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 computational complexity and memory demand resulting from a lifting of the image to a large structured matrix. We introduce a fast and memory efficient algorithm that exploits the convolution structure of the structured matrix to work in the original non-lifted domain, thus considerably reducing the complexity. Our experiments on the recovery of images from undersampled Fourier measurements show that the resulting algorithm provides improved reconstructions over TV regularization with comparable computation time.
['Greg Ongie', 'Mathews Jacob']
GIRAF: A Fast Algorithm for Structured Low-Rank Matrix Recovery