PUSTELNIK, Nelly; DOSSAL, Charles; TURCU, Flavius; BERTHOUMIEU, Yannick; RICOUX, Philippe

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PUSTELNIK, Nelly
Laboratoire de Physique de l'ENS Lyon [Phys-ENS]

DOSSAL, Charles
Institut de Mathématiques de Bordeaux [IMB]

TURCU, Flavius
Laboratoire de l'intégration, du matériau au système [IMS]

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EUSIPCO 2012. 2012-08-27p. x+5

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This paper investigates the problem of designing a deterministic system matrix, that is measurement matrix, for sparse recovery. An efficient greedy algorithm is proposed in order to extract the class of sparse signal/image which cannot be reconstructed by $\ell_1$-minimization for a fixed system matrix. Based on the polytope theory, the algorithm provides a geometric interpretation of the recovery condition considering the seminal work by Donoho. The paper presents an additional condition, extending the Fuchs/Tropp results, in order to deal with noisy measurements. Simulations are conducted for tomography-like imaging system in which the design of the system matrix is a difficult task consisting of the selection of the number of views according to the sparsity degree.< Réduire

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Compressed sensing

tomography

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A greedy algorithm to extract sparsity degree for l1/l0-equivalence in a deterministic context

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