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Onebit Compressed Sensing: Provable Support and Vector Recovery
"... In this paper, we study the problem of onebit compressed sensing (1bit CS), where the goal is to design a measurement matrix A and a recovery algorithm such that a ksparse unit vector x ∗ can be efficiently recovered from the sign of its linear measurements, i.e., b = sign(Ax ∗). This is an import ..."
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In this paper, we study the problem of onebit compressed sensing (1bit CS), where the goal is to design a measurement matrix A and a recovery algorithm such that a ksparse unit vector x ∗ can be efficiently recovered from the sign of its linear measurements, i.e., b = sign
Praneeth Netrapalli Onebit Compressed Sensing: Provable Support and Vector Recovery 1bit CS Support Approx. Summary Quantization
, 2013
"... Goal: Reconstruct a sparse signal using very few linear measurements Tremendous amount of work in the last decade O (k log n) measurements to reconstruct ksparse signals in Rn ..."
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Goal: Reconstruct a sparse signal using very few linear measurements Tremendous amount of work in the last decade O (k log n) measurements to reconstruct ksparse signals in Rn
Onebit Compressed Sensing with the kSupport Norm
"... Abstract In onebit compressed sensing (1bit CS), one attempts to estimate a structured parameter (signal) only using the sign of suitable linear measurements. In this paper, we investigate 1bit CS problems for sparse signals using the recently proposed ksupport norm. We show that the new estima ..."
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Abstract In onebit compressed sensing (1bit CS), one attempts to estimate a structured parameter (signal) only using the sign of suitable linear measurements. In this paper, we investigate 1bit CS problems for sparse signals using the recently proposed ksupport norm. We show that the new
A Note on Optimal Support Recovery in Compressed Sensing
, 2009
"... Recovery of the support set (or sparsity pattern) of a sparse vector from a small number of noisy linear projections (or samples) is a “compressed sensing ” problem that arises in signal processing and statistics. Although many computationally efficient recovery algorithms have been studied, the opt ..."
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Cited by 18 (0 self)
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Recovery of the support set (or sparsity pattern) of a sparse vector from a small number of noisy linear projections (or samples) is a “compressed sensing ” problem that arises in signal processing and statistics. Although many computationally efficient recovery algorithms have been studied
Informationtheoretic limits on sparsity recovery in the highdimensional and noisy setting
, 2007
"... Abstract—The problem of sparsity pattern or support set recovery refers to estimating the set of nonzero coefficients of an un3 p known vector 2 based on a set of n noisy observations. It arises in a variety of settings, including subset selection in regression, graphical model selection, signal de ..."
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Cited by 131 (2 self)
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thresholds for support set recovery over the same set of random measurement ensembles using the polynomialtime Lasso method (`1constrained quadratic programming). Index Terms—Compressed sensing, `1relaxation, Fano’s method, highdimensional statistical inference, informationtheoretic
Robust support recovery using sparse compressive sensing matrices
 in Proc. 45th Annual Conf. on Information Sciences and Systems
, 2011
"... Abstract—This paper considers the task of recovering the support of a sparse, highdimensional vector from a small number of measurements. The procedure proposed here, which we call the SignSketch procedure, is shown to be a robust recovery method in settings where the measurements are corrupted by ..."
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Cited by 5 (1 self)
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(n log n) total operations for both acquisition and inference. Index Terms—Support recovery, sparsity pattern recovery, model selection, feature selection, sparse recovery, robust inference, sketching, compressive sensing.
Index Terms Compressed Sensing
, 2011
"... Consider a BernoulliGaussian complex nvector whose components are Vi = XiBi, with Xi ∼ CN (0,Px) and binary Bi mutually independent and iid across i. This random qsparse vector is multiplied by a square random matrix U, and a randomly chosen subset, of average size np, p ∈ [0, 1], of the resultin ..."
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], of the resulting vector components is then observed in additive Gaussian noise. We extend the scope of conventional noisy compressive sampling models where U is typically a matrix with iid components, to allow U satisfying a certain freeness condition. This class of matrices encompasses Haar matrices and other
Compressed Sensing over the Grassmann Manifold: A Unified Analytical Framework
"... Abstract—It is well known that compressed sensing problems reduce to finding the sparse solutions for large underdetermined systems of equations. Although finding the sparse solutions in general may be computationally difficult, starting with the seminal work of [2], it has been shown that linear p ..."
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Cited by 45 (8 self)
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Abstract—It is well known that compressed sensing problems reduce to finding the sparse solutions for large underdetermined systems of equations. Although finding the sparse solutions in general may be computationally difficult, starting with the seminal work of [2], it has been shown that linear
Results 1  10
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135