MRI reconstruction via manifold constrained low rank regularization

Abstract

Low rank property of a group constructed by similar patches has been exploited in compressed sensing magnetic resonance imaging (CS-MRI). However, current approaches are insufficient to characterize varying degrees of self-similarity in realistic image regions. In this paper, we design a non-convex and bounded L_a,ε norm to better approximate the rank function than existing surrogate functions, and thus used as the low rank regularization to sufficiently enforce low rank property over groups. An iterative formula for calculating the proximal map of L_a,ε norm is derived via fixed point iteration, which is proven to guarantee the convergence to the optimal solution. Furthermore, for each group, a graph model is built to characterize the unique manifold structure reflecting the different correlation among its inner patches. The generalized P-Laplacian manifold constraint is formulated to preserve the local geometry of each group manifold more effectively than standard Laplacian manifold constraint. Finally, the manifold constrained low rank regularization (MCLR) model is established and efficiently solved under the frameworks of alternating direction method of multipliers (ADMM) and non-convex accelerated proximal gradient method (NcAPG). The experimental results demonstrate that L_a,ε norm and P-Laplacian manifold constraint bring a considerable performance gain of the proposed method.