction of the convective velocity field. By using these PDE-enhanced interpolating functions an "implicit upwinding" effect is achieved, whereby the flow of information naturally respects the specifics of the local convective field. This implicit upwinding effect allows high-convergence solutions to be obtained on centred stencils for advection problems. The method is formulated using a high-convergence implicit timestepping algorithm based on Richardson extrapolation. The spatial and temporal convergence of the proposed approach is demonstrated using smooth functions with large gradients. The capture of discontinuities is then investigated, showing how the addition of a dynamic stabilisation parameter can damp the neutrally stable oscillations with limited smearing of the shock front.
Well-conditioned fractional collocation methods using fractional Birkhoff interpolation basis
NASA Astrophysics Data System (ADS)
Jiao, Yujian; Wang, Li-Lian; Huang, Can
2016-01-01
The purpose of this paper is twofold. Firstly, we provide explicit and compact formulas for computing both Caputo and (modified) Riemann-Liouville (RL) fractional pseudospectral differentiation matrices (F-PSDMs) of any order at general Jacobi-Gauss-Lobatto (JGL) points. We show that in the Caputo case, it suffices to compute F-PSDM of order μ ∈ (0 , 1) to compute that of any order k + μ with integer k ≥ 0, while in the modified RL case, it is only necessary to evaluate a fractional integral matrix of order μ ∈ (0 , 1). Secondly, we introduce suitable fractional JGL Birkhoff interpolation problems leading to new interpolation polynomial basis functions with remarkable properties: (i) the matrix generated from the new basis yields the exact inverse of F-PSDM at "interior" JGL points; (ii) the matrix of the highest fractional derivative in a collocation scheme under the new basis is diagonal; and (iii) the resulted linear system is well-conditioned in the Caputo case, while in the modified RL case, the eigenvalues of the coefficient matrix are highly concentrated. In both cases, the linear systems of the collocation schemes using the new basis can be solved by an iterative solver within a few iterations. Notably, the inverse can be computed in a very stable manner, so this offers optimal preconditioners for usual fractional collocation methods for fractional differential equations (FDEs). It is also noteworthy that the choice of certain special JGL points with parameters related to the order of the equations can ease the implementation. We highlight that the use of the Bateman's fractional integral formulas and fast transforms between Jacobi polynomials with different parameters, is essential for our algorithm development.
Spectral optical layer properties of cirrus from collocated airborne measurements and simulations
NASA Astrophysics Data System (ADS)
Finger, Fanny; Werner, Frank; Klingebiel, Marcus; Ehrlich, André; Jäkel, Evelyn; Voigt, Matthias; Borrmann, Stephan; Spichtinger, Peter; Wendisch, Manfred
2016-06-01
Spectral upward and downward solar irradiances from vertically collocated measurements above and below a cirrus layer are used to derive cirrus optical layer properties such as spectral transmissivity, absorptivity, reflectivity, and cloud top albedo. The radiation measurements are complemented by in situ cirrus crystal size distribution measurements and radiative transfer simulations based on the microphysical data. The close collocation of the radiative and microphysical measurements, above, beneath, and inside the cirrus, is accomplished by using a research aircraft (Learjet 35A) in tandem with the towed sensor platform AIRTOSS (AIRcraft TOwed Sensor Shuttle). AIRTOSS can be released from and retracted back to the research aircraft by means of a cable up to a distance of 4 km. Data were collected from two field campaigns over the North Sea and the Baltic Sea in spring and late summer 2013. One measurement flight over the North Sea proved to be exemplary, and as such the results are used to illustrate the benefits of collocated sampling. The radiative transfer simulations were applied to quantify the impact of cloud particle properties such as crystal shape, effective radius reff, and optical thickness τ on cirrus spectral optical layer properties. Furthermore, the radiative effects of low-level, liquid water (warm) clouds as frequently observed beneath the cirrus are evaluated. They may cause changes in the radiative forcing of the cirrus by a factor of 2. When low-level clouds below the cirrus are not taken into account, the radiative cooling effect (caused by reflection of solar radiation) due to the cirrus in the solar (shortwave) spectral range is significantly overestimated.
