# Nonlocal Patch-Based Fully-Connected Tensor Network Decomposition for Remote Sensing Image Inpainting

arXiv: https://arxiv.org/abs/2109.05889 · HTML: https://mlsanity.com/paper/2109.05889/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 25 references that are in the map.
- First posted on arXiv 13 Sep 2021.

## Builds on (most cited first, 8 of 8)

- [Efficient tensor completion for color image and video recovery: Low-rank tensor train](https://mlsanity.com/paper/1606.01500/) (2016)
- [Hyperspectral Image Denoising Employing a Spatial-Spectral Deep Residual Convolutional Neural Network](https://mlsanity.com/paper/1806.00183/) (2018)
- [Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion](https://mlsanity.com/paper/1809.02288/) (2018)
- [Non-local Meets Global: An Integrated Paradigm for Hyperspectral Denoising](https://mlsanity.com/paper/1812.04243/) (2018)
- [Hybrid Noise Removal in Hyperspectral Imagery With a Spatial-Spectral Gradient Network](https://mlsanity.com/paper/1810.00495/) (2018)
- [Learning Shared Cross-modality Representation Using Multispectral-LiDAR and Hyperspectral Data](https://mlsanity.com/paper/1912.08837/) (2019)
- [Hyperspectral Image Denoising and Anomaly Detection Based on Low-rank and Sparse Representations](https://mlsanity.com/paper/2103.07437/) (2021)
- [Tensor train rank minimization with nonlocal self-similarity for tensor completion](https://mlsanity.com/paper/2004.14273/) (2020)

## Built on by (most cited first, 6 of 6)

- [Revisiting Nonlocal Self-Similarity from Continuous Representation](https://mlsanity.com/paper/2401.00708/) (2024)
- [The Change You Want To Detect: Semantic Change Detection In Earth Observation With Hybrid Data Generation](https://mlsanity.com/paper/2503.15683/) (2025)
- [Haar Nuclear Norms with Applications to Remote Sensing Imagery Restoration](https://mlsanity.com/paper/2407.08509/) (2024)
- [Latent Matrices for Tensor Network Decomposition and to Tensor Completion](https://mlsanity.com/paper/2210.03392/) (2022)
- [Hyperspectral Image Recovery Constrained by Multi-Granularity Non-Local Self-Similarity Priors](https://mlsanity.com/paper/2508.01435/) (2025)
- [3D Reconstruction from Transient Measurements with Time-Resolved Transformer](https://mlsanity.com/paper/2510.09205/) (2025)

## Abstract (arXiv)

Remote sensing image (RSI) inpainting plays an important role in real applications. Recently, fully-connected tensor network (FCTN) decomposition has been shown the remarkable ability to fully characterize the global correlation. Considering the global correlation and the nonlocal self-similarity (NSS) of RSIs, this paper introduces the FCTN decomposition to the whole RSI and its NSS groups, and proposes a novel nonlocal patch-based FCTN (NL-FCTN) decomposition for RSI inpainting. Different from other nonlocal patch-based methods, the NL-FCTN decomposition-based method, which increases tensor order by stacking similar small-sized patches to NSS groups, cleverly leverages the remarkable ability of FCTN decomposition to deal with higher-order tensors. Besides, we propose an efficient proximal alternating minimization-based algorithm to solve the proposed NL-FCTN decomposition-based model with a theoretical convergence guarantee. Extensive experiments on RSIs demonstrate that the proposed method achieves the state-of-the-art inpainting performance in all compared methods.