MR Image Reconstruction from Undersampled k-Space with Bayesian Dictionary Learning

We develop an algorithm for reconstructing magnetic resonance images (MRI) from highly undersampled k-space data. While existing methods focus on either image-level or patch-level sparse regularization strategies, we present a regularization framework that uses both image and patch-level sparsity constraints. The proposed regularization enforces image-level sparsity in terms of 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 several MR images, which show that the proposed regularization framework can improve reconstruction accuracy over other methods.