Compressed sensing with structured sparsity and structured acquisition - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Applied and Computational Harmonic Analysis Année : 2017

Compressed sensing with structured sparsity and structured acquisition

Résumé

Compressed Sensing (CS) is an appealing framework for applications such as Magnetic Resonance Imaging (MRI). However, up-to-date, the sensing schemes suggested by CS theories are made of random isolated measurements, which are usually incompatible with the physics of acquisition. To reflect the physical constraints of the imaging device, we introduce the notion of blocks of measurements: the sensing scheme is not a set of isolated measurements anymore, but a set of groups of measurements which may represent any arbitrary shape (parallel or radial lines for instance). Structured acquisition with blocks of measurements are easy to implement, and provide good reconstruction results in practice. However, very few results exist on the theoretical guarantees of CS reconstructions in this setting. In this paper, we derive new CS results for structured acquisitions and signals satisfying a prior structured sparsity. The obtained results provide a recovery probability of sparse vectors that explicitly depends on their support. Our results are thus support-dependent and offer the possibility for flexible assumptions on the sparsity structure. Moreover, the results are drawing-dependent, since we highlight an explicit dependency between the probability of reconstructing a sparse vector and the way of choosing the blocks of measurements. Numerical simulations show that the proposed theory is faithful to experimental observations.
Fichier principal
Vignette du fichier
CS_Structured_Sparsity_Sampling_2016v2.pdf (9.4 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01149456 , version 1 (07-05-2015)
hal-01149456 , version 2 (10-04-2017)

Identifiants

  • HAL Id : hal-01149456 , version 2

Citer

Claire Boyer, Jérémie Bigot, Pierre Weiss. Compressed sensing with structured sparsity and structured acquisition. Applied and Computational Harmonic Analysis, 2017. ⟨hal-01149456v2⟩
296 Consultations
333 Téléchargements

Partager

Gmail Facebook X LinkedIn More