A two-step low rank matrices approach for constrained MR image reconstruction

Low-rank structure is a powerful priori characteristic that is exploited in constrained magnetic resonance imaging (MRI). In this paper, we build two low rank matrices T _V and T _H from weighted k-space data according to the duality between the sparsity in the difference image and the low-rankness of a reciprocal spectral domain. Then, we propose a two-step constrained MR image reconstruction method. First, the vertical and horizontal difference images are recovered via enforcing low-rankness of matrices T _V and T _H . Then, the image is reconstructed via the least squares method. In the first step, the nuclear norm of a matrix is replaced by the minimum Frobenius norm of two factorization matrices and the alternating direction method of multipliers (ADMM) algorithm is applied to recover the difference images. This singular value decomposition (SVD) free method leads to fast reconstruction. The experimental results demonstrate that the proposed method outperforms other low rank based methods.