The Experts below are selected from a list of 246 Experts worldwide ranked by ideXlab platform
Alan Willsky - One of the best experts on this subject based on the ideXlab platform.
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Multiscale system theory
IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1994Co-Authors: Albert Benveniste, Ramine Nikoukhah, Alan WillskyAbstract:In many applications it is of interest to analyze and recognize phenomena occurring at different scales. The recently introduced wavelet transforms provide a time-and-scale decomposition of signals that offers the possibility of such an analysis. Until recently, however, there has been no corresponding statistical framework to support the development of optimal, multiscale statistical signal processing algorithms. A recent work of some of the present authors and co-authors proposed such a framework via models of "stochastic fractals" on the Dyadic Tree. This paper investigates some of the fundamental issues that are relevant to system theories on the Dyadic Tree, both for systems and signals. >
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Multiscale systems, Kalman filters, and Riccati equations
IEEE Transactions on Automatic Control, 1994Co-Authors: K.c. Chou, Alan Willsky, Ramine NikoukhahAbstract:An algorithm analogous to the Rauch-Tung-Striebel algorithm/spl minus/consisting of a fine-to-coarse Kalman filter-like sweep followed by a coarse-to-fine smoothing step/spl minus/was developed previously by the authors (ibid. vol.39, no.3, p.464-78 (1994)). In this paper they present a detailed system-theoretic analysis of this filter and of the new scale-recursive Riccati equation associated with it. While this analysis is similar in spirit to that for standard Kalman filters, the structure of the Dyadic Tree leads to several significant differences. In particular, the structure of the Kalman filter error dynamics leads to the formulation of an ML version of the filtering equation and to a corresponding smoothing algorithm based on triangularizing the Hamiltonian for the smoothing problem. In addition, the notion of stability for dynamics requires some care as do the concepts of reachability and observability. Using these system-theoretic constructs, the stability and steady-state behavior of the fine-to-coarse Kalman filter and its Riccati equation are analysed. >
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Multiscale recursive estimation, data fusion, and regularization
IEEE Transactions on Automatic Control, 1994Co-Authors: K.c. Chou, Alan Willsky, Albert BenvenisteAbstract:We describe a framework for modeling stochastic phenomena at multiple scales and for their efficient estimation or reconstruction given partial and/or noisy measurements which may also be at several scales. In particular multiscale signal representations lead naturally to pyramidal or Tree-like data structures in which each level in the Tree corresponds to a particular scale of representation. A class of multiscale dynamic models evolving on Dyadic Trees is introduced. The main focus of this paper is on the description, analysis, and application of an extremely efficient optimal estimation algorithm for this class of models. This algorithm consists of a fine-to-coarse filtering sweep, followed by a coarse-to-fine smoothing step, corresponding to the Dyadic Tree generalization of Kalman filtering and Rauch-Tung-Striebel smoothing. The Kalman filtering sweep consists of the recursive application of three steps: a measurement update step, a fine-to-coarse prediction step, and a fusion step. We illustrate the use of our methodology for the fusion of multiresolution data and for the efficient solution of "fractal regularizations" of ill-posed signal and image processing problems encountered. >
Peter J. Ramadge - One of the best experts on this subject based on the ideXlab platform.
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ICIP - Learning a wavelet Tree for multichannel image denoising
2011 18th IEEE International Conference on Image Processing, 2011Co-Authors: Zhen James Xiang, Pingmei Xu, Zhuo Zhang, Peter J. RamadgeAbstract:We propose a new multichannel image denoising algorithm. To exploit important inter-channel dependencies, we first use dynamic programming to learn an explicit Dyadic Tree representation of the common structure of the channels. Based on this Dyadic Tree, optimal Haar wavelet thresholding is then applied to denoise the image. In addition to the original channels, the algorithm can employ multiple derived channels to improve Tree learning. Experimental results confirm that the approach improves multichannel image denoising performance both in PSNR and in edge preservation.
