Compressed sensing in MRI with a Markov random field prior for spatial clustering of subband coefficients

Recent work in compressed sensing of magnetic resonance images (CS-MRI) concentrates on encoding structured sparsity in acquisition or in the reconstruction stages. Subband coefficients of typical images obey a certain structure, which can be viewed in terms of fixed groups (like wavelet trees) or statistically (certain configurations are more likely than others). Approaches using wavelet tree-sparsity have already demonstrated excellent performance in MRI. However, the use of statistical models for spatial clustering of the subband coefficients has not been studied well in CS-MRI yet, although the potentials of such an approach have been indicated. In this paper, we design a practical reconstruction algorithm as a variant of the proximal splitting methods, making use of a Markov Random Field prior model for spatial clustering of subband coefficients. The results for different undersampling patterns demonstrate an improved reconstruction performance compared to both standard CS-MRI methods and methods based on wavelet tree sparsity.