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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Superresolution ISAR Imaging Based on Sparse Bayesian Learning
TL;DR: A fully automated ISAR imaging algorithm based on sparse Bayesian learning (SBL), which keeps a better balance between the computation load and the sparsity of the reconstruction signal than the existing algorithms.
Journal ArticleDOI
Spectral analysis of fluid flows using sub-Nyquist-rate PIV data
TL;DR: This work proposes a new approach that combines ideas from DMD and compressed sensing to accommodate sub-Nyquist-rate sampling, and correctly identifies the characteristic frequencies and oscillatory modes dominating the signal.
Journal ArticleDOI
Deblurring From Highly Incomplete Measurements for Remote Sensing
Jianwei Ma,F.-X. Le Dimet +1 more
TL;DR: A decoding algorithm based on Poisson singular integral and iterative curvelet thresholding is proposed to correct the deblurring problem with surprisingly incomplete measurements.
Posted Content
Histopathological Image Classification using Discriminative Feature-oriented Dictionary Learning
TL;DR: In this paper, a discriminative feature-oriented dictionary learning (DFDL) method is proposed to learn class-specific dictionaries such that under a sparsity constraint, the learned dictionaries allow representing a new image sample parsimoniously via the dictionary corresponding to the class identity of the sample.
Proceedings ArticleDOI
Practical near-optimal sparse recovery in the L1 norm
TL;DR: This work focuses on the sparse recovery problem in the l1 norm: for a parameter k, given the sketch Ax, compute an approximation xcirc of x such that the l2 approximation error parx - xcircpar1 is close to minx' parX - x'par1, where x' ranges over all vectors with at most k terms.
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.