An evaluation of the sparsity degree for sparse recovery with deterministic measurement matrices
| hal.structure.identifier | Laboratoire de l'intégration, du matériau au système [IMS] | |
| dc.contributor.author | BERTHOUMIEU, Yannick | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DOSSAL, Charles | |
| hal.structure.identifier | Laboratoire de Physique de l'ENS Lyon [Phys-ENS] | |
| dc.contributor.author | PUSTELNIK, Nelly | |
| dc.contributor.author | RICOUX, Philippe | |
| hal.structure.identifier | Laboratoire de l'intégration, du matériau au système [IMS] | |
| dc.contributor.author | TURCU, Flavius | |
| dc.date.accessioned | 2024-04-04T02:21:10Z | |
| dc.date.available | 2024-04-04T02:21:10Z | |
| dc.date.issued | 2013-08-01 | |
| dc.identifier.issn | 0924-9907 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189549 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.subject.en | Compressed sensing | |
| dc.subject.en | Deterministic matrix | |
| dc.subject.en | Sparsity degree | |
| dc.subject.en | Greedy algorithm | |
| dc.title.en | An evaluation of the sparsity degree for sparse recovery with deterministic measurement matrices | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s10851-013-0453-4 | |
| dc.subject.hal | Sciences de l'ingénieur [physics]/Traitement du signal et de l'image | |
| dc.subject.hal | Informatique [cs]/Traitement du signal et de l'image | |
| bordeaux.journal | Journal of Mathematical Imaging and Vision | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00878620 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00878620v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Mathematical%20Imaging%20and%20Vision&rft.date=2013-08-01&rft.eissn=0924-9907&rft.issn=0924-9907&rft.au=BERTHOUMIEU,%20Yannick&DOSSAL,%20Charles&PUSTELNIK,%20Nelly&RICOUX,%20Philippe&TURCU,%20Flavius&rft.genre=article |
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