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

Abstract : 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.
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Nelly Pustelnik, Charles Dossal, Flavius Turcu, Yannick Berthoumieu, Philippe Ricoux. A greedy algorithm to extract sparsity degree for l1/l0-equivalence in a deterministic context. EUSIPCO 2012, 2012, pp.x+5. ⟨hal-00826821⟩

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