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
More filters
Journal ArticleDOI
Exploiting chaos-based compressed sensing and cryptographic algorithm for image encryption and compression
TL;DR: A solution for simultaneous image encryption and compression using compressed sensing using structurally random matrix (SRM), and permutation-diffusion type image encryption using 3-D cat map is presented.
Journal ArticleDOI
A Nonuniform Sampler for Wideband Spectrally-Sparse Environments
Michael B. Wakin,Stephen Becker,E. B. Nakamura,Michael C. Grant,Emilio A. Sovero,D. Ching,Juhwan Yoo,Justin Romberg,Azita Emami-Neyestanak,Emmanuel J. Candès +9 more
TL;DR: A wide bandwidth, compressed sensing based nonuniform sampling (NUS) system with a custom sample-and-hold chip designed to take advantage of a low average sampling rate is presented.
Journal ArticleDOI
Non-negative infrared patch-image model: Robust target-background separation via partial sum minimization of singular values
TL;DR: Considering the fact that the infrared small target is always brighter than its adjacent background, an additional non-negative constraint to the sparse target patch-image is proposed, which could not only wipe off more undesirable components ulteriorly but also accelerate the convergence rate.
Posted Content
Greedy Sparsity-Constrained Optimization
TL;DR: In this article, a greedy gradient support pursuit (GraSP) algorithm is proposed to approximate sparse minima of cost functions of arbitrary form, where a cost function has a Stable Restricted Hessian (SRH) or a Stably Restricted Linearization (SRL) and the greedy algorithm is guaranteed to produce a sparse vector within a bounded distance from the true sparse optimum.
Journal ArticleDOI
Watermarking With Flexible Self-Recovery Quality Based on Compressive Sensing and Compositive Reconstruction
TL;DR: It is shown that the proposed scheme outperforms previous techniques in general and the smaller the tampered area, the more available watermark data will result in a better quality of recovered content.
References
More filters
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.