LASSI: A low-rank and adaptive sparse signal model for highly accelerated dynamic imaging

Sparsity-based approaches have been popular in many applications in image processing and imaging. Recent research has shown the usefulness of sparsity or low-rank techniques for solving inverse problems such as those in dynamic imaging. In particular, the imaged temporal data sequence is modeled as a sum of low-rank and sparse components that are estimated from measurements. In this work, we instead decompose the temporal image sequence into a low-rank component and a component whose spatiotemporal patches are assumed sparse in some adaptive dictionary domain. We present a methodology to jointly estimate the underlying signal components and the spatiotemporal dictionary from highly under-sampled measurements. Our numerical experiments demonstrate the promising performance of our scheme for dynamic magnetic resonance image reconstruction from undersampled k-t space data.