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
More filters
Journal ArticleDOI
Performance Analysis for Sparse Support Recovery
Gongguo Tang,Arye Nehorai +1 more
TL;DR: This study provides an alternative performance measure, one that is natural and important in practice, for signal recovery in Compressive Sensing and other application areas exploiting signal sparsity, and offers surprising insights into sparse signal recovery.
Journal ArticleDOI
Adaptive Sparse Representations for Video Anomaly Detection
TL;DR: A new joint sparsity model for anomaly detection is developed that enables the detection of joint anomalies involving multiple objects and introduces nonlinearity into the linear sparsityModel, that is, kernelize to enable superior class separability and hence anomaly detection.
Journal ArticleDOI
Sparse Recovery of Nonnegative Signals With Minimal Expansion
TL;DR: This paper introduces sparse measurement matrices for the recovery of nonnegative vectors, using perturbations of the adjacency matrices of expander graphs requiring much smaller expansion coefficients, hereby referred to as minimal expanders and presents a novel recovery algorithm that exploits expansion and is much more computationally efficient compared to minimization.
Journal ArticleDOI
Millimeter Wave Channel Estimation via Exploiting Joint Sparse and Low-Rank Structures
TL;DR: In this paper, a two-stage compressed sensing method for mmWave channel estimation is proposed, where the sparse and low-rank properties are respectively utilized in two consecutive stages, namely, a matrix completion stage and a sparse recovery stage.
Journal ArticleDOI
ISAR 2-D Imaging of Uniformly Rotating Targets via Matching Pursuit
TL;DR: An algorithm based on matching pursuit (MP) is proposed for inverse synthetic aperture radar (ISAR) two-dimensional (2-D) imaging of uniformly rotating targets.
References
More filters
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.