MR image reconstruction with block sparsity and iterative support detection

This work aims to develop a novel magnetic resonance (MR) image reconstruction approach motivated by the recently proposed sampling framework with union-of-subspaces model (SUoS). Based on SUoS, we propose a mathematical formalism that effectively integrates a block sparsity constraint and support information which is estimated in an iterative fashion. The resulting optimization problem consists of a data fidelity term and a support detection based block sparsity (SDBS) promoting term penalizing entries within the complement of the estimated support. We provide optional strategies for block assignment, and we also derive unique and robust recovery conditions in terms of the structured restricted isometric property (RIP), namely the block-RIP. The block-RIP constant we derive is lower than that of the previous structured sparse method, which leads to a reduction of the measurements. Simulation results for reconstructing individual and multiple T1/T2-weighted images demonstrate the consistency with our theoretical claims, and show considerable improvement in comparison with methods using only block sparsity or support information.