Hyperspectral Image Denoising Using Low Rank Tensor Decomposition and Weighted Group Sparse Regularization

doi:10.3969/j.issn.1006-2475.2025.01.006

Abstract

Abstract: Hyperspectral images have significant reference value in fields such as environmental monitoring， remote sensing science， and medical imaging. However， the imaging process is susceptible to contamination by mixed noise due to limitations in the imaging acquisition equipment and adverse weather conditions， leading to a significant decline in image quality. To tackle this problem， we propose a denoising model for hyperspectral images based on low rank tensor decomposition and weighted group sparsity-regularized. Specifically， to effectively retain the edge information of the hyperspectral image and extract sparse structural features， we propose a group sparse regularization method based on the [l2,1] norm， which aims to weight and constrain the differential images in the spatial and spectral directions. Then， a combined approach is proposed， which utilizes the [l1] norm and Frobenius norm， to effectively eliminate complex mixed noise in the images， thereby enhancing the overall image quality. Furthermore， we use ADMM algorithm to solve the model proposed in this paper. Experimental evaluations of the model are conducted using both simulated and real data， and the results demonstrate the superiority of the proposed model over the baseline model in terms of various evaluation metrics， particularly the proposed model has obvious advantages in hyperspectral image recovery.

Key words: hyperspectral images, image denoising, group sparsity, mixed noise, alternating direction method of multiplier

CLC Number:

TP751

WANG Yefang1, JIA Xiaoning1, 2, CHENG Libo1, 2, LI Zhe1, 2. Hyperspectral Image Denoising Using Low Rank Tensor Decomposition and Weighted Group Sparse Regularization[J]. Computer and Modernization, 2025, 0(01): 30-36.

