# Nonlocal Low-Rank Tensor Factor Analysis for Image Restoration

## TL;DR

This paper introduces NLR-TFA, a novel low-rank tensor factor analysis method for image restoration that effectively captures non-local correlations, improving reconstruction especially at low sampling rates.

## Contribution

It proposes a new low-rank tensor factorization approach combined with ADMM and deep learning to enhance image reconstruction in compressive sensing.

## Key findings

- Outperforms existing methods at low CS sampling rates
- Effective in both noiseless and noisy measurements
- Demonstrates superior image quality in experiments

## Abstract

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.