An algorithm for variable density sampling with block-constrained acquisition
Langue
en
Article de revue
Ce document a été publié dans
SIAM Journal on Imaging Sciences. 2014-05, vol. 7, n° 2, p. 1080--1107
Society for Industrial and Applied Mathematics
Résumé en anglais
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 ...Lire la suite >
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.< Réduire
Mots clés en anglais
blocks of measurements
Compressed Sensing
optimization on metric spaces
dissimilarity measure between discrete probabilities
blocks-constrained acquisition
optimization on metric spaces.
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