自适应全变差和低秩约束的高光谱图像稀疏解混  

Sparse Unmixing of Hyperspectral Images Based on Adaptive Total Variation and Low-Rank Constraints

作　　者：徐晨光[1,2] 郭禹 李峰 刘翼 李艳 邓承志 刘燕德[2] XU Chen-guang;GUO Yu;LI Feng;LIU Yi;LI Yan;DENG Chen-zhi;LIU Yan-de(Jiangxi Province Key Laboratory of Water Information Cooperative Sensing and Intelligent Processing,Nanchang Institute of Technology,Nanchang 330099,China;School of Intelligent Electromechanical Equipment Innovation Research Institute,East China Jiaotong University,Nanchang 330013,China)

机构地区：[1]南昌工程学院江西省水信息协同感知与智能处理重点实验室,江西南昌330099 [2]华东交通大学智能机电创新研究院,江西南昌330013

出　　处：《光谱学与光谱分析》2025年第4期1071-1081,共11页Spectroscopy and Spectral Analysis

基　　金：江西省科技厅重大科技研发专项“揭榜挂帅”制项目(20213AAG01012);江西省2024年度研究生创新专项资金项目(YC2024-B200)资助。

摘　　要：高光谱稀疏解混是利用一个含有丰富的端元光谱信息的光谱库作为先验,并对高光谱数据进行分解,得到与光谱库中各端元光谱对应的丰度的图像处理技术。然而目前大多数稀疏解混方法,在高噪声条件下的解混效果不佳,且很多去噪解混算法只是片面的利用了高光谱的某些特性,并没有对高光谱特性进行全面考虑,从而影响了解混算法的精度。为了解决这一问题,创新地提出了一种基于自适应全变差和低秩约束的高光谱图像稀疏解混方法。首先对稀疏解混算法进行了详细的介绍,接着对自适应全变差和低秩约束的高光谱图像稀疏解混算法进行建模,提出自适应全变差和低秩约束的高光谱图像稀疏解混算法。该算法把高光谱数据的低秩特性和自适应TV空间特性进行了融合,在保持丰度的低秩性和稀疏性的同时,自适应调整丰度矩阵在不同结构下全变差正则化的水平差和垂直差比例,达到更好的去噪效果。然后,使用ADMM算法对新的模型进行求解。最后,利用SUnSAL-TV,ADSpLRU,S2WSU,SU-ATV等几种比较经典的算法与本算法比较,通过两组模拟数据和一组真实数据来实验验证算法的好坏。两组模拟数据分别是在背景单一的DC1和背景复杂的DC2中各自加入10、15和20 dB三种高斯噪声得到的数据。模拟数据实验通过利用不同算法对这两组数据解混,对解混结果的信号与重建误差比、丰度重构正确率和稀疏度三个数值来比较,并对几种算法解混后的丰度图像、丰度图像与真实图像的差值图等信息进行观察对比,从而分析几种算法的好坏。真实数据实验是利用了内华达州的Cuprite矿区高光谱真实数据对解混结果进行分析对比,进一步用真实数据验证本算法的优势。实验结果表明:本方法相对于较为流行的几种解混方法具有更好的鲁棒性和解混效果,在SRE方面提高了11.4%~310.2%,拥有更出色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,S 2WSU,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 reco

关 键 词：稀疏解混 自适应全变差 低秩约束 高光谱图像 

分 类 号：P258[天文地球—测绘科学与技术]