The Cosparse Analysis Model and Algorithms
TLDR
In this article, the authors take a closer look at the analysis approach, better define it as a generative model for signals, and contrast it with the synthesis one, and propose effective pursuit methods that aim to solve inverse problems regularized with the analysis-model prior.About:
This article is published in Applied and Computational Harmonic Analysis.The article was published on 2013-01-01 and is currently open access. It has received 421 citations till now. The article focuses on the topics: Generative model & Sparse approximation.read more
Citations
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Analysis K-SVD: A Dictionary-Learning Algorithm for the Analysis Sparse Model
TL;DR: This paper presents an alternative, analysis-based model, where an analysis operator-hereafter referred to as the analysis dictionary-multiplies the signal, leading to a sparse outcome.
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An introduction to continuous optimization for imaging
Antonin Chambolle,Thomas Pock +1 more
TL;DR: The state of the art in continuous optimization methods for such problems, and particular emphasis on optimal first-order schemes that can deal with typical non-smooth and large-scale objective functions used in imaging problems are described.
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Sparse Regularization via Convex Analysis
TL;DR: A class of nonconvex penalty functions that maintain the convexity of the least squares cost function to be minimized, and avoids the systematic underestimation characteristic of L1 norm regularization are proposed.
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Stable Image Reconstruction Using Total Variation Minimization
Deanna Needell,Rachel Ward +1 more
TL;DR: It is shown that from nonadaptive linear measurements, an image can be reconstructed to within the best best-term approximation of its gradient up to a logarithmic factor, and this factor can be removed by taking slightly more measurements.
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Nonconvex Sparse Regularization and Convex Optimization for Bearing Fault Diagnosis
TL;DR: A nonconvex sparse regularization method for bearing fault diagnosis is proposed based on the generalized minimax-concave (GMC) penalty, which maintains the convexity of the sparsity-regularized least squares cost function, and thus the global minimum can be solved by convex optimization algorithms.
References
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Book
A wavelet tour of signal processing
TL;DR: An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.
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Nonlinear total variation based noise removal algorithms
TL;DR: In this article, a constrained optimization type of numerical algorithm for removing noise from images is presented, where the total variation of the image is minimized subject to constraints involving the statistics of the noise.
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Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
TL;DR: In this paper, the authors considered the model problem of reconstructing an object from incomplete frequency samples and showed that with probability at least 1-O(N/sup -M/), f can be reconstructed exactly as the solution to the lscr/sub 1/ minimization problem.
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Atomic Decomposition by Basis Pursuit
TL;DR: Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions.
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Matching pursuits with time-frequency dictionaries
Stéphane Mallat,Zhifeng Zhang +1 more
TL;DR: The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions, chosen in order to best match the signal structures.