中文摘要：

目的光谱解混是高光谱遥感图像处理的核心技术。当图像不满足纯像元假设条件时，传统算法难以适用，基于（单形体）体积最小化方法提供了一种有效的解决途径。然而这是一个复杂的约束最优化问题，更由于图像噪声等不确定性因素的存在，导致算法容易陷入局部解。方法引入一种群智能优化技术．差分进化算法（DE），借助其较强的全局搜索能力以及优越的处理高维度问题的能力，并通过对问题编码，提出了一种体积最小化的差分进化（VolMin—DE）光谱解混算法。结果模拟数据和真实数据实验的结果表明，与现有算法相比，该算法在15端元时精度（光谱角距离）可提高7．8％，当端元数目少于15个时，其精度普遍可以提高15％以上，特别是10端元时精度可以提高41．3％；在20～50dB的噪声范围内，精度变化在1．9～3．2（单位：角度）之间，传统算法在2．2～3．5之间，表明该算法具有相对较好的噪声鲁棒性。结论本文算法适用于具有纯像元以及不存在纯像元（建议最大纯度不低于0．8）这两种情况的高光谱遥感图像，并可在原始光谱维度进行光谱解混，从而避免降维所带来的累计误差，因此具有更好的适应范围和应用前景。

英文摘要：

Objective Spectral unmixing is a key hyperspectral remote sensing image processing technique. Many spectral unmixing algorithms have been proposed. Most of these algorithms are based on the assumption that pure pixels exist in the hyperspectral imagery. However, when pure pixels are lacking, the performance of these algorithms may deteriorate. The simplex volume minimization （VolMin） method provides a good means to overcome this problem. However, VolMin is a complex constraint optimization problem. Owing to the uncertainty that noise exists in an image, the algorithm is easily trapped into local optima. Method Thus, we introduce a swarm intelligence technique, i. e. , differential evolution （DE） algorithm, into the VolMin procedure. By utilizing the powerful global searching capability and high-dimensional adaptability of DE, we develop a minimum simplex volume DE （VolMin-DE） spectral unmixing algorithm through VolMin-DE encoding. Result Synthetic mixture and real image data are utilized for comparative experiments on unmixing accuracy. The proposed VolMin-DE algorithm, vertex component analysis, minimum distance constrained non-negative matrix factorization （NMF）, and minimum volume constrained NMF are compared. Experimental results indicate that the proposed VolMin-DE algorithm outperforms the other algorithms. The precision （ spectral angle distance） of VolMin-DE can be increased by 7.8% , especially when the accuracy of 10 endmembers is improved by 41.3%. In the noise range of 20 dB to 50 dB, the performance of VolMin-DE varies from 1.9 to 3.2 （ unit ： degrees）, whereas that of the traditional algorithm varies from 2. 2 to 3.5. This result demonstrates that the proposed algorithm has better noise robustness than other algorithms. Conclusion The proposed VolMin-DE algorithm can be applied to hyperspectral imagery regardless of the pure pixel assumption （ maximum purity level equal to or greater than 0. 8 is recommended） . The algorithm does not require dimensional reduction; hence