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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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Journal ArticleDOI
Simultaneous learning of several materials properties from incomplete databases with multi-task SISSO
TL;DR: This work describes a powerful extension of the SISSO methodology to a 'multi-task learning' approach, which identifies a single descriptor capturing multiple target materials properties at the same time, specifically suited for a heterogeneous materials database with scarce or partial data.
DissertationDOI
Practical Compressed Sensing: Modern data acquisition and signal processing
TL;DR: Inspired by the need for a fast method to solve reconstruction problems for the RMPI, two efficient large-scale optimization methods are developed that are applicable to a wide range of other problems, such as image denoising and deblurring, MRI reconstruction, and matrix completion (including the famous Netflix problem).
Journal ArticleDOI
On the Relation Between Sparse Reconstruction and Parameter Estimation With Model Order Selection
TL;DR: The structural assumption used in compressive sensing to guarantee reconstruction performance-the Restricted Isometry Property-is not satisfied in the general parameter estimation context, and a method for selecting sparsity parameters such that sparse reconstruction mimics classic order selection criteria such as Akaike information criterion and Bayesian information criterion is developed.
Dissertation
Random Observations on Random Observations: Sparse Signal Acquisition and Processing
TL;DR: Random Observations on Random Observations: Sparse Signal Acquisition and Processing is concerned with sparse signal acquisition and processing.
Proceedings ArticleDOI
Design and implementation of a fully integrated compressed-sensing signal acquisition system
Juhwan Yoo,Stephen Becker,Manuel Monge,Matthew Loh,Emmanuel J. Candès,Azita Emami-Neyestanak +5 more
TL;DR: The design of the first physically realized fully-integrated CS based Analog-to-Information pre-processor known as the Random-Modulation Pre-Integrator (RMPI) is presented.
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.