Fourier-domain structured low-rank matrix priors are emerging as powerful alternatives to traditional image recovery methods such as total variation and wavelet regularization. These priors specify that a convolutional structured matrix, i.e., Toeplitz, Hankel, or their multilevel generalizations, built from Fourier data of the image should be low-rank. The main challenge in applying these schemes to large-scale problems is the computational complexity and memory demand resulting from lifting the image data to a large-scale matrix. We introduce a fast and memory-efficient approach called the generic iterative reweighted annihilation filter algorithm that exploits the convolutional structure of the lifted matrix to work in the original unlifted domain, thus considerably reducing the complexity. Our experiments on the recovery of images from undersampled Fourier measurements show that the resulting algorithm is considerably faster than previously proposed algorithms and can accommodate much larger problem sizes than previously studied. Index Terms-Annihilating filter, compressed sensing, finite rate of innovation, multi-level Toeplitz matrices, MRI reconstruction, structured low-rank matrix recovery.
Ongie et al. REF proposed an image inpainting method called the generic iterative reweighed annihilation filter (GIRAF) algorithm, which works in the original unlifted domain by exploiting the convolutional structure of the lifted matrix.
A Fast Algorithm for Convolutional Structured Low-Rank Matrix Recovery
IEEE Transactions on Computational Imaging
IEEE Transactions on Computational Imaging
Mathematics Medicine Computer Science