1. A method for motion-compensation and regional sparsity in accelerated magnetic resonance imaging (MRI), comprising: (a) acquiring undersampled MRI data corresponding to a set of consecutive dynamic images associated with an area of interest of a subject; (b) defining the set of consecutive dynamic images as an initial set of estimated images; (c) separating an image of the initial set of estimated images into a plurality of image regions; (d) performing motion tracking for each image region of the plurality of image regions, throughout the initial set of estimated images, based at least in part on motion data associated with motion of the subject; (e) grouping the motion-tracked image regions into a plurality of clusters, based at least in part on spatial contents; (f) applying a sparsity transform to the plurality of clusters to form a plurality of sparsity-exploited, transformed image regions; (g) forming a set of merged images from the plurality of sparsity-exploited, transformed image regions; and (h) updating the set of merged images based on data fidelity, to form an updated set of estimated images.