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Edge-Preserving Image Regularization Based on Morphological Wavelets and Dyadic Trees
IEEE transactions on image processing : a publication of the IEEE Signal Processing Society, 2011Co-Authors: Z. J. Xiang, Peter J. RamadgeAbstract:Despite the tremendous success of wavelet-based image regularization, we still lack a comprehensive understanding of the exact factor that controls edge preservation and a principled method to determine the wavelet decomposition structure for dimensions greater than 1. We address these issues from a machine learning perspective by using Tree classifiers to underpin a new image regularizer that measures the complexity of an image based on the complexity of the Dyadic-Tree representations of its sublevel sets. By penalizing unbalanced Dyadic Trees less, the regularizer preserves sharp edges. The main contribution of this paper is the connection of concepts from structured Dyadic-Tree complexity measures, wavelet shrinkage, morphological wavelets, and smoothness regularization in Besov space into a single coherent image regularization framework. Using the new regularizer, we also provide a theoretical basis for the data-driven selection of an optimal Dyadic wavelet decomposition structure. As a specific application example, we give a practical regularized image denoising algorithm that uses this regularizer and the optimal Dyadic wavelet decomposition structure.
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ICIP - Morphological wavelet transform with adaptive Dyadic structures
2010 IEEE International Conference on Image Processing, 2010Co-Authors: Zhen James Xiang, Peter J. RamadgeAbstract:We propose a two component method for denoising multidimensional signals, e.g. images. The first component uses a dynamic programing algorithm of complexity O (N log N) to find an optimal Dyadic Tree representation of a given multidimensional signal of N samples. The second component takes a signal with given Dyadic Tree representation and formulates the denoising problem for this signal as a Second Order Cone Program of size O (N). To solve the overall denoising problem, we apply these two algorithms iteratively to search for a jointly optimal denoised signal and Dyadic Tree representation. Experiments on images confirm that the approach yields denoised signals with improved PSNR and edge preservation.
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ICASSP - Morphological wavelets and the complexity of Dyadic Trees
2010 IEEE International Conference on Acoustics Speech and Signal Processing, 2010Co-Authors: Zhen James Xiang, Peter J. RamadgeAbstract:In this paper we reveal a connection between the coefficients of the morphological wavelet transform and complexity measures of Dyadic Tree representations of level sets. This leads to better understanding of the edge preserving property that has been discovered in both areas. As an immediate application, we examine a depth-adaptive soft thresholding scheme on morphological wavelet coefficients in which the threshold decays geometrically as the resolution increases. A greater decay rate gives greater preference towards unbalanced Trees and this can control edge enhancement in denoised signals.
Ramine Nikoukhah - One of the best experts on this subject based on the ideXlab platform.
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Multiscale system theory
IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1994Co-Authors: Albert Benveniste, Ramine Nikoukhah, Alan WillskyAbstract:In many applications it is of interest to analyze and recognize phenomena occurring at different scales. The recently introduced wavelet transforms provide a time-and-scale decomposition of signals that offers the possibility of such an analysis. Until recently, however, there has been no corresponding statistical framework to support the development of optimal, multiscale statistical signal processing algorithms. A recent work of some of the present authors and co-authors proposed such a framework via models of "stochastic fractals" on the Dyadic Tree. This paper investigates some of the fundamental issues that are relevant to system theories on the Dyadic Tree, both for systems and signals. >
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Multiscale systems, Kalman filters, and Riccati equations
IEEE Transactions on Automatic Control, 1994Co-Authors: K.c. Chou, Alan Willsky, Ramine NikoukhahAbstract:An algorithm analogous to the Rauch-Tung-Striebel algorithm/spl minus/consisting of a fine-to-coarse Kalman filter-like sweep followed by a coarse-to-fine smoothing step/spl minus/was developed previously by the authors (ibid. vol.39, no.3, p.464-78 (1994)). In this paper they present a detailed system-theoretic analysis of this filter and of the new scale-recursive Riccati equation associated with it. While this analysis is similar in spirit to that for standard Kalman filters, the structure of the Dyadic Tree leads to several significant differences. In particular, the structure of the Kalman filter error dynamics leads to the formulation of an ML version of the filtering equation and to a corresponding smoothing algorithm based on triangularizing the Hamiltonian for the smoothing problem. In addition, the notion of stability for dynamics requires some care as do the concepts of reachability and observability. Using these system-theoretic constructs, the stability and steady-state behavior of the fine-to-coarse Kalman filter and its Riccati equation are analysed. >
Minh N. - One of the best experts on this subject based on the ideXlab platform.
