Ongie Greg, Jacob Mathews
Department of Mathematics, University of Iowa, IA, USA.
Department of Electrical and Computer Engineering, University of Iowa, IA, USA.
Proc IEEE Int Symp Biomed Imaging. 2016 Apr;2016:522-525. doi: 10.1109/isbi.2016.7493322. Epub 2016 Jun 16.
Structured low-rank matrix priors are emerging as powerful alternatives to traditional image recovery methods such as total variation (TV) and wavelet regularization. The main challenge in applying these schemes to large-scale problems is the computational complexity and memory demand resulting from a lifting of the image to a high-dimensional dense matrix. We introduce a fast and memory efficient algorithm that exploits the convolutional structure of the lifted matrix to work in the original non-lifted domain, thus considerably reducing the complexity. Our experiments on the recovery of MR images from undersampled measurements show that the resulting algorithm provides improved reconstructions over TV regularization with comparable computation time.
结构化低秩矩阵先验正成为传统图像恢复方法（如图像的总变分（TV）和小波正则化）的有力替代方案。将这些方案应用于大规模问题的主要挑战在于，将图像提升为高维密集矩阵会导致计算复杂度和内存需求增加。我们引入了一种快速且内存高效的算法，该算法利用提升矩阵的卷积结构在原始未提升域中工作，从而显著降低了复杂度。我们对从欠采样测量中恢复磁共振图像的实验表明，所得算法在可比的计算时间内，相较于TV正则化提供了更好的重建效果。
