Summary

We develop fast algorithms with wavelet regularization for general acquisition schemes in Magnetic Resonance Imaging. We also develop tools for the validation of MRI reconstruction methods.

Introduction

Classical MRI uses Cartesian sampling in k -space which facilitates the reconstruction process (simple inverse Fourier transform). Currently, the research focus is on more-general acquisition schemes ( e.g. , non-Cartesian, or with missing data) that offer more flexibility, but require more-complicated reconstruction procedures. The state-of-the-art algorithms are linear, but there is evidence that the quality of reconstruction can be improved by using nonlinear iterative techniques.

Main Contribution

To have a better-conditioned reconstruction problem, we propose to favor solutions that have a sparse representation in the wavelet domain (which is the case for natural-looking images). Our mathematical efforts will focus on the design of an algorithm with fast convergence that exploits the specificity of the problem settings. As a first step, we design an algorithm adapted to the single-coil case that can handle general non-Cartesian k -space sampling. Next, we extend it to the multiple-coil problem. We validate the reconstruction process on to both simulated and real data. We obtain equal or superior results in quality and speed with respect to the current state-of-the-art techniques.