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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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The Group Lasso for Stable Recovery of Block-Sparse Signal Representations
Xiaolei Lv,Guoan Bi,Chunru Wan +2 more
TL;DR: The possibility of stably recovering original signals from the noisy data using the adaptive group Lasso with a combination of sufficient block-sparsity and favorable block structure of the overcomplete dictionary is established.
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Data-driven multitask sparse dictionary learning for noise attenuation of 3D seismic data
TL;DR: A novel data-driven 3D DL algorithm is introduced that is extended from the 2D nonnegative DL scheme via the multitasking strategy for random noise attenuation of seismic data and exploits nonnegativity constraint to induce sparsity on the data transformation and reduce the space of the solution and, consequently, the computational cost.
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Random-Frequency SAR Imaging Based on Compressed Sensing
TL;DR: If the targets are sparse or compressible, it is sufficient to transmit only a small number of random frequencies to reconstruct the image of the targets, which means that the limitations of the stepped-frequency technique for SAR can be overcome.
Proceedings ArticleDOI
In-situ soil moisture sensing: measurement scheduling and estimation using compressive sensing
Xiaopei Wu,Mingyan Liu +1 more
TL;DR: This paper constructs a representation basis and shows that this basis attains very good tradeoff between its ability to sparsify the signal and its incoherence with measurement matrices that are consistent with the physical constraints.
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.