Accelerated methods for low-rank plus sparse image reconstruction
The low-rank plus sparse (L+S) decomposition model enables the reconstruction of undersampled dynamic magnetic resonance imaging (MRI) data. Solving for the L and S components is anonsmooth composite convex minimization problem. While current techniques for this model are based on the classical iterative soft thresholding algorithm (ISTA), accelerated methods can be applied to obtain faster rate of convergence of the algorithm. This paper proposes two alternative methods for solving the L+S problem, one based on the fast iterative shrinkage-thresholding algorithm (FISTA), and the other based on the recent proximal optimized gradient method (POGM). Numerical results suggest faster convergence than the traditional ISTA, while preserving its computational simplicity.