Denoising and robust non-linear wavelet analysis
NASA Astrophysics Data System (ADS)
Bruce, Andrew G.; Donoho, David L.; Gao, Hong-Ye; Martin, R. D.
1994-04-01
In a series of papers, Donoho and Johnstone develop a powerful theory based on wavelets for extracting non-smooth signals from noisy data. Several nonlinear smoothing algorithms are presented which provide high performance for removing Gaussian noise from a wide range of spatially inhomogeneous signals. However, like other methods based on the linear wavelet transform, these algorithms are very sensitive to certain types of non-Gaussian noise, such as outliers. In this paper, we develop outlier resistance wavelet transforms. In these transforms, outliers and outlier patches are localized to just a few scales. By using the outlier resistant wavelet transforms, we improve upon the Donoho and Johnstone nonlinear signal extraction methods. The outlier resistant wavelet algorithms are included with the S+Wavelets object-oriented toolkit for wavelet analysis.
Lossless Video Sequence Compression Using Adaptive Prediction
NASA Technical Reports Server (NTRS)
Li, Ying; Sayood, Khalid
2007-01-01
We present an adaptive lossless video compression algorithm based on predictive coding. The proposed algorithm exploits temporal, spatial, and spectral redundancies in a backward adaptive fashion with extremely low side information. The computational complexity is further reduced by using a caching strategy. We also study the relationship between the operational domain for the coder (wavelet or spatial) and the amount of temporal and spatial redundancy in the sequence being encoded. Experimental results show that the proposed scheme provides significant improvements in compression efficiencies.
A Fourier collocation time domain method for numerically solving Maxwell's equations
NASA Technical Reports Server (NTRS)
Shebalin, John V.
1991-01-01
A new method for solving Maxwell's equations in the time domain for arbitrary values of permittivity, conductivity, and permeability is presented. Spatial derivatives are found by a Fourier transform method and time integration is performed using a second order, semi-implicit procedure. Electric and magnetic fields are collocated on the same grid points, rather than on interleaved points, as in the Finite Difference Time Domain (FDTD) method. Numerical results are presented for the propagation of a 2-D Transverse Electromagnetic (TEM) mode out of a parallel plate waveguide and into a dielectric and conducting medium.
Application of Collocated GPS and Seismic Sensors to Earthquake Monitoring and Early Warning
Li, Xingxing; Zhang, Xiaohong; Guo, Bofeng
2013-01-01
We explore the use of collocated GPS and seismic sensors for earthquake monitoring and early warning. The GPS and seismic data collected during the 2011 Tohoku-Oki (Japan) and the 2010 El Mayor-Cucapah (Mexico) earthquakes are analyzed by using a tightly-coupled integration. The performance of the integrated results is validated by both time and frequency domain analysis. We detect the P-wave arrival and observe small-scale features of the movement from the integrated results and locate the epicenter. Meanwhile, permanent offsets are extracted from the integrated displacements highly accurately and used for reliable fault slip inversion and magnitude estimation. PMID:24284765
Legendre spectral-collocation method for solving some types of fractional optimal control problems.
Sweilam, Nasser H; Al-Ajami, Tamer M
2015-05-01
In this paper, the Legendre spectral-collocation method was applied to obtain approximate solutions for some types of fractional optimal control problems (FOCPs). The fractional derivative was described in the Caputo sense. Two different approaches were presented, in the first approach, necessary optimality conditions in terms of the associated Hamiltonian were approximated. In the second approach, the state equation was discretized first using the trapezoidal rule for the numerical integration followed by the Rayleigh-Ritz method to evaluate both the state and control variables. Illustrative examples were included to demonstrate the validity and applicability of the proposed techniques.
Legendre spectral-collocation method for solving some types of fractional optimal control problems
Sweilam, Nasser H.; Al-Ajami, Tamer M.
