Sparse Recovery in Magnetic Resonance Imaging With a Markov Random Field Prior

Recent research in compressed sensing of magnetic resonance imaging (CS-MRI) emphasizes the importance of modeling structured sparsity, either in the acquisition or in the reconstruction stages. Subband coefficients of typical images show certain structural patterns, which can be viewed in terms of fixed groups (like wavelet trees) or statistically (certain configurations are more likely than others). Wavelet tree models have already demonstrated excellent performance in MRI recovery from partial data. However, much less attention has been given in CS-MRI to modeling statistically spatial clustering of subband data, although the potentials of such models have been indicated. In this paper, we propose a practical CS-MRI reconstruction algorithm making use of a Markov random field prior model for spatial clustering of subband coefficients and an efficient optimization approach based on proximal splitting. The results demonstrate an improved reconstruction performance compared with both the standard CS-MRI methods and the recent related methods.