Dynamic Magnetic Resonance Imaging via Nonconvex Low-Rank Matrix Approximation

Abstract

Reconstruction of highly accelerated dynamic magnetic resonance imaging (MRI) is of crucial importance for the medical diagnosis. The application of general robust principal component analysis (RPCA) to MRI can increase imaging speed and efficiency. However, conventional RPCA makes use of nuclear norm as convex surrogate of the rank function, whose drawbacks have been mentioned in plenty of literature. Recently, nonconvex surrogates of the rank function in RPCA have been widely investigated and proved to be tighter rank approximation than nuclear norm by the massive experimental results. Motivated by this, we propose a nonconvex alternating direction method based on nonconvex rank approximation to reconstruct dynamic MRI data from undersampled $k-t$ space data. We solve the associated nonconvex model by the alternating direction method and difference of convex programming. The convergence analysis provided guarantees the effectiveness of our algorithm. Experimental results on cardiac perfusion and cardiac cine MRI data demonstrate that our method outperforms the state-of-the-art MRI reconstruction methods in both image clarity and computation efficiency.