# Non-Convex Tensor Low-Rank Approximation for Infrared Small Target Detection

arXiv: https://arxiv.org/abs/2105.14974 · HTML: https://mlsanity.com/paper/2105.14974/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 64 references that are in the map.
- First posted on arXiv 31 May 2021.

## Builds on (most cited first, 9 of 9)

- [Asymmetric Contextual Modulation for Infrared Small Target Detection](https://mlsanity.com/paper/2009.14530/) (2020)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Reweighted Infrared Patch-Tensor Model With Both Non-Local and Local Priors for Single-Frame Small Target Detection](https://mlsanity.com/paper/1703.09157/) (2017)
- [Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition](https://mlsanity.com/paper/1707.02477/) (2017)
- [Novel methods for multilinear data completion and de-noising based on tensor-SVD](https://mlsanity.com/paper/1407.1785/) (2014)
- [Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization](https://mlsanity.com/paper/1708.04181/) (2017)
- [On Tensor Completion via Nuclear Norm Minimization](https://mlsanity.com/paper/1405.1773/) (2014)
- [Weighted Schatten p-Norm Minimization for Image Denoising and Background Subtraction](https://mlsanity.com/paper/1512.01003/) (2015)
- [Iterative Block Tensor Singular Value Thresholding for Extraction of Low Rank Component of Image Data](https://mlsanity.com/paper/1701.04043/) (2017)

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

- [Mapping Degeneration Meets Label Evolution: Learning Infrared Small Target Detection with Single Point Supervision](https://mlsanity.com/paper/2304.01484/) (2023)
- [Local Motion and Contrast Priors Driven Deep Network for Infrared Small Target Super-Resolution](https://mlsanity.com/paper/2201.01014/) (2022)
- [Small Aerial Target Detection for Airborne Infrared Detection Systems using LightGBM and Trajectory Constraints](https://mlsanity.com/paper/2407.01278/) (2024)
- [Noise-Robust Box-Supervised Infrared Small Target Detection via Physics-Inspired Soft Label Optimization](https://mlsanity.com/paper/2607.17148/) (2026)

## Abstract (arXiv)

Infrared small target detection is an important fundamental task in the infrared system. Therefore, many infrared small target detection methods have been proposed, in which the low-rank model has been used as a powerful tool. However, most low-rank-based methods assign the same weights for different singular values, which will lead to inaccurate background estimation. Considering that different singular values have different importance and should be treated discriminatively, in this paper, we propose a non-convex tensor low-rank approximation (NTLA) method for infrared small target detection. In our method, NTLA regularization adaptively assigns different weights to different singular values for accurate background estimation. Based on the proposed NTLA, we propose asymmetric spatial-temporal total variation (ASTTV) regularization to achieve more accurate background estimation in complex scenes. Compared with the traditional total variation approach, ASTTV exploits different smoothness intensities for spatial and temporal regularization. We design an efficient algorithm to find the optimal solution of our method. Compared with some state-of-the-art methods, the proposed method achieves an improvement in terms of various evaluation metrics. Extensive experimental results in various complex scenes demonstrate that our method has strong robustness and low false-alarm rate. Code is available at https://github.com/LiuTing20a/ASTTV-NTLA.