Nuclear Norm-Regularized K-Space-based Parallel Imaging Reconstruction

Parallel imaging reconstruction suffers from serious noise amplification at high accelerations that can be alleviated with regularization by imposing some prior information or constraints on image. Nevertheless, point-wise interpolation of missing k-space data restricts the use of prior information in k-space-based parallel imaging reconstructions like generalized auto-calibrating partial acquisitions (GRAPPA). In this study, a regularized k-space based parallel imaging reconstruction is presented. We first formulate the reconstruction of missing data within a patch as a linear inverse problem. Instead of exploiting prior information on image or its transform domain, the proposed method exploits the rank deficiency of structured matrix consisting of vectorized patches form entire k-space, which leads to a nuclear norm-regularized problem solved by the numeric algorithms iteratively. Brain imaging studies are performed, demonstrating that the proposed method is capable of mitigating noise at high accelerations in GRAPPA reconstruction.