A blind compressive sensing frame work for accelerated dynamic MRI

We propose a novel blind compressive sensing (BCS) frame work to recover dynamic images from under-sampled measurements. This scheme models the the dynamic signal as a sparse linear combination of temporal basis functions, chosen from a large dictionary. The dictionary and the sparse coefficients are simultaneously estimated from the under-sampled measurements. Since the number of degrees of freedom of this model is much smaller than that of current low-rank methods, this scheme is expected to provide improved reconstructions for datasets with considerable inter-frame motion. We develop an efficient majorize-minimize algorithm to solve for the dynamic images. We use a continuation strategy to minimize the convergence of the algorithm to local minima. Numerical comparisons of the BCS scheme with low-rank methods demonstrate the significant improvement in performance in the presence of motion.