Open Access
Signal Recovery from Random Measurements Via Orthogonal Matching Pursuit: The Gaussian Case
Joel A. Tropp,Anna C. Gilbert +1 more
TLDR
In this paper, a greedy algorithm called Orthogonal Matching Pursuit (OMP) was proposed to recover a signal with m nonzero entries in dimension 1 given O(m n d) random linear measurements of that signal.Abstract:
This report demonstrates theoretically and empirically that a greedy algorithm called
Orthogonal Matching Pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension
d given O(mln d) random linear measurements of that signal. This is a massive improvement
over previous results, which require O(m2) measurements. The new results for OMP are comparable
with recent results for another approach called Basis Pursuit (BP). In some settings, the
OMP algorithm is faster and easier to implement, so it is an attractive alternative to BP for signal
recovery problems.read more
Citations
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Journal ArticleDOI
Video summarization via block sparse dictionary selection
TL;DR: Experimental results on two benchmark datasets demonstrate that the proposed SBOMP based VS method clearly outperforms several state-of-the-art sparse representation based methods in terms of F-score, redundancy among keyframes and robustness to outlier frames.
Posted Content
Sparsity in time-frequency representations
Goetz E. Pfander,Holger Rauhut +1 more
TL;DR: It is shown that an S-sparse Gabor representation in ℂn with respect to a random unimodular window can be recovered by Basis Pursuit with high probability provided that S≤Cn/log (n).
Journal ArticleDOI
Reduced Reference Stereoscopic Image Quality Assessment Based on Binocular Perceptual Information
Feng Qi,Debin Zhao,Wen Gao +2 more
TL;DR: Experimental results show that the proposed reduced reference stereoscopic image quality assessment (RR-SIQA) metric achieves significantly higher prediction accuracy than the state-of-the-art reduced reference SIQA methods and better than several state- of- the-art full reference SIZA methods on the LIVE phase II asymmetric databases.
Journal ArticleDOI
Blind Separation of Image Sources via Adaptive Dictionary Learning
TL;DR: This paper defines a cost function based on this idea and proposes an extension of the denoising method in the work of Elad and Aharon to minimize it, and proposes a feasible approach via fusing the dictionary learning into the source separation.
Journal ArticleDOI
Hyperspectral Unmixing in the Presence of Mixed Noise Using Joint-Sparsity and Total Variation
TL;DR: This work addresses the hyperspectral unmixing problem in a general scenario that considers the presence of mixed noise, and the split-Bregman technique has been utilized to derive an algorithm for solving resulting optimization problem.
References
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Book
Compressed sensing
TL;DR: It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients, and a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing.
Journal ArticleDOI
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.
Journal ArticleDOI
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.
Journal ArticleDOI
Least angle regression
Bradley Efron,Trevor Hastie,Iain M. Johnstone,Robert Tibshirani,Hemant Ishwaran,Keith Knight,Jean-Michel Loubes,Jean-Michel Loubes,Pascal Massart,Pascal Massart,David Madigan,David Madigan,Greg Ridgeway,Greg Ridgeway,Saharon Rosset,Saharon Rosset,Ji Zhu,Robert A. Stine,Berwin A. Turlach,Sanford Weisberg +19 more
TL;DR: A publicly available algorithm that requires only the same order of magnitude of computational effort as ordinary least squares applied to the full set of covariates is described.