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

TL;DR

This paper compares theoretical and heuristic sampling strategies in variable density compressed sensing for MRI, demonstrating that a two-stage approach with dense center sampling and optimal distribution sampling significantly improves image reconstruction quality.

Contribution

It introduces a novel two-stage sampling strategy combining dense center sampling with optimal distribution sampling, enhancing MRI reconstruction performance.

Findings

Two-stage sampling improves MRI reconstruction quality

Optimal distribution sampling outperforms heuristic methods

Dense center sampling is crucial for accurate MRI recovery

Abstract

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.