Hu Yue, Liu Xiaohan, Jacob Mathews
Department of Electronics and Information Technology, Harbin Institute of Technology, Harbin, China.
Department of Electrical and Computer Engineering, University of Iowa, IA, USA.
Proc IEEE Int Symp Biomed Imaging. 2018 Apr;2018:1260-1263. doi: 10.1109/isbi.2018.8363800. Epub 2018 May 24.
We introduce an adaptive structured low rank algorithm to recover MR images from their undersampled Fourier coefficients. The image is modeled as a combination of a piecewise constant component and a piecewise linear component. The Fourier coefficients of each component satisfy an annihilation relation, which results in a structured Toeplitz matrix. We exploit the low rank property of the matrices to formulate a combined regularized optimization problem, which can be solved efficiently. Numerical experiments indicate that the proposed algorithm provides improved recovery performance over the previously proposed algorithms.
我们引入一种自适应结构化低秩算法，用于从欠采样的傅里叶系数中恢复磁共振（MR）图像。图像被建模为一个分段常数分量和一个分段线性分量的组合。每个分量的傅里叶系数满足一个湮灭关系，这导致一个结构化托普利兹矩阵。我们利用矩阵的低秩特性来制定一个组合正则化优化问题，该问题可以高效求解。数值实验表明，与先前提出的算法相比，所提算法具有更好的恢复性能。
