Balachandrasekaran Arvind, Ongie Greg, Jacob Mathews
Department of Electrical and Computer Engineering, University of Iowa, IA, USA.
Department of Mathematics, University of Iowa, IA, USA.
Proc Int Conf Image Proc. 2016 Sep;2016:1858-1862. doi: 10.1109/icip.2016.7532680. Epub 2016 Aug 19.
We introduce a fast structured low-rank matrix completion algorithm with low memory & computational demand to recover the dynamic MRI data from undersampled measurements. The 3-D dataset is modeled as a piecewise smooth signal, whose discontinuities are localized to the zero sets of a bandlimited function. We show that a structured matrix corresponding to convolution with the Fourier coefficients of the signal derivatives is highly low-rank. This property enables us to recover the signal from undersampled measurements. The application of this scheme in dynamic MRI shows significant improvement over state of the art methods.
我们引入一种快速的结构化低秩矩阵补全算法,该算法具有低内存和计算需求,用于从欠采样测量中恢复动态磁共振成像(MRI)数据。三维数据集被建模为一个分段平滑信号,其不连续性局限于一个带限函数的零集。我们表明,与信号导数的傅里叶系数进行卷积对应的结构化矩阵具有高度低秩性。这一特性使我们能够从欠采样测量中恢复信号。该方案在动态MRI中的应用显示出比现有方法有显著改进。