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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Proceedings ArticleDOI
Variational Depth Superresolution Using Example-Based Edge Representations
TL;DR: A novel method for depth image superresolution which combines recent advances in example based upsampling with variational superresolution based on a known blur kernel is proposed and clearly outperforms existing approaches on multiple real and synthetic datasets.
Journal ArticleDOI
Smoothing and Decomposition for Analysis Sparse Recovery
TL;DR: The bound proves that the methods can recover a signal sparse in a redundant tight frame when the measurement matrix satisfies a properly adapted restricted isometry property and converges faster than the decomposition-based alternative in real applications, such as MRI image reconstruction.
Journal ArticleDOI
State-of-the-art review on Bayesian inference in structural system identification and damage assessment
TL;DR: The focus is on meeting challenges that arise from system identification and damage assessment for the civil infrastructure but the presented theories also have a considerably broader applicability for inverse problems in science and technology.
Journal ArticleDOI
Passive Beamforming and Information Transfer via Large Intelligent Surface
TL;DR: Numerical results show that the proposed PBIT system, especially with the optimized passive beamforming, significantly outperforms the system without LIS enhancement, and a tradeoff between the passive-beamforming gain and the information rate of the LIS has been demonstrated.
Journal ArticleDOI
Screening Tests for Lasso Problems
TL;DR: Using a geometrically intuitive framework, this paper provides basic insights for understanding useful lasso screening tests and their limitations, and provides illustrative numerical studies on several datasets.
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.