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650
Singularity Detection And Processing With Wavelets
 IEEE Transactions on Information Theory
, 1992
"... Most of a signal information is often found in irregular structures and transient phenomena. We review the mathematical characterization of singularities with Lipschitz exponents. The main theorems that estimate local Lipschitz exponents of functions, from the evolution across scales of their wavele ..."
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Cited by 595 (13 self)
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Most of a signal information is often found in irregular structures and transient phenomena. We review the mathematical characterization of singularities with Lipschitz exponents. The main theorems that estimate local Lipschitz exponents of functions, from the evolution across scales
Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps
 Proceedings of the National Academy of Sciences
, 2005
"... of contexts of data analysis, such as spectral graph theory, manifold learning, nonlinear principal components and kernel methods. We augment these approaches by showing that the diffusion distance is a key intrinsic geometric quantity linking spectral theory of the Markov process, Laplace operators ..."
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Cited by 257 (45 self)
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operators, or kernels, to the corresponding geometry and density of the data. This opens the door to the application of methods from numerical analysis and signal processing to the analysis of functions and transformations of the data. Abstract. We provide a framework for structural multiscale geometric
TOEPLITZSTRUCTURED COMPRESSED SENSING MATRICES
"... The problem of recovering a sparse signal x ∈ R n from a relatively small number of its observations of the form y = Ax ∈ R k, where A is a known matrix and k ≪ n, has recently received a lot of attention under the rubric of compressed sensing (CS) and has applications in many areas of signal proces ..."
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Cited by 92 (7 self)
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algorithms; and (iii) Toeplitzstructured matrices arise naturally in certain application areas such as system identification. Index Terms — Compressed sensing, restricted isometry property, system identification, Toeplitz matrices, underdetermined systems of linear equations 1.1. Background 1.
SPIRAL: Code Generation for DSP Transforms
 PROCEEDINGS OF THE IEEE SPECIAL ISSUE ON PROGRAM GENERATION, OPTIMIZATION, AND ADAPTATION
"... Fast changing, increasingly complex, and diverse computing platforms pose central problems in scientific computing: How to achieve, with reasonable effort, portable optimal performance? We present SPIRAL that considers this problem for the performancecritical domain of linear digital signal proces ..."
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Cited by 222 (41 self)
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processing (DSP) transforms. For a specified transform, SPIRAL automatically generates high performance code that is tuned to the given platform. SPIRAL formulates the tuning as an optimization problem, and exploits the domainspecific mathematical structure of transform algorithms to implement a feedback
A Fast Eigenvalue Algorithm for Hankel Matrices
 Linear Algebra Appl
, 1998
"... We present an algorithm that can nd all the eigenvalues of an nn complex Hankel matrix in O(n 2 log n) operations. Our scheme consists of an O(n 2 log n) Lanczostype tridiagonalization procedure and an O(n) QRtype diagonalization method. Keywords: Hankel matrix, Toeplitz matrix, circulant mat ..."
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Cited by 10 (5 self)
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matrix, fast Fourier transform, Lanczos tridiagonalization, eigenvalue decomposition, complexsymmetric matrix, complexorthogonal transformations. 1 INTRODUCTION The eigenvalue decomposition of a structured matrix has important applications in signal processing. Common occurring structures include an n
A Fast Algorithm for Deblurring Models with Neumann Boundary Conditions
, 1999
"... Blur removal is an important problem in signal and image processing. The blurring matrices obtained by using the zero boundary condition (corresponding to assuming dark background outside the scene) are Toeplitz matrices for 1dimensional problems and blockToeplitz Toeplitzblock matrices for 2dim ..."
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Cited by 107 (25 self)
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Blur removal is an important problem in signal and image processing. The blurring matrices obtained by using the zero boundary condition (corresponding to assuming dark background outside the scene) are Toeplitz matrices for 1dimensional problems and blockToeplitz Toeplitzblock matrices for 2
Bayesian TreeStructured Image Modeling using Waveletdomain Hidden Markov Models
 IEEE Trans. Image Processing
, 1999
"... Waveletdomain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hidden Markov tree (HMT) model captures the key features of the joint probability density of the wavelet coefficients of realworld data. One potential drawback to the HMT framework ..."
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Cited by 184 (15 self)
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using a series of image estimation /denoising experiments that these two new models retain nearly all of the key structure modeled by the full HMT. Finally, we propose a fast shiftinvariant HMT estimation algorithm that outperforms other waveletbased estimators in the current literature, both
A Fast Eigenvalue Algorithm for Hankel Matrices
 Linear Algebra Appl
, 1998
"... We present an algorithm that can nd all the eigenvalues of an nn complex Hankel matrix in O(n 2 log n) operations. Our scheme consists of an O(n 2 log n) Lanczostype tridiagonalization procedure and an O(n) QRtype diagonalization method. Keywords: Hankel matrix, Toeplitz matrix, circulant mat ..."
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matrix, fast Fourier transform, Lanczos tridiagonalization, eigenvalue decomposition, complexsymmetric matrix, complexorthogonal transformations. 1 INTRODUCTION The eigenvalue decomposition of a structured matrix has important applications in signal processing. Common occurring structures include an n
Conjugate Gradient Methods for Toeplitz Systems
 SIAM Review
, 1996
"... In this expository paper, we survey some of the latest developments on using preconditioned conjugate gradient methods for solving Toeplitz systems. One of the main results is that the complexity of solving a large class of nbyn Toeplitz systems is reduced to O(n log n) operations as compared to O ..."
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Cited by 174 (40 self)
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series analysis are given. Key words. Toeplitz matrices, preconditioners, preconditioned conjugate gradient methods, differential equations, signal and image processing, time series, queueing problems, integral equations. AMS Subject classifications. 45E10, 62M10, 65F10, 65N22, 65P05, 68U10, 93E11
FAST COMPRESSIVE SAMPLING WITH STRUCTURALLY RANDOM MATRICES
"... This paper presents a novel framework of fast and efficient compressive sampling based on the new concept of structurally random matrices. The proposed framework provides four important features. (i) It is universal with a variety of sparse signals. (ii) The number of measurements required for exact ..."
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Cited by 34 (7 self)
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This paper presents a novel framework of fast and efficient compressive sampling based on the new concept of structurally random matrices. The proposed framework provides four important features. (i) It is universal with a variety of sparse signals. (ii) The number of measurements required
Results 1  10
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