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Best basis search in lapped dictionaries
IEEE Transactions on Signal Processing, 2006Co-Authors: Yan Huang, Ilya Pollak, Charles A. Bouman, Minh N.Abstract:This paper proposes, analyzes, and illustrates several best basis search algorithms for dictionaries consisting of lapped orthogonal bases. It improves upon the best local cosine basis selection based on a Dyadic Tree , by considering larger dictionaries of bases. It is shown that this can result in sparser representations and approximate shift invariance. An algorithm that is strictly shift invariant is also provided. The experiments in this paper suggest that the new dictionaries can be advantageous for time-frequency analysis, compression, and noise removal. Accelerated versions of the basic algorithm are provided that explore various tradeoffs between computational efficiency and adaptability. It is shown that the proposed algorithms are in fact applicable to any finite dictionary comprised of lapped orthogonal bases. One such novel dictionary is proposed that constructs the best local cosine representation in the frequency domain, and it is shown that the new dictionary is better suited for representing certain types of signals.
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Computational Imaging - Time-frequency analysis with best local cosine bases
Computational Imaging II, 2004Co-Authors: Yan Huang, Ilya Pollak, Charles A. Bouman, Minh N.Abstract:We propose new best basis search algorithms for local cosine dictionaries. We provide several algorithms for dictionaries of various complexity. Our framework generalizes the classical best local cosine basis selection based on a Dyadic Tree.
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ICASSP (2) - New algorithms for best local cosine basis search
2004 IEEE International Conference on Acoustics Speech and Signal Processing, 1Co-Authors: Yan Huang, Ilya Pollak, Charles A. Bouman, Minh N.Abstract:We propose a best basis search algorithm for local cosine dictionaries. We improve upon the classical best local cosine basis selection based on a Dyadic Tree (Coifman, R.R. and Wickerhauser, M.V., IEEE Trans. Inf. Th., vol.38, no.2, p.713-18, 1992), by considering a larger dictionary of bases. This results in more compact representations, lower costs, and approximate shift-invariance. We also provide a version of our algorithm which is strictly shift-invariant.
K.c. Chou - One of the best experts on this subject based on the ideXlab platform.
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Multiscale systems, Kalman filters, and Riccati equations
IEEE Transactions on Automatic Control, 1994Co-Authors: K.c. Chou, Alan Willsky, Ramine NikoukhahAbstract:An algorithm analogous to the Rauch-Tung-Striebel algorithm/spl minus/consisting of a fine-to-coarse Kalman filter-like sweep followed by a coarse-to-fine smoothing step/spl minus/was developed previously by the authors (ibid. vol.39, no.3, p.464-78 (1994)). In this paper they present a detailed system-theoretic analysis of this filter and of the new scale-recursive Riccati equation associated with it. While this analysis is similar in spirit to that for standard Kalman filters, the structure of the Dyadic Tree leads to several significant differences. In particular, the structure of the Kalman filter error dynamics leads to the formulation of an ML version of the filtering equation and to a corresponding smoothing algorithm based on triangularizing the Hamiltonian for the smoothing problem. In addition, the notion of stability for dynamics requires some care as do the concepts of reachability and observability. Using these system-theoretic constructs, the stability and steady-state behavior of the fine-to-coarse Kalman filter and its Riccati equation are analysed. >
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Multiscale recursive estimation, data fusion, and regularization
IEEE Transactions on Automatic Control, 1994Co-Authors: K.c. Chou, Alan Willsky, Albert BenvenisteAbstract:We describe a framework for modeling stochastic phenomena at multiple scales and for their efficient estimation or reconstruction given partial and/or noisy measurements which may also be at several scales. In particular multiscale signal representations lead naturally to pyramidal or Tree-like data structures in which each level in the Tree corresponds to a particular scale of representation. A class of multiscale dynamic models evolving on Dyadic Trees is introduced. The main focus of this paper is on the description, analysis, and application of an extremely efficient optimal estimation algorithm for this class of models. This algorithm consists of a fine-to-coarse filtering sweep, followed by a coarse-to-fine smoothing step, corresponding to the Dyadic Tree generalization of Kalman filtering and Rauch-Tung-Striebel smoothing. The Kalman filtering sweep consists of the recursive application of three steps: a measurement update step, a fine-to-coarse prediction step, and a fusion step. We illustrate the use of our methodology for the fusion of multiresolution data and for the efficient solution of "fractal regularizations" of ill-posed signal and image processing problems encountered. >
