Open Access
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
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Posted Content
Alternating Direction Algorithms for $\ell_1$-Problems in Compressive Sensing
Junfeng Yang,Yin Zhang +1 more
TL;DR: In this article, alternating direction algorithms are used for solving the basis pursuit problem and the basis-pursuit denoising problem in both unconstrained and constrained forms, respectively.
Journal ArticleDOI
Broad Learning System: An Effective and Efficient Incremental Learning System Without the Need for Deep Architecture
C. L. Philip Chen,Zhulin Liu +1 more
TL;DR: Compared with existing deep neural networks, experimental results on the Modified National Institute of Standards and Technology database and NYU NORB object recognition dataset benchmark data demonstrate the effectiveness of the proposed Broad Learning System.
Journal ArticleDOI
Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
Deanna Needell,Roman Vershynin +1 more
TL;DR: This paper finds a simple regularized version of Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of L1-minimization.
Proceedings ArticleDOI
Compressive Radar Imaging
TL;DR: It is demonstrated that CS has the potential to make two significant improvements to radar systems: eliminating the need for the pulse compression matched filter at the receiver, and reducing the required receiver analog-to-digital conversion bandwidth so that it need operate only at the radar reflectivity's potentially low "information rate" rather than at its potentially high Nyquist rate.
Journal ArticleDOI
Sparse Unmixing of Hyperspectral Data
TL;DR: The experimental results, conducted using both simulated and real hyperspectral data sets collected by the NASA Jet Propulsion Laboratory's Airborne Visible Infrared Imaging Spectrometer and spectral libraries publicly available from the U.S. Geological Survey, indicate the potential of SR techniques in the task of accurately characterizing the mixed pixels using the library spectra.
References
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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.