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Journal Articles Journal of Mathematical Imaging and Vision Year : 2013

An evaluation of the sparsity degree for sparse recovery with deterministic measurement matrices

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Charles H Dossal
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  • PersonId : 1069990
Nelly Pustelnik
Philippe Ricoux
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  • PersonId : 938361

Abstract

The paper deals with the estimation of the maximal sparsity degree for which a given measurement matrix allows sparse reconstruction through l1-minimization. This problem is a key issue in different applications featuring particular types of measurement matrices, as for instance in the framework of tomography with low number of views. In this framework, while the exact bound is NP hard to compute, most classical criteria guarantee lower bounds that are numerically too pessimistic. In order to achieve an accurate estimation, we propose an efficient greedy algorithm that provides an upper bound for this maximal sparsity. Based on polytope theory, the algorithm consists in finding sparse vectors that cannot be recovered by l1-minimization. Moreover, in order to deal with noisy measurements, theoretical conditions leading to a more restrictive but reasonable bounds are investigated. Numerical results are presented for discrete versions of tomo\-graphy measurement matrices, which are stacked Radon transforms corresponding to different tomograph views.
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Dates and versions

hal-00878620 , version 1 (30-10-2013)

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Yannick Berthoumieu, Charles H Dossal, Nelly Pustelnik, Philippe Ricoux, Flavius Turcu. An evaluation of the sparsity degree for sparse recovery with deterministic measurement matrices. Journal of Mathematical Imaging and Vision, 2013, ⟨10.1007/s10851-013-0453-4⟩. ⟨hal-00878620⟩
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