Low-rank signal modeling has been widely leveraged to capture non-local correlation in image processing applications. We propose a new method that employs low-rank tensor factor analysis for tensors generated by grouped image patches. The low-rank tensors are fed into the alternative direction multiplier method (ADMM) to further improve image reconstruction. The motivating application is compressive sensing (CS), and a deep convolutional architecture is adopted to approximate the expensive matrix inversion in CS applications. An iterative algorithm based on this low-rank tensor factorization strategy, called NLR-TFA, is presented in detail. Experimental results on noiseless and noisy CS measurements demonstrate the superiority of the proposed approach, especially at low CS sampling rates.
@article{arxiv.1803.06795,
title = {Nonlocal Low-Rank Tensor Factor Analysis for Image Restoration},
author = {Xinyuan Zhang and Xin Yuan and Lawrence Carin},
journal= {arXiv preprint arXiv:1803.06795},
year = {2018}
}