منابع مشابه
s-Goodness for Low-Rank Matrix Recovery
and Applied Analysis 3 If there does not exist such y for some X as above, we set γ s (A, β) = +∞ and to be compatible with the special case given by [24] we write γ s (A), γ s (A) instead of γ s (A, +∞), γ s (A, +∞), respectively. From the above definition, we easily see that the set of values that γ takes is closed. Thus, when γ s (A, β) < +∞, for every matrix X ∈ Rm×n with s nonzero singular...
متن کاملS-goodness for Low-rank Matrix Recovery, Translated from Sparse Signal Recovery
Low-rank matrix recovery (LMR) is a rank minimization problem subject to linear equality constraints, and it arises in many fields such as signal and image processing, statistics, computer vision, system identification and control. This class of optimization problems is generally NP-hard. A popular approach replaces the rank function with the nuclear norm of the matrix variable. In this paper, ...
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We extend and characterize the concept of s-semigoodness for a sensing matrix in sparse nonnegative recovery (proposed by Juditsky , Karzan and Nemirovski [Math Program, 2011]) to the linear transformations in low-rank semidefinite matrix recovery. We show that ssemigoodness is not only a necessary and sufficient condition for exact s-rank semidefinite matrix recovery by a semidefinite program,...
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We study Sigma-Delta quantization methods coupled with appropriate reconstruction algorithms for digitizing randomly sampled low-rank matrices. We show that the reconstruction error associated with our methods decays polynomially with the oversampling factor, and we leverage our results to obtain root-exponential accuracy by optimizing over the choice of quantization scheme. Additionally, we sh...
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Low-rank matrix recovery addresses the problem of recovering an unknown low-rank matrix from few linear measurements. Nuclear-norm minimization is a tractable approach with a recent surge of strong theoretical backing. Analagous to the theory of compressed sensing, these results have required random measurements. For example, m ≥ Cnr Gaussian measurements are sufficient to recover any rank-r n ...
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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2013
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2013/101974