Sparse and dense hybrid representation via subspace modeling for dynamic MRI

Recent theoretical results on compressed sensing and low-rank matrix recovery have inspired significant interest in joint sparse and low rank modeling of dynamic magnetic resonance imaging (dMRI). Existing approaches usually describe these two respective prior information with different formulations. In this paper, we present a novel sparse and dense hybrid representation (SDR) model which describes the sparse plus low rank properties by a unified way. More specifically, under the learned dictionary consisting of temporal basis functions, SDR models the spatial coefficients in two subspaces with Laplacian and Gaussian prior distributions, respectively. This results in the objective function consisting of L1-L2 hybrid penalty term for the coefficients and Frobenius norm term for the dictionary. An efficient algorithm utilizing alternating direction technique is developed to solve the proposed model. Extensive experiments under a variety of test images and a comprehensive evaluation against existing state-of-the-art methods consistently demonstrate the potential of the proposed model and algorithm, in terms of reconstruction and separation comparisons.