2014-01-01
In this paper, the Legendre spectral-collocation method was applied to obtain approximate solutions for some types of fractional optimal control problems (FOCPs). The fractional derivative was described in the Caputo sense. Two different approaches were presented, in the first approach, necessary optimality conditions in terms of the associated Hamiltonian were approximated. In the second approach, the state equation was discretized first using the trapezoidal rule for the numerical integration followed by the Rayleigh–Ritz method to evaluate both the state and control variables. Illustrative examples were included to demonstrate the validity and applicability of the proposed techniques. PMID:26257937
Sinc-Chebyshev Collocation Method for a Class of Fractional Diffusion-Wave Equations
Mao, Zhi; Xiao, Aiguo; Yu, Zuguo; Shi, Long
2014-01-01
This paper is devoted to investigating the numerical solution for a class of fractional diffusion-wave equations with a variable coefficient where the fractional derivatives are described in the Caputo sense. The approach is based on the collocation technique where the shifted Chebyshev polynomials in time and the sinc functions in space are utilized, respectively. The problem is reduced to the solution of a system of linear algebraic equations. Through the numerical example, the procedure is tested and the efficiency of the proposed method is confirmed. PMID:24977177
A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation
NASA Technical Reports Server (NTRS)
Jones, Brandon A.; Anderson, Rodney L.
2012-01-01
Demands on numerical integration algorithms for astrodynamics applications continue to increase. Common methods, like explicit Runge-Kutta, meet the orbit propagation needs of most scenarios, but more specialized scenarios require new techniques to meet both computational efficiency and accuracy needs. This paper provides an extensive survey on the application of symplectic and collocation methods to astrodynamics. Both of these methods benefit from relatively recent theoretical developments, which improve their applicability to artificial satellite orbit propagation. This paper also details their implementation, with several tests demonstrating their advantages and disadvantages.
Numerical Algorithm Based on Haar-Sinc Collocation Method for Solving the Hyperbolic PDEs
Javadi, H. H. S.; Navidi, H. R.
2014-01-01
The present study investigates the Haar-Sinc collocation method for the solution of the hyperbolic partial telegraph equations. The advantages of this technique are that not only is the convergence rate of Sinc approximation exponential but the computational speed also is high due to the use of the Haar operational matrices. This technique is used to convert the problem to the solution of linear algebraic equations via expanding the required approximation based on the elements of Sinc functions in space and Haar functions in time with unknown coefficients. To analyze the efficiency, precision, and performance of the proposed method, we presented four examples through which our claim was confirmed. PMID:25485295
The solution of singular optimal control problems using direct collocation and nonlinear programming
NASA Astrophysics Data System (ADS)
Downey, James R.; Conway, Bruce A.
1992-08-01
This paper describes work on the determination of optimal rocket trajectories which may include singular arcs. In recent years direct collocation and nonlinear programming has proven to be a powerful method for solving optimal control problems. Difficulties in the application of this method can occur if the problem is singular. Techniques exist for solving singular problems indirectly using the associated adjoint formulation. Unfortunately, the adjoints are not a part of the direct formulation. It is shown how adjoint information can be obtained from the direct method to allow the solution of singular problems.
Modelling Of Displacement Washing Of Pulp Bed Using Orthogonal Collocation On Finite Elements
NASA Astrophysics Data System (ADS)
Arora, Shelly; PotÅ¯ček, František; Dhaliwal, S. S.; Kukreja, V. K.
2009-07-01
Mechanism of displacement washing of packed bed of porous, compressible and cylindrical particles, e.g., fibers is presented with the help of an axial dispersion model involving Peclet number (Pe) and Biot number (Bi). Bulk fluid concentration and intra-pore solute concentration are related by Langmuir adsorption isotherm. Model equations have been solved using orthogonal collocation on finite elements using Lagrangian interpolating polynomials as base functions. Displacement washing has been simulated using a laboratory washing cell and experiments have been performed on pulp beds formed from unbeaten, unbleached kraft fibers. Model predicted values have been compared with experimental values to check the applicability of the method.