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
Overview of Compressed Sensing: Sensing Model, Reconstruction Algorithm, and Its Applications
TL;DR: An overview of recent CS studies is given, along the issues of sensing models, reconstruction algorithms, and their applications, and several common sensing methods for CS, like sparse dictionary sensing, block-compressed sensing, and chaotic compressed sensing are introduced.
Journal ArticleDOI
SDL: Saliency-Based Dictionary Learning Framework for Image Similarity
Rituparna Sarkar,Scott T. Acton +1 more
TL;DR: A saliency guided dictionary learning method and subsequently an image similarity technique for histo-pathological image classification, which outperform the state of the art with an increase of 14.2% in the average classification accuracy over all data sets.
Proceedings ArticleDOI
A hybrid compressed sensing algorithm for sparse channel estimation in MIMO OFDM systems
Chenhao Qi,Lenan Wu +1 more
TL;DR: Simulation results based on 3GPP spatial channel model (SCM) demonstrate that SOMP performs better than OMP, SP and interpolated least square (LS) in terms of normalized mean square error (NMSE).
Journal ArticleDOI
Investigation of Kronecker-Based Recovery of Compressed ECG Signal
TL;DR: A detailed investigation of Kronecker-based recovery technique of compressed ECG signal is presented using ECG signals from MIT-BIH Arrhythmia Database and deterministic sensing with deterministic binary block diagonal matrix and discrete cosine transform as sparsifying basis is seen to provide the best recovery.
Proceedings ArticleDOI
Enabling Efficient Analog Synthesis by Coupling Sparse Regression and Polynomial Optimization
TL;DR: This paper uses recent progress on Semidefinite Programming (SDP) relaxations of polynomial (non-convex) optimization to solve the challenge of equation-based analog synthesis of SPICE-generated data with much more accurate fitting.
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.