基于约束非负矩阵分解的高光谱解混

Hyperspectral Unmixing Based on Constrained Nonnegative Matrix Factorization

为了得到改进的优化解,提出一种基于丰度和端元约束下非负矩阵分解的解混方法。首先,基于丰度矩阵稀疏性特点,将重加权稀疏正则化引入到非负矩阵分解模型中,其中权重根据丰度矩阵自适应更新。其次,根据同一地物在相邻像素中分布的相似性先验,进一步将全变差正则化引入到非负矩阵分解模型中,以改进其丰度平滑性。最后,通过一个马尔可夫随机场模型中的势函数,实现端元光谱平滑性的约束。为了验证所提算法的性能,在一个模拟数据集和两个真实数据集(Jasper Ridge和Cuprite)进行了测试。结果表明:所提方法在端元光谱相似性和丰度估计精度等方面都有所改进。

To obtain an improved optimal solution,a nonnegative matrix factorization method based on abundance and endmember constraints for hyperspectral unmixing is proposed.First,considering the sparseness of the abundance matrix,a weighted sparse regularization is introduced to the Nonnegative Matrix Factorization(NMF)model to ensure the sparseness of the abundance matrix.The weights are updated adaptively according to the abundance matrix.Second,given the priori knowledge of the distribution of adjacent pixels,a total variation regularization is further added to the NMF model to promote the smoothness of the abundance map.Finally,a new constraint given by a potential function from the Markov random field model is introduced to improve the spectral smoothness of the endmembers.Experiments are conducted to evaluate the effectiveness of the proposed method based on three different data sets,including a synthetic data set and two real-life data sets(Jasper Ridge and Cuprite)respectively.From the experimental results,it is found that the proposed method got better performances both on the spectral similarity and the estimation accuracy for abundance.