传统基于约束非负矩阵分解NMF (Nonnegative Matrix Factorization)的高光谱端元提取算法一般存在两个问题:一方面,以固定惩罚系数方法处理端元提取的约束优化问题,难以较好权衡目标项与约束项间的关系,影响提取效果;另一方面,求解过程通常基于梯度算法,依赖于初始值和步长的设定,容易陷入局部最优。针对这些问题本文提出约束NMF框架下高维自适应粒子群端元提取算法HAPSO(High-dimension Adaptive Particle Swarm Optimization)。该算法在端元距离最小约束的NMF框架下,利用粒子群算法PSO替代原梯度算法以增强全局搜索能力;采用高维PSO方法解决了多波段高维问题,并结合种群信息构建自适应惩罚机制以实现端元提取中目标与约束的合理权衡。通过模拟影像和真实影像的实验,证实该算法与传统的NMF端元提取算法相比能够更合理地权衡约束和避免局部最优,具有较好的端元提取效果。

Endmember extraction from hyper spectral data is an important procedure of hyper spectral unmixing. Nonnegative Matrix Factorization (NMF) has been widely used in the last few years for endmember extraction without assuming the presence of pure pixels. Many methods that incorporate different types of constraints into the NMF objective function have been proposed to accurately extract endmembers. However, traditional constrained NMF algorithms generally have two limitations. First, controlling the tradeoff between the accurate reconstruction and constraint well through the fixed penalty coefficient is difficult. Second, most traditional methods are usually trapped in a local optimum that renders the global optimum difficult to find. To overcome these constraints, we present a novel method called the High-dimension Adaptive Particle Swarm Optimization (HAPSO) for endmember extraction based on the minimum distance constrained NMF (MDC-NMF)scheme.HAPSO enhances the global search ability through PSO. Two key improvements—the high-dimensional PSO and adaptive penalty coefficient method based on swarm information—are considered. The standard PSO algorithm particularly suffers from the "curse of dimensionality", such that it is more likely to plunge into local optima as the dimensionality of the search space increases. To overcome this problem, high-dimensional PSO divides the complex high-dimensional constrained NMF problem into several simple low-dimensional sub problems according to the characteristics of objective function and hyper spectral data. Thus, each particle in the swarm can search for increasingly accurate positions in a detailed manner that significantly improves the accuracy of the results. Furthermore, particle information, such as the positions and feasibility of the PSO algorithm, can be easily applied to balance the search bias between objective functions and constraints. Thus, this study proposes an adaptive penalty coefficient method according to the proportion of feasible solutions in the swarm, instead of the fixed penalty coefficient. The penalty coefficient particularly increases when the proportion of feasible solutions is low in the preliminary stage and decreases as the proportion of feasible solutions increases. The proposed HAPSO algorithm, MDC-NMF, minimum volume constrained NMF, and vertex component analysis are compared. Both synthetic and real data are considered. For the synthetic data, different numbers of endmembers and signal-to-noise ratio are considered. Real hypers pectral data, including AVIRIS and HYDICE images are used. Results demonstrate that the proposed HAPSO algorithm outperforms other algorithms; it extracts more accurate endmembers and causes less reconstruction error.HAPSO is a method that applies PSO for endmember extraction based on the MDC-NMF scheme. The proposed method can effectively overcome the disadvantages of the traditional constrained NMF endmember extraction algorithms and solve high-dimensional and adaptive penalty coefficient problems for NMF endmember extraction. We will consider the influence of many endmembers that can decrease accuracy in future work. More reasonable and effective constraint handling approaches should be studied, although an adaptive penalty coefficient method performs well. The algorithm accuracy should also be further improved because not all endmembers are perfectly extracted by the proposed algorithm in the experiments.