Variable Density Compressed Sensing In MRI. Theoretical vs Heuristic Sampling Strategies

Nicolas Chauffert (1) , Philippe Ciuciu (1) , Pierre Weiss (2)

1 PARIETAL - Modelling brain structure, function and variability based on high-field MRI data
2 PRIMO (ITAV)

The structure of Magnetic Resonance Images (MRI) and especially their compressibility in an appropriate representation basis enables the application of the compressive sensing theory, which guarantees exact image recovery from incomplete measurements. According to recent theoretical conditions on the reconstruction guarantees, the optimal strategy is to downsample the k-space using an independent drawing of the acquisition basis entries. Here, we first bring a novel answer to the synthesis problem, which amounts to deriving the op- timal distribution (according to a given criterion) from which the data should be sampled. Then, given that the sparsity hypothesis is not fulfilled in the k-space center in MRI, we extend this approach by densely sampling this center and drawing the remaining samples from the optimal distribution. We compare this theoretical approach to heuristic strategies, and show that the proposed two-stage process drastically improves reconstruction results on anatomical MRI.

Mots clés: MRI; Compressive sensing; Wavelets; Synthesis problem; variable density sampling

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Imagerie

Nicolas Chauffert, Philippe Ciuciu, Pierre Weiss. Variable Density Compressed Sensing In MRI. Theoretical vs Heuristic Sampling Strategies. ISBI - 10th International Symposium on Biomedical Imaging, Apr 2013, San Francisco, United States. ⟨hal-00848271⟩