  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.
