基于张量字典学习的高光谱图像稀疏表示分类  

Tensor-Based Dictionary Learning Sparse Representation Classification for Hyperspectral Image

作　　者：宫学亮 李玉[1] 贾淑涵 赵泉华[1] 王丽英[1] GONG Xue-liang;LI Yu;JIA Shu-han;ZHAO Quan-hua;WANG Li-ying(School of Geomatics,Liaoning Technical University,Fuxin 123000,China)

机构地区：[1]辽宁工程技术大学测绘与地理科学学院,辽宁阜新123000

出　　处：《光谱学与光谱分析》2025年第3期798-807,共10页Spectroscopy and Spectral Analysis

基　　金：国家自然科学基金项目(42201482);辽宁省教育厅基本科研项目(重点攻关项目)(LJKZZ20220048);辽宁省自然科学基金计划(面上项目)(2022-MS-400)资助。

摘　　要：高光谱图像因其蕴含十分丰富的光谱和空间信息已被广泛应用于生产生活的各个领域。为了充分挖掘高光谱图像中蕴含的光谱和空间信息,从高光谱数据固有的三维属性出发,以空-谱张量为基本处理单元,提出一种基于张量字典学习的稀疏表示分类(Tensor-DLSRC)算法,以提高高光谱图像分类精度。首先,构建以像素及其空间邻域像素光谱向量组成的像素空-谱张量;其次,将作为训练样本像素的空-谱张量按照不同维度展开成矩阵,并以其列向量均值作为字典原子组成初始化张量字典;同时,在张量稀疏性约束条件下构建张量稀疏表示(Tensor-SR)模型,并利用张量字典学习算法学习一组能够精确刻画该类张量空-谱特征的字靛矩阵;最后,对待分类像素利用Tensor-SR模型求解其空-谱张量的稀疏表示系数张量,根据重构残差最小化原则确定该像素类别。为了分析参数对提出算法分类精度的影响,在进行分类对比实验之前,通过一系列实验分别讨论训练样本数M、邻域窗口尺寸(2δ+1)×(2δ+1)、字典学习阶段的稀疏度μ1和稀疏表示阶段的稀疏度μ2等参数对总体分类精度(OA)的影响。为了验证提出算法的有效性,分别在Indian Pines、Salinas和Xuzhou三个高光谱数据上进行实验,对比分析本算法与基于光谱向量的SRC算法和DLSRC算法、增加邻域空间信息的JSRC算法和DLJSRC算法和基于空-谱张量的Tensor-DLSRC算法等五种算法的分类结果,并采用基于混淆矩阵的平均准确率(APR)、平均精度(PA)、OA和Kappa系数对分类结果定量分析。所提出的Tensor-DLSRC算法在OA和Kappa系数的平均值水平是六种算法中最高的,且具有最小的标准差,说明本算法与五种其他算法相比能够提供更准确且稳定的分类结果。Hyperspectral images(HSI)have been widely used in various fields of production and life due to their rich spectral and spatial information.This paper proposes a tensor dictionary learning-based sparse representation classification(Tensor-DLSRC)algorithm,which directly takes the spatial-spectral tensor as the basic unit to exploit the spectral and spatial information and improve the accuracy of hyperspectral image classification.Firstly,the spatial-spectral tensor comprises the spectral vectors of all pixels in the spatial neighborhood of the central pixels.Secondly,the mean vectors of each order fiber of the training spatial-spectral tensor are used as dictionary atoms to generate an initialized dictionary.The tensor-based dictionary learning(TDL)algorithm is proposed to train a set of structured dictionaries from the training samples.Then,a tensor-based sparse representation model is constructed based on the sparsity constraints of the tensor,and the sparse representation coefficient tensor corresponding to the test spatial-spectral tensor is obtained by solving the model.Finally,the class of the test sample is determined according to the minimization of the reconstruction residuals.To analyze the impact of parameters on the classification accuracy of the proposed algorithm,a series of experiments were conducted to discuss the effects of parameters such as training sample size M,neighborhood window size(2δ+1)×(2δ+1),sparsityμ1 in dictionary learning stage,and sparsityμ2 in sparse representation stage on overall accuracy(OA)before conducting classification comparison experiments.To verify the effectiveness of the proposed algorithm,a series of experiments were conducted on three HSIs,(e.g.,Indian Pines,Salinas,and Xuzhou)to compare and analyze the classification results of our algorithm with five comparative algorithms:SRC and DLSRC algorithms based on spectral vectors,JSRC and DLSJSC algorithms with added neighborhood spatial information,and Tensor DLSRC algorithm based on spatial-spectral tensor.The classi

关 键 词：高光谱图像 空-谱张量 稀疏表示 张量字典学习 张量稀疏表示分类 

分 类 号：TH761[机械工程—仪器科学与技术]