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
Low-Rank Matrix Completion: A Contemporary Survey
TL;DR: A contemporary survey on low-rank matrix completion (LRMC), which classifies the state-of-the-art LRMC techniques into two main categories and then explains each category in detail.
Posted Content
Algorithmic linear dimension reduction in the l_1 norm for sparse vectors
TL;DR: A new method for recovering msparse signals that is simultaneously uniform and quick is developed, and vectors of support m in dimension d can be linearly embedded into O(m log d) dimensions with polylogarithmic distortion.
Multi-Task Compressive Sensing
TL;DR: This paper addresses the problem within a multi-task learning setting, wherein the mapping vi !
Journal ArticleDOI
Adaptive Compressed Sensing Radar Oriented Toward Cognitive Detection in Dynamic Sparse Target Scene
TL;DR: This work proposes the notion of adaptive compressed sensing radar (ACSR) whose transmission waveform and sensing matrix can be updated by the target scene information fed back by the recovery algorithm.
Journal ArticleDOI
Single-Pixel Remote Sensing
TL;DR: A new sampling theory named compressed sensing for aerospace remote sensing is applied to reduce data acquisition and imaging cost and would lead to new instruments with less storage space, less power consumption, and smaller size than currently used charged coupled device cameras, which would match effective needs particularly for probes sent very far away.
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.