A Fast Low-Rank Matrix Factorization Method for Dynamic Magnetic Resonance Imaging Restoration

Abstract

Nowadays, over 90 percent of the medical data comes from the medical image. People can reduce the medical faults in diagnoses by using computer to analyze and process these medical image data. In this paper, we focus on the reconstruction of dynamic magnetic resonance imaging (MRI), which is crucial to medical diagnoses. Considering the successful application of the robust principal component analysis (RPCA) in MRI to increase the imaging speed and improve the imaging quality, we propose a model based on RPCA. However, the conventional models based on RPCA have two drawbacks: one is that the nuclear norm is often inexact rank approximation, especially when there exist some large singular values; the other is that dealing with the whole data matrix is always time consuming. Our strategies are to adopt a more exact nonconvex rank approximation and matrix factorization, respectively. The former has been proved to be better than the nuclear norm, while the latter can reduce computation complexity by turning the computing object into a core matrix, which is much smaller than the original data matrix. Then the alternating direction method (ADM) is used to solve the well-designed model. Experiments of cardiac cine and abdomen MRI data are conducted to verify the superior performance of our method in both image clarity and computation efficiency when compared with the conventional MRI reconstruction methods.