# Nonlocal Low-Rank Tensor Factor Analysis for Image Restoration

arXiv: https://arxiv.org/abs/1803.06795 · HTML: https://mlsanity.com/paper/1803.06795/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2018.

## Built on by (most cited first, 4 of 4)

- [Revisiting Nonlocal Self-Similarity from Continuous Representation](https://mlsanity.com/paper/2401.00708/) (2024)
- [SVDinsTN: A Tensor Network Paradigm for Efficient Structure Search from Regularized Modeling Perspective](https://mlsanity.com/paper/2305.14912/) (2023)
- [Tensor Robust PCA with Nonconvex and Nonlocal Regularization](https://mlsanity.com/paper/2211.02404/) (2022)
- [Affine Subspace Models and Clustering for Patch-Based Image Denoising](https://mlsanity.com/paper/2512.07259/) (2025)

## Abstract (arXiv)

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.