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Exact Support Recovery for Sparse Spikes Deconvolution

Duval, Vincent; Peyré, Gabriel (2015), Exact Support Recovery for Sparse Spikes Deconvolution, Foundations of Computational Mathematics, 15, 5, p. 1315-1355. 10.1007/s10208-014-9228-6

Type
Article accepté pour publication ou publié
Date
2015
Journal name
Foundations of Computational Mathematics
Volume
15
Number
5
Publisher
Springer
Pages
1315-1355
Publication identifier
10.1007/s10208-014-9228-6
Metadata
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Author(s)
Duval, Vincent cc
Peyré, Gabriel
Abstract (EN)
This paper studies sparse spikes deconvolution over the space of measures. For non-degenerate sums of Diracs, we show that, when the signal-to-noise ratio is large enough, total variation regularization (which the natural extension of L1 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 converge toward those of the input measure when the noise drops to zero. The exact speed of convergence is governed by a specific dual certificate, which can be computed by solving a linear system. Finally we draw connections between the performances of sparse recovery on a continuous domain and on a discretized grid.
Subjects / Keywords
Deconvolution; dual certificates; inverse problem; sparsity

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    Support Recovery for Sparse Super-Resolution of Positive Measures 
    Denoyelle, Quentin; Duval, Vincent; Peyré, Gabriel (2016) Article accepté pour publication ou publié
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    Sparse Spikes Deconvolution on Thin Grids 
    Duval, Vincent; Peyré, Gabriel (2015) Document de travail / Working paper
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