Exact Support Recovery for Sparse Spikes Deconvolution
نویسندگان
چکیده
منابع مشابه
Exact Support Recovery for Sparse Spikes Deconvolution
This paper studies sparse spikes deconvolution over the space of measures. For non-degenerate sums of Diracs, we show that, when the signalto-noise ratio is large enough, total variation regularization (which the natural extension of ` norm of vector to the setting of measures) recovers the exact same number of Diracs. We also show that both the locations and the heights of these Diracs converg...
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Deconvolution is usually regarded as one of the ill-posed problems in applied mathematics if no constraints on the unknowns are assumed. In this paper, we discuss the idea of welldefined statistical models being a counterpart of the notion of well-posedness. We show that constraints on the unknowns such as positivity and sparsity can go a long way towards overcoming the ill-posedness in deconvo...
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We study sparse spikes deconvolution over the space of Radon measures when the input measure is a finite sum of positive Dirac masses using the BLASSO convex program. We focus on the recovery properties of the support and the amplitudes of the initial measure in the presence of noise as a function of the minimum separation t of the input measure (the minimum distance between two spikes). We sho...
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This article analyzes the recovery performance of two popular finite dimensional approximations of the sparse spikes deconvolution problem over Radon measures. We examine in a unified framework both the l regularization (often referred to as Lasso or Basis-Pursuit) and the Continuous Basis-Pursuit (C-BP) methods. The Lasso is the de-facto standard for the sparse regularization of inverse proble...
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Deconvolution is usually regarded as one of the so called ill-posed problems of applied mathematics if no constraints on the unknowns can be assumed. In this paper, we discuss the idea of well-de ned statistical models being a counterpart of the notion of well-posedness. We show that constraints on the unknowns such as non-negativity and sparsity can help a great deal to get over the inherent i...
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ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2014
ISSN: 1615-3375,1615-3383
DOI: 10.1007/s10208-014-9228-6