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

Nelly Pustelnik (1) , Charles H Dossal (2) , Flavius Turcu (3) , Yannick Berthoumieu (3) , Philippe Ricoux (4)

1 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
2 IMB - Institut de Mathématiques de Bordeaux
3 IMS - Laboratoire de l'intégration, du matériau au système
4 TOTAL S.A.

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.

Mots clés: Compressed sensing; tomography; polytope theory

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Nelly Pustelnik, Charles H Dossal, Flavius Turcu, Yannick Berthoumieu, Philippe Ricoux. A greedy algorithm to extract sparsity degree for l1/l0-equivalence in a deterministic context. European Signal Processing Conference (EUSIPCO), Aug 2012, Bucharest, Romania. pp.x+5. ⟨hal-00826828⟩