基于自适应空谱约束的加权残差NMF高光谱图像解混  

Weighted Residual NMF for Hyperspectral Image Unmixing Based on an Adaptive Spatial-Spectral Constraint

作　　者：陈善学[1] 戚俊杰 CHEN Shanxue;QI Junjie(Chongqing Key Laboratory of Mobile Communications Technology,School of Communications and Information Engineering,Chongqing University of Posts and Telecommunications,Chongqing 400065,China)

机构地区：[1]重庆邮电大学通信与信息工程学院,移动通信技术重庆市重点实验室,重庆400065

出　　处：《信号处理》2025年第3期553-568,共16页Journal of Signal Processing

摘　　要：标准的非负矩阵分解(Nonnegative Matrix Factorization,NMF)模型应用于高光谱图像解混时,由于模型的非凸性、光谱和空间先验信息未充分利用的问题,导致解混精度不高。为提高解混性能,提出了一种基于自适应空谱约束的加权残差非负矩阵分解高光谱图像解混算法。该算法首先,对传统的NMF模型进行改进,利用在迭代过程中原始高光谱图像矩阵与重构图像矩阵之间的残差来构建残差权重因子,为损失函数的每一行分配贡献权重,以减轻噪声的影响,提高算法的鲁棒性。其次,为利用高光谱图像丰富的先验信息,算法引入像元空谱相似度来衡量像元间的相似性以捕获像元在空间及光谱上的联系,并由相似度矩阵自适应地确定像元邻域来构造空间权重因子,提升了丰度的分段平滑性。此外,结合丰度矩阵的固有特征,构造光谱权重因子,促进了丰度的稀疏性。最后,由于高光谱图像具有较高的光谱分辨率,相邻波段的反射值变化较小,因此端元光谱具有一定的平滑度,算法通过端元光谱反射值间的差异分配平滑权重,以调整在迭代过程中端元光谱的平滑程度。本文利用梯度下降推导出算法的乘法更新规则,为证明所提算法的有效性,将其与其他几种算法在模拟数据以及Jasper Ridge和Urban两个真实高光谱数据上进行实验,实验结果验证了该算法具有更好的解混性能。When the standard nonnegative matrix factorization(NMF)model was applied to hyperspectral image unmixing,the nonconvexity of the model and insufficient utilization of spectral and spatial prior information resulted in low unmixing accuracy.To improve the unmixing performance,a weighted residual NMF for hyperspectral image unmixing based on an adaptive spatial-spectral constraint was proposed.The algorithm initially enhanced the traditional NMF model by utilizing the residuals between the original hyperspectral and reconstructed image matrices in the iterative process to construct the residual weight factors.This algorithm assigned contribution weights to each row of the loss function to alleviate the influence of noise and improve its robustness.Additionally,to leverage the rich a priori information in hyperspectral images,the algorithm introduced pixel spatial-spectral similarity to gauge the similarity between pixels,capturing the spatial and spectral connections among them.It then constructed the spatial weight factors by adaptively determining the pixel neighborhoods from the similarity matrix,thereby enhancing the piecewise smoothing of the abundance.Moreover,spectral weighting factors were constructed by integrating the inherent characteristics of the abundance matrix,which promoted the sparsity of the abundance.Finally,owing to the high spectral resolution of hyperspectral images and small variation in reflection values between adjacent bands,the endmember spectra exhibit a certain degree of smoothness.The algorithm assigned smoothing weights using the differences between the spectral reflectance values of endmembers to adjust the degree of spectral smoothing of the endmembers during the iterative process.This study utilized gradient descent to derive the multiplicative update rules for the algorithm.To demonstrate the effectiveness of the proposed algorithm,it was compared with several other algorithms using simulated data as well as two real hyperspectral datasets,namely,Jasper Ridge and Urban.The experi

关 键 词：高光谱图像解混 非负矩阵分解 加权残差 像元空谱相似度 平滑权重 

分 类 号：TP751[自动化与计算机技术—检测技术与自动化装置]