An algorithm for variable density sampling with block-constrained acquisition
| hal.structure.identifier | Institut de Mathématiques de Toulouse UMR5219 [IMT] | |
| dc.contributor.author | BOYER, Claire | |
| hal.structure.identifier | PRIMO (ITAV) | |
| dc.contributor.author | WEISS, Pierre | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BIGOT, Jérémie | |
| dc.date.accessioned | 2024-04-04T03:10:20Z | |
| dc.date.available | 2024-04-04T03:10:20Z | |
| dc.date.issued | 2014-05 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193681 | |
| dc.description.abstractEn | Reducing acquisition time is of fundamental importance in various imaging modalities. The concept of variable density sampling provides a nice framework to achieve this. It was justified recently from a theoretical point of view in the compressed sensing (CS) literature. Unfortunately, the sampling schemes suggested by current CS theories may not be relevant since they do not take the acquisition constraints into account (for example, continuity of the acquisition trajectory in Magnetic Resonance Imaging - MRI). In this paper, we propose a numerical method to perform variable density sampling with block constraints. Our main contribution is to propose a new way to draw the blocks in order to mimic CS strategies based on isolated measurements. The basic idea is to minimize a tailored dissimilarity measure between a probability distribution defined on the set of isolated measurements and a probability distribution defined on a set of blocks of measurements. This problem turns out to be convex and solvable in high dimension. Our second contribution is to define an efficient minimization algorithm based on Nesterov's accelerated gradient descent in metric spaces. We study carefully the choice of the metrics and of the prox function. We show that the optimal choice may depend on the type of blocks under consideration. Finally, we show that we can obtain better MRI reconstruction results using our sampling schemes than standard strategies such as equiangularly distributed radial lines. | |
| dc.language.iso | en | |
| dc.publisher | Society for Industrial and Applied Mathematics | |
| dc.subject.en | blocks of measurements | |
| dc.subject.en | Compressed Sensing | |
| dc.subject.en | optimization on metric spaces | |
| dc.subject.en | dissimilarity measure between discrete probabilities | |
| dc.subject.en | blocks-constrained acquisition | |
| dc.subject.en | optimization on metric spaces. | |
| dc.title.en | An algorithm for variable density sampling with block-constrained acquisition | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Théorie de l'information et codage [math.IT] | |
| dc.subject.hal | Informatique [cs]/Théorie de l'information [cs.IT] | |
| dc.subject.hal | Mathématiques [math]/Optimisation et contrôle [math.OC] | |
| dc.identifier.arxiv | 1310.4393 | |
| bordeaux.journal | SIAM Journal on Imaging Sciences | |
| bordeaux.page | 1080--1107 | |
| bordeaux.volume | 7 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 2 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00873873 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00873873v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=SIAM%20Journal%20on%20Imaging%20Sciences&rft.date=2014-05&rft.volume=7&rft.issue=2&rft.spage=1080--1107&rft.epage=1080--1107&rft.au=BOYER,%20Claire&WEISS,%20Pierre&BIGOT,%20J%C3%A9r%C3%A9mie&rft.genre=article |
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