Sparse Unmixing of Hyperspectral Images Based on Adaptive Total
Variation and Low-Rank Constraints
XU Chen-guang1, 2, GUO Yu1, LI Feng1, LIU Yi1, LI Yan1, DENG Chen-zhi1*, LIU Yan-de2*
1. Jiangxi Province Key Laboratory of Water Information Cooperative Sensing and Intelligent Processing, Nanchang Institute of Technology, Nanchang 330099, China
2. School of Intelligent Electromechanical Equipment Innovation Research Institute，East China Jiaotong University，Nanchang
330013，China
Abstract：Hyperspectral sparse unmixing is an image processing technique that uses a spectral library containing rich endmember spectral information as a prior and decomposes the hyperspectral data to obtain the abundance corresponding to each endmember spectrum in the spectral library. However, most of the current sparse unmixing methods have poor unmixing effect under high noise conditions, and many de-noising unmixing methods only make partial use of some characteristics of hyperspectrum and do not fully consider the characteristics of hyperspectrum, thus affecting the accuracy of understanding the mixing algorithm. To solve this problem, an innovative hyperspectral image sparse unmixing method based on adaptive total variation and low-rank constraints is proposed. In this paper, the sparse unmixing algorithm is introduced in detail. Then, the hyperspectral image's adaptive total variation and low-rank constraint sparse unmixing algorithm are modeled. The hyperspectral image's adaptive total variation and low-rank constraint sparse unmixing algorithm is proposed. The algorithm combines the low-rank characteristics of hyperspectral data with the adaptive TV spatial characteristics. While maintaining the low rank and sparsity of abundance, it adaptively adjusts the ratio of horizontal and vertical differences of total variation regularization of the abundance matrix under different structures to achieve a better denoising effect. Then, the ADMM algorithm is used to solve the new model. Finally, several classical algorithms, such as SUnSAL-TV, ADSpLRU, S2WSU, and SU-ATV, are compared with the proposed algorithm, and two sets of simulation data and one set of real data are used to verify the quality of the algorithm. Two sets of simulation data are obtained by adding 10, 15, and 20 dB high Gaussian noise to DC1 with a single background and DC2 with a complex background, respectively. In the simulation data experiment, different algorithms were used to unmix the two data groups, and the three values of signal and reconstruction error ratio, abundance reconstruction accuracy, and sparsity of the unmixing results were compared. Moreover, the abundance image after unmixing several algorithms and the difference graph between the abundance image and the real image was observed and compared to analyze the quality of several algorithms. The real data experiment uses hyperspectral real data from a Cuprite mining area in Nevada to analyze and compare the unmixing results and further verify the advantages of the proposed algorithm with real data. The experimental results show that the proposed method improves SRE by 11.4%~310.2% with better robustness and performance than several popular methods.
Key words：Sparse unmixing; Adaptive total variation; Low-rank constraint; Hyperspectral image
徐晨光，郭 禹，李 峰，刘 翼，李 艳，邓承志，刘燕德. 自适应全变差和低秩约束的高光谱图像稀疏解混[J]. 光谱学与光谱分析, 2025, 45(04): 1071-1081.
XU Chen-guang, GUO Yu, LI Feng, LIU Yi, LI Yan, DENG Chen-zhi, LIU Yan-de. Sparse Unmixing of Hyperspectral Images Based on Adaptive Total
Variation and Low-Rank Constraints. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2025, 45(04): 1071-1081.
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