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
Joint Label Consistent Dictionary Learning and Adaptive Label Prediction for Semisupervised Machine Fault Classification
TL;DR: This paper proposes a semisupervised label consistent dictionary learning (SSDL) framework for machine fault classification, and applies the discriminant sparse codes as the adaptive reconstruction weights for label prediction to update the estimated labels of unlabeled training data and the discriminative sparse codes matrix for label consistent Dictionary learning.
Posted Content
Sharp Time--Data Tradeoffs for Linear Inverse Problems
TL;DR: The results demonstrate that a linear convergence rate is attainable even though the least squares objective is not strongly convex in these settings, and present a unified convergence analysis of the gradient projection algorithm applied to such problems.
Journal ArticleDOI
Hyperspectral Image Target Detection Improvement Based on Total Variation
Shuo Yang,Zhenwei Shi +1 more
TL;DR: This work proposes a novel supervised target detection algorithm which uses a single target spectrum as the prior knowledge, and demonstrates that the proposed algorithm outperforms the other algorithms for the experimental data sets.
Journal ArticleDOI
Regularized Simultaneous Forward–Backward Greedy Algorithm for Sparse Unmixing of Hyperspectral Data
Wei Tang,Zhenwei Shi,Ying Wu +2 more
TL;DR: The RSFoBa has low computational complexity of getting an approximate solution for the l0 problem directly and can exploit the joint sparsity among all the pixels in the hyperspectral data and can serve as input for any other sparse unmixing algorithms to make them more accurate and time efficient.
Proceedings ArticleDOI
Using Locally Corresponding CAD Models for Dense 3D Reconstructions from a Single Image
TL;DR: This paper proposes a two-step strategy that employs orthogonal matching pursuit to rapidly choose the closest single CAD model in the authors' dictionary to the projected image and employs a novel graph embedding based on local dense correspondence to allow for sparse linear combinations of CAD models.
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.