Compressed sensing MRI with Bayesian dictionary learning

We present an inversion algorithm for magnetic resonance images (MRI) that are highly undersampled in k-space. The proposed method incorporates spatial finite differences (total variation) and patch-wise sparsity through in situ dictionary learning. We use the beta-Bernoulli process as a Bayesian prior for dictionary learning, which adaptively infers the dictionary size, the sparsity of each patch and the noise parameters. In addition, we employ an efficient numerical algorithm based on the alternating direction method of multipliers (ADMM). We present empirical results on two MR images.