Low-Rank and Sparse Matrix Decomposition Based on Schatten p=1/2 and L1/2 Regularizations for Separation of Background and Dynamic Components for Dynamic MRI

摘要

A method for determining a background component and a dynamic component of an image frame from an under-sampled data sequence obtained in a dynamic MRI application is provided. The two components are determined by optimizing a low-rank component and a sparse component of the image frame in a sense of minimizing a weighted sum of terms. The terms include a Schatten_p=1/2 (S_1/2-norm) of the low-rank component, an L_1/2-norm of the sparse component additionally sparsified by a sparsifying transform, and an L₂-norm of a difference between the sensed data sequence and a reconstructed data sequence. The reconstructed one is obtained by sub-sampling the image frame according to an encoding or acquiring operation. The background and dynamic components are the low-rank and sparse components, respectively. Experimental results demonstrate that the method outperforms an existing technique that minimizes a nuclear-norm of the low-rank component and an L₁-norm of the sparse component.