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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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Robust sparse phase retrieval made easy
TL;DR: A simple two-stage sparse phase retrieval strategy that uses a near-optimal number of measurements, and is both computationally efficient and robust to measurement noise is proposed.
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DOA Estimation Exploiting Sparse Array Motions
TL;DR: Sparse array motion is utilized to increase the numbers of achievable both degrees of freedom (DOFs) and consecutive lags in direction-of-arrival (DOA) estimation problems and shows the respective DOA estimation performance based on sparse reconstruction techniques.
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A survey on representation-based classification and detection in hyperspectral remote sensing imagery
TL;DR: This paper reviews the state-of-the-art representation-based classification and detection approaches for hyperspectral remote sensing imagery, including sparse representation-Based classification (SRC), collaborative representation- based classification (CRC), and their extensions.
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Harnessing Sparsity Over the Continuum: Atomic norm minimization for superresolution
TL;DR: In this paper, the signal of interest can be modeled as a linear superposition of translated or modulated versions of some template [e.g., a point spread function (PSF) or a Green's function] and the fundamental problem is to estimate the translation or modulation parameters (i.e., delays, locations, or Dopplers) from noisy measurements.
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Enhanced ISAR Imaging by Exploiting the Continuity of the Target Scene
TL;DR: A novel inverse synthetic aperture radar (ISAR) imaging method by exploiting the inherent continuity of the scatterers on the target scene to obtain enhanced target images within a Bayesian framework that can achieve substantial improvements in the scenarios of limited measurements and low signal-to-noise ratio compared with other reported algorithms for ISAR imaging problems.
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.