A fast algorithm for structured low-rank matrix recovery with applications to undersampled MRI reconstruction

Structured low-rank matrix priors are emerging as powerful alternatives to traditional image recovery methods such as total variation (TV) and wavelet regularization. The main challenge in applying these schemes to large-scale problems is the dramatic increase in computational complexity and memory demand that results from a lifting of the image to a high-dimensional structured matrix. We introduce a fast and memory efficient algorithm that exploits the structure of the lifted matrix to work in the original non-lifted domain, thus considerably reducing the complexity. Our experiments on the recovery of MR images from undersampled measurements show that the resulting algorithm provides improved reconstructions over TV regularization with comparable computation time.