References

［1］ LIU C， TAO R， LI W， et al. Joint classification of hyper-spectral and multispectral images for mapping coastal wetlands［J］. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing， 2020，14：982-996.
［2］ WANG R， NIE F Q， WANG Z， et al. Multiple features and isolation forest-based fast anomaly detector for hyperspectral imagery［J］. IEEE Transactions on Geoscience and Remote Sensing， 2020，58（9）：6664-6676.
［3］ ZHONG Y， RU C L， WANG S F， et al. An online， non-destructive method for simultaneously detecting chemical， biological， and physical properties of herbal injections using hyperspectral imaging with artificial intelligence［J］. Spectrochimica Acta Part A： Molecular and Biomolecular Spectroscopy， 2022，264. DOI：10.1016/j.saa.2021.120250.
［4］张兵. 高光谱图像处理与信息提取前沿［J］. 遥感学报， 2016，20（5）：1062-1090.
［5］杜培军，夏俊士，薛朝辉，等. 高光谱遥感影像分类研究进展［J］. 遥感学报， 2021，20（2）：236-256.
［6］贺霖，潘泉，邸韡，等. 高光谱图像目标检测研究进展［J］. 电子学报， 2009，37（9）：2016-2024.
［7］郝儒儒. 基于矩阵分解的低秩张量恢复算法及其应用［D］.大连：大连理工大学， 2017.
［8］许洋洋. 基于组稀疏非负矩阵分解的高光谱图像去噪方法研究［D］. 杭州：浙江大学， 2017.
［9］ CHEN Y Y， WANG S Q， ZHOU Y C. Tensor nuclear norm-based low-rank approximation with total variation regularization［J］. IEEE Journal of Selected Topics in Signal Processing， 2018，12（6）：1364-1377.
［10］黎波. 基于张量低秩稀疏恢复理论的遥感高光谱图像降噪研究［D］. 成都：成都理工大学， 2020.
［11］陶泽锐. 低秩张量去噪的自适应奇异值收缩算法［D］ .兰州：兰州大学， 2020.
［12］ FAN H Y， LI C L， GUO Y， et al. Spatial-spectral total variation regularized low-rank tensor decomposition for hyperspectral image denoising［J］. IEEE Transactions on Geoscience and Remote Sensing， 2018，56（10）：6196-6213.
［13］ ZHANG H Y， CAI J Y， HE W， et al. Double low-rank matrixdecomposition for hyperspectral image denoising and destriping［J］. IEEE Transactions on Geoscience and Remote Sensing， 2022，60. DOI： 10.1109/TGRS.2021.3061148.
［14］ YANG F， CHEN X， CHAI L. Hyperspectral Image destriping and denoising using stripe and spectral low-rank matrix recovery and global spatial-spectral total variation［J］. Remote Sensing， 2021，13（4）. DOI： 10.3390/rs13040827.
［15］ XU S， ZHANG J S， ZHANG C X. Hyperspectral image denoising by low-rank models with hyper-laplacian total variation prior［J］. Signal Processing， 2022，201. DOI： 10.
1016/j.sigpro.2022.108733.
［16］ BEHROOZI Y， YAZDI M， ASLI A Z. Hyperspectral image denoising based on superpixel segmentation low-rank matrix approximation and total variation［J］. Circuits， Systems， and Signal Processing， 2022，41（6）：3372-3396.
［17］ ZHANG H， HUANG T Z， ZHAO X L， et al. Hyperspectral image denoising： Reconciling sparse and low-tensor-ring-rank priors in the transformed domain［J］. IEEE Transactions on Geoscience and Remote Sensing， 2023，61. DOI： 10.1109/TGRS.2023.3237865.
［18］ ZENG H J， XIE X Z， NING J F. Hyperspectral image denoising via global spatial-spectral total variation regularized nonconvex local low-rank tensor approximation［J］. Signal Processing， 2021，178. DOI： 10.1016/j.sigpro.2020.
107805.
［19］周航，苏延池，李占山，等. 基于子空间表示和加权低秩张量正则化的高光谱图像混合噪声去除方法［J］. 吉林大学学报（理学版）， 2023，61（1）：118-126.
［20］ CHEN Y， HUANG T Z， HE W， et al. Hyperspectral image denoising using factor group sparsity-regularizednonconvex low-rank approximation［J］. IEEE Transactions on Geoscience and Remote Sensing， 2021，60. DOI： 10.1109/TGRS.
2021.3110769.
［21］ CHEN Y， HE W， YOKOYA N， et al. Hyperspectral image restoration using weighted group sparsity-regularized low-rank tensor composition［J］. IEEE Transactions on Cybernetics， 2020，50（8）：3556-3570.
［22］ BOYD S， PARIKH N， CHU E， et al. Distributed optimization and statistical learning via the alternating direction method of multipliers［J］. Foundations and Trends in Machine Learning， 2011，3（1）：1-122.
［23］ KOLDA T G， BADER B W. Tensor decompositions and applications［J］. SIAM Review， 2009，51（3）：455-500.
［24］ BIRGIN E G， MARTÍNEZ J M. Practical Augmented Lagrangian Methods for Constrained Optimization［M］. Society for Industrial and Applied Mathematics， 2014.
［25］ LIU G C， LIN Z C， YAN S C， et al. Robust recovery of subspace structures by low-rank representation［J］. IEEE Transactions on Pattern Analysis and Machine Intelligence， 2012，35（1）：171-184.
［26］ WANG Y， PENG J J， ZHAO Q， et al. Hyperspectral image restoration via total variation regularized low-rank tensor decomposition［J］. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing， 2018，11（4）：1227-1243.
［27］ ZHANG H Y， HE W， ZHANG L P， et al. Hyperspectral image restoration using low-rank matrix recovery［J］. IEEE Transactions on Geoscience and Remote Sensing， 2014，52（8）：4729-4743.
［28］ PENG J J， WANG Y， ZHANG H Y， et al. Exact decomposition of joint low rankness and local smoothness plus sparse matrices［J］. IEEE Transactions on Pattern Analysis and Machine Intelligence， 2023，45（5）：5766-5781.

[1]	YIN Xue-jie, MA Yu-mei, PAN Zhen-kuan. #br# Image Denoising Algorithm Based on Stochastic Resonance of Saturating System [J]. Computer and Modernization, 2019, 0(12): 44-.
[2]	GOU Rong. An Image Denoising Algorithm of RiemannLiouville Fractional Integral [J]. Computer and Modernization, 2016, 0(5): 13-17.
[3]	YANG Xing-jiang1,3, LIAO Zhi-wu2, PU Yong-hua3. Anisotropic Diffusion Image Denoising Based on Grey System Theory [J]. Computer and Modernization, 2016, 0(2): 21-23,27.
[4]	LI Lei, REN Yue-mei. Image Denoising Based on Shearlet Transform and Improved Anisotropic Diffusion [J]. Computer and Modernization, 2015, 0(5): 53-56.
[5]	WANG Qi1, CHENG Bin2, DU Juan1, XU Guo-qing1. An Improved Method for Image Denoising Based on Wavelet Thresholding [J]. Computer and Modernization, 2015, 0(4): 65-69.
[6]	TU Guang-yi;LU Jian;CAI Zhi-gang. An Image Denoising Algorithm Based on Huber Surface Fitting [J]. Computer and Modernization, 2013, 1(3): 165-167,.
[7]	LONG Junyu;YU Aimin. Nonlocal Mean Algorithm Based on Wavelet Packet Transform [J]. Computer and Modernization, 2013, 1(11): 13-16.