一种基于噪声水平估计的扩展线性光谱分解算法

针对传统的光谱分解算法忽略了影像在不同波段的不同噪声水平，导致分解精度提高受限。为克服这个问题，以高光谱影像为基础，提出了一种基于噪声水平估计的扩展线性光谱分解算法（NELMM）。首先，根据高光谱应用中的多元回归理论，估计相邻波段的噪声；其次，从估计噪声中获得噪声权重矩阵；最后，将噪声权重矩阵引入到线性混合像元的框架中，可以减轻不同波段噪声水平的影响。为验证算法精度，利用全约束最小二乘法（FCLS）和协同稀疏分解算法（CLSUnSAL）来进行对比分析，并通过此算法反演TM影像的植被覆盖度来验证其在多光谱影像上的实用性。结果表明：NELMM算法对高光谱影像分解的结果比FCLS和CLSUnSAL好，其噪声权重矩阵很好地平衡了波段间的噪声，使NELMM算法分解影像的精度显著提高；同时，此算法对多光谱影像分解呈现很好的适用性。

A Kind of Extended Linear Spectral Unmixing Algorithm based on Noise Level Estimation

The traditional spectralunmixing algorithm ignores the different noise levels of the image in different bands， which leads to the limited accuracy of unmixing. To overcome this problem， based on the hyperspectral imagery， an Extended linear spectral unmixing algorithm based on noise level estimation （NELMM） is proposed. First， according to the multivariate regression theory in hyperspectral applications， the noise in adjacent bands is estimated. Second， the noise weight matrix is obtained from the estimated noise. Finally，the noise weighting matrix is integrated into the linear spectral unmixing framework， which can alleviate the impact of different noise levels at different bands. In order to verify the accuracy of the algorithm， the Fully Constrained Least Squares （FCLS） and Collaborative Sparse Unmixing by variable Splitting and Augmented Lagrangian（CLSUnSAL） are used for comparative analysis， and the vegetation coverage of the TM image is inverted by this algorithm to verify its practicality on multispectral images. The final test results show that the NELMM algorithm is better than the FCLS and CLSUnSAL for the unmixing of hyperspectral images. The noise weight matrix balances the noise between the bands， and the accuracy of the NELMM algorithm for unmixing images is significantly improved. At the same time， this algorithm shows good applicability to multi-spectral image unmixing.