Compressed sensing with structured sparsity and structured acquisition

Abstract : 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.
Document type :
Journal articles
Liste complète des métadonnées

Cited literature [38 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01149456
Contributor : Claire Boyer <>
Submitted on : Monday, April 10, 2017 - 3:51:20 PM
Last modification on : Friday, April 12, 2019 - 4:23:33 PM
Document(s) archivé(s) le : Tuesday, July 11, 2017 - 1:50:22 PM

File

CS_Structured_Sparsity_Samplin...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01149456, version 2

Citation

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

Share

Metrics

Record views

193

Files downloads

81