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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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Simultaneous Sparsity Model for Histopathological Image Representation and Classification
TL;DR: A new simultaneous sparsity model for multi-channel histopathological image representation and classification (SHIRC) is proposed that exhibits a more graceful decay in classification accuracy against the number of training images which is highly desirable in practice where generous training per class is often not available.
Journal ArticleDOI
Compressed Sensing Detector Design for Space Shift Keying in MIMO Systems
Chia-Mu Yu,Sung-Hsien Hsieh,Han-Wen Liang,Chun-Shien Lu,Wei-Ho Chung,Sy-Yen Kuo,Soo-Chang Pei +6 more
TL;DR: This work proposes a compressed sensing based detector, NCS, by formulating the SSK-type detection criterion as a convex optimization problem, which requires only O(ntNrNt) complexity, outperforming the O(NRNtnt) complexity in the ML detector, at the cost of slight fidelity degradation.
Journal ArticleDOI
Joint Sparse Representation and Multitask Learning for Hyperspectral Target Detection
TL;DR: This paper proposes the joint sparse representation and MTL (JSR-MTL) method for hyperspectral target detection, which generally shows a better detection performance than the other target detection methods.
Journal ArticleDOI
Reduced-Reference Image Quality Assessment in Free-Energy Principle and Sparse Representation
TL;DR: This paper approximate the internal generative model with sparse representation and proposes an image quality metric accordingly, which is named FSI (free-energy principle and sparse representation-based index for image quality assessment), which only needs a single number from the reference image for quality estimation.
Journal ArticleDOI
Harmless Interpolation of Noisy Data in Regression
TL;DR: It is shown that the fundamental generalization (mean-squared) error of any interpolating solution in the presence of noise decays to zero with the number of features, and overparameterization can be beneficial in ensuring harmless interpolation of noise.
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.