Open Access
Signal Recovery from Random Measurements Via Orthogonal Matching Pursuit: The Gaussian Case
Joel A. Tropp,Anna C. Gilbert +1 more
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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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Quantized Compressive Sensing with RIP Matrices: The Benefit of Dithering
Chunlei Xu,Laurent Jacques +1 more
TL;DR: In this article, the authors show that a large class of random matrix constructions known to respect the restricted isometry property (RIP) is "compatible" with a simple scalar and uniform quantization if a uniform random vector, or a random dither, is added to the compressive signal measurements before quantization.
Journal ArticleDOI
High-Resolution Bistatic ISAR Imaging Based on Two-Dimensional Compressed Sensing
TL;DR: A new framework of high-resolution bistatic inverse synthetic aperture radar (Bi-ISAR) imaging based on CS is presented and a phase-preserved CS approach for high-range resolution imaging is proposed.
Journal ArticleDOI
DOA estimation exploiting a uniform linear array with multiple co-prime frequencies
TL;DR: A novel co-prime array structure that exploits a single uniform linear array and a co- prime set of frequencies is proposed, enabling direction-of-arrival (DOA) estimation of more targets than the number of physical sensors.
Posted Content
Low-Cost Compressive Sensing for Color Video and Depth
Xin Yuan,Patrick Llull,Xuejun Liao,Jianbo Yang,Guillermo Sapiro,David J. Brady,Lawrence Carin +6 more
TL;DR: In this paper, a simple and inexpensive modification is made to a conventional off-the-shelf color video camera, from which they recover {multiple} color frames for each of the original measured frames, and each recovered frames can be focused at a different depth.
Journal ArticleDOI
Sequential Lasso Cum EBIC for Feature Selection With Ultra-High Dimensional Feature Space
Shan Luo,Zehua Chen +1 more
TL;DR: It is shown that, with probability converging to 1, the SLasso first selects all the relevant features before any irrelevant features can be selected, and that the EBIC decreases until it attains the minimum at the model consisting of exactly all therelevant features and then begins to increase, which establishes the selection consistency of SLasso.
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.