Low-rank and (X-F)-space sparsity via fast composite splitting for accelerated dynamic MR imaging

The combination of low-rank and sparsity priors has attracted growing interest in dynamic MRI reconstruction from partial measurements. While classical optimization methods can be employed to minimize the corresponding objective functions, it generally requires their modification leading to computationally-intensive optimization problems. In this paper, the fast composite splitting method, a generalization of fast iterative shrinkage-thresholding algorithm for multiple penalties, is introduced in the context of dynamic MRI reconstruction from under-sampled data. This method, based on proximal gradient operators and splitting techniques, minimizes efficiently the convex image reconstruction problem formulated with low-rank and sparsity penalties, besides having low computational time and performing well for high acceleration factor.