BOYER, Claire; BIGOT, Jérémie; WEISS, Pierre

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BOYER, Claire
Institut de Mathématiques de Toulouse UMR5219 [IMT]

BIGOT, Jérémie
Institut de Mathématiques de Bordeaux [IMB]

WEISS, Pierre
Institut des Technologies Avancées en sciences du Vivant [ITAV]
Institut de Mathématiques de Toulouse UMR5219 [IMT]

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Applied and Computational Harmonic Analysis. 2017-05-26

Elsevier

Résumé en anglais

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.< Réduire

Mots clés en anglais

Compressed Sensing

blocks of measurements

structured sparsity

MRI

exact recovery

l1 minimization

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Compressed sensing with structured sparsity and structured acquisition

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