A Fast Algorithm for Convolutional Structured Low-rank Matrix Recovery.
A Fast Algorithm for Convolutional Structured Low-rank Matrix Recovery.
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DOI：
10.1109/tci.2017.2721819
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发表时间：
2017-12
影响因子：
5.4
通讯作者：
Jacob M
中科院分区：
文献类型：
--
作者：
Ongie G;Jacob M
傅立叶域构造的低阶矩阵先验是传统图像恢复方法的有力替代，如全变分(TV)和小波正则化。这些先验规定，从图像的傅立叶数据建立的卷积结构矩阵，即Toeplitz、Hankel或它们的多级推广应该是低阶的。将这些方案应用于大规模问题的主要挑战是将图像数据提升到大规模矩阵所产生的计算复杂性和内存需求。提出了一种快速高效的迭代重加权湮没滤波(Giraf)算法，该算法利用提升矩阵的卷积结构在原始的非提升域中工作，从而大大降低了算法的复杂度。对欠采样傅立叶测量值图像恢复的实验表明，所得到的算法比以前提出的算法要快得多，并且可以适应比以前研究的更大的问题规模。
Fourier domain structured low-rank matrix priors are emerging as powerful alternatives to traditional image recovery methods such as total variation (TV) and wavelet regularization. These priors specify that a convolutional structured matrix, i.e., Toeplitz, Hankel, or their multi-level generalizations, built from Fourier data of the image should be low-rank. The main challenge in applying these schemes to large-scale problems is the computational complexity and memory demand resulting from a lifting the image data to a large scale matrix. We introduce a fast and memory efficient approach called the Generic Iterative Reweighted Annihilation Filter (GIRAF) algorithm that exploits the convolutional structure of the lifted matrix to work in the original un-lifted domain, thus considerably reducing the complexity. Our experiments on the recovery of images from undersampled Fourier measurements show that the resulting algorithm is considerably faster than previously proposed algorithms, and can accommodate much larger problem sizes than previously studied.