Ma Shuli, Du Huiqian, Mei Wenbo
School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China.
School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China.
Magn Reson Imaging. 2019 Jul;60:20-31. doi: 10.1016/j.mri.2019.03.019. Epub 2019 Mar 29.
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 and T 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 and T. 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.
低秩结构是一种强大的先验特征，在约束磁共振成像（MRI）中得到了应用。在本文中，我们根据差异图像中的稀疏性与互易谱域的低秩性之间的对偶性，从加权k空间数据构建两个低秩矩阵T和T。然后，我们提出了一种两步约束MR图像重建方法。首先，通过强制矩阵T和T的低秩性来恢复垂直和水平差异图像。然后，通过最小二乘法重建图像。在第一步中，矩阵的核范数被两个因子分解矩阵的最小Frobenius范数所取代，并应用交替方向乘子法（ADMM）算法来恢复差异图像。这种无需奇异值分解（SVD）的方法实现了快速重建。实验结果表明，所提出的方法优于其他基于低秩的方法
