基于超像素的流形正则化稀疏约束NMF混合像元分解算法

针对传统非负矩阵分解(NMF)法用于高光谱图像混合像元分解时产生的分解结果精度不高、对噪声敏感等问题,提出一种基于超像素的流形正则化稀疏约束NMF混合像元分解算法——MRS-NMF。首先,通过基于熵率的超像素分割来构造高光谱图像的流形结构,把原图像分割为k个超像素块并把每个超像素块中具有相似性质的数据点标上相同的标签,定义像素块内有相同标签的任意两个数据点之间的权重矩阵,然后将权重矩阵应用于NMF的目标函数中以构造出流形正则化约束项;第二,在目标函数中添加二次抛物线函数以完成稀疏约束;最后,采用乘法迭代更新法则求解目标函数以得到端元矩阵和丰度矩阵的求解公式,同时设置最大迭代次数和容忍误差阈值,迭代运算得到最终结果。该方法有效利用了高光谱图像的光谱和空间信息。实验结果表明,在模拟的高光谱数据中,与传统的流形稀疏约束的非负矩阵分解(GLNMF)、L1/2-NMF和顶点成分分析全约束最小二乘法(VCA-FCLS)等方法相比,MRS-NMF可以提高0.016~0.063的端元分解精度和0.01~0.05的丰度分解精度;而在真实的高光谱图像中,MRS-NMF较传统的GLNMF、顶点成分分析法(VCA)、最小体积约束的非负矩阵分解(MVCNMF)等方法可以平均提高0.001~0.0437的端元分解精度。所提MRS-NMF算法有效地提高了混合像元分解的精度,同时具有较好的抗噪性能。

Manifold regularized sparse constraint nonnegative matrix factorization with superpixel algorithm for hyperspectral unmixing

For the problems such as poor unmixing results and sensitivity to noise of traditional Nonnegative Matrix Factorization (NMF) applied to hyperspectral unmixing, a Manifold Regularized Sparse NMF with superpixel (MRS-NMF) algorithm for hyperspectral unmixing was proposed. Firstly, the manifold structure of hyperspectral image was constructed by superpixel segmentation based on entropy. The original image was divided into k-superpixel blocks, and the data points in each superpixel block with same property were labeled the same label. Weight matrices were defined between any two data points with the similar label in a superpixel block, and then the weight matrices were applied to the objective function of NMF to construct the manifold regularization constraint. Secondly, a quadratic parabola function was added to the objective function to complete the sparse constraint. Finally, the multiplicative iterative update rule was used to solve the objective function to obtain the solution formulas of endmember matrix and abundance matrix. At the same time, maximum iteration times and tolerate error threshold were set to get the final results by iterative operation. The proposed method makes full use of spectral and spatial information of hyperspectral images. Experimental results show that on synthetic data the unmixing accuracies of endmember and abundance based on proposed MRS-NMF are 0.016-0.063 and 0.01-0.05 respectively higher than those based on traditional methods like Graph-regularized L1/2-Nonnegative Matrix Factorization (GLNMF), L1/2NMF and Vertex Component Analysis-Fully Constrained Least Squares (VCA-FCLS); while on real hyperspectral images, the average unmixing accurary of endmember based on proposed MRS-NMF is 0.001-0.0437 higher than that of traditional GLNMF, Vertex Component Analysis (VCA) and Minimum Volume Constrained Nonnegative Matrix Factorization (MVCNMF). This proposed algorithm improves the accuracy of unmixing effectively with good robustness to noise.