一种稀疏约束的图正则化非负矩阵光谱解混方法

A Sparse Constrained Graph Regularized Nonnegative Matrix Factorization Algorithm for Hyperspectral Unmixing

由于受到高光谱遥感图像传感器平台的限制,图像的空间分辨率受到一定影响,这导致高光谱遥感图像的像元通常是多种地物的混合,也叫做混合像元。混合像元的存在制约了高光谱遥感图像的准确分析和应用领域。采用高光谱解混技术可将混合像元分解为纯净的物质光谱(Endmember,端元)和每种物质光谱所对应的混合比例(Abundance,丰度),为获取更多更精细的光谱提供了可能。这对高精度的地物分类识别、目标检测和定量遥感分析等研究领域具有重要的意义。因此,解混技术成为高光谱遥感图像领域的一个研究热点。基于线性光谱混合模型(linear spectral mixing model, LMM),提出了一种端元丰度联合稀疏约束的图正则化非负矩阵分解(endmember and abundance sparse constrained graph regularized nonnegative matrix factorization, EAGLNMF)算法。该算法通过研究基于非负矩阵分解(nonnegative matrix factorization, NMF)的方法,结合图正则化理论来考虑高光谱数据内部的几何结构,将端元光谱稀疏约束和丰度稀疏约束应用于其中,从而能够对高光谱数据的内部流形结构进行更为有效的表达。首先,构造了EAGLNMF算法的损失函数,采用VCA-FCLS方法进行初始化,然后,设定相关参数,包括图正则化权重矩阵参数、端元光谱稀疏约束因子和丰度矩阵稀疏约束因子,最后,通过推导得到了端元矩阵与丰度矩阵的迭代公式,并且设置了迭代停止条件。该方法不受图像中是否有纯像元的限制。实际上,在现行高光谱遥感传感器平台情况下,高光谱遥感图像中几乎不存在纯像元,因此, EAGLNMF方法为高光谱遥感图像的实际应用提供了一种思路。采用合成的高光谱数据,构造了4个实验来分析该方法的可行性和有效性,实验将该算法与VCA-FCLS,标准NMF及GLNMF等经典的解混算法进行比较,通过光谱角距离(spectral angle distance, SAD)和丰度角距离(abundance angle distance, AAD)这两个度量标准来进行比较。实验1是总体分析实验。在固定的信噪比和固定端元数目的情况下,用以上三种经典方法与EAGLNMF同时进行解混。实验2是SNR影响分析实验。在固定端元数目和不同信噪比的情况下,用这四种方法进行解混。实验3端元数目分析实验。在固定信噪比和不同端元数目的情况下,用四种方法进行解混,并且将结果进行对比。实验结果发现提出的EAGLNMF方法在提取端元精度和估计丰度精度上都更为准确。同时,实验4是稀疏因子分析实验。对端元稀疏约束和丰度稀疏约束之间的影响因子进行分析,实验结果表明引入的端元稀疏约束对于解混结果也具有较好的影响,并且端元稀疏约束和丰度稀疏约束之间的影响因子也对解混结果具有一定影响。最后,将该算法应用于AVIRIS所采集的真实高光谱图像数据,将其解混结果与美国地质勘探局光谱库中光谱进行匹配对比,其提取的平均端元精度相比于其他三种方法要稍好。

The space resolution of hyperspectral image is influenced due to the restriction of sensor platform, which results in more than one material in one pixel. Such kind of pixel is called mixed pixel. The existence of mixed pixels restricts accurate analysis and application of hyperspectral images. Hyperspectralunmixing technique can factorize mixed pixels to pure material signatures(endmembers) and corresponding proportion(abundance), which makes more accurate material signature available. Unmxing is very important to accurate classification and identification, anomaly detection and quantitative analysis for hyperspectral imagery. Based on linear spectral mixing model, this paper develops an endmember and abundance sparse constrained graph regularized nonnegative matrix factorization(EAGLNMF) algorithm for hyperspectral imagery unmixing. The algorithm is based on nonnegative matrix factorization, and integrates graph regularization and both endmember and abundance sparse constraints to the object function. Graph regularization is used to consider the geometrical structure of the hyperspectral image and sparse constraints can demonstrate the inner manifoldstructure. First, the lost function of EAGLNMF is constructed, and VCA-FCLS method is used as initial value. And then, the value of the parameters is set, including weighting matrix of graph regularization, sparse factors for both endmember signature matrix and abundance matrix. At last, the iteration equations for endmember matrix and abundance matrix are both obtained, and stopping criteria is given. The algorithm does not require pure pixel in the hyperspectral image. In fact, there are little pure pixel in real hyperspectral imagerydue to the sensors platform. Thus, EAGLNMF algorithm provides a kind of solution for real hyperspectral imagery. The availability and effect of EAGLNMF are verified by synthetic data via four experiments. The experiments compare EAGLNMF with VCA-FCLS, standard NMF and GLNMF. Two metrics, spectral angle distance(SAD) and abundance angle distance(AAD) are used to compare the four methods. Experiment 1 is total comparison experiment of the four methods. SNR and the number of endmembers are constant, and the value of SAD and AAD are compared. Experiment 2 evaluates the influence of SNR. Different value for SNR and constant value for number of endmembers are given to different runs. Experiment 3 evaluates the influence of number of endmembers. Different value for number of endmembers and constant value for SNR are given to different runs. The experiment result shows that EAGLNMF method obtains more accurate result for both endmebers and abundance. Moreover, experiment 4 evaluates the influence of sparse factor between endmember signature and abundance. The result demonstrates that endmember sparse constraint shows a positive effect to unmixing. And, sparse factor between endmember signature and abundance shows effect to unmixing result. In addition, real AVIRIS hyperspectral image is applied to VCA-FCLS, standard NMF, GLNMF and the proposed EAGLNMF, and compared with the ground truth of USGS, the result shows that EAGLNMF obtains best unmixing result among the four algorithms and the accuracy of the estimated endmembers is good.