在观测空间碎片时, 受碎片结构紧凑、 组成材料复杂, 以及地基观测设备空间分辨率的限制, 同一像元中通常会包含多种材料的信息, 即产生“混合像元”。 目前国内外对混合像元的研究主要集中在获取混合像元的纯物质光谱以及丰度上, 往往忽略了高光谱数据中纯物质个数的确定对于没有任何先验信息的混合像元分析是至关重要的。 如果估计的材料数目过少, 将会导致解混出的材料光谱仍然是混合状态的像元; 如果估计的材料数目过多, 提取出的端元中将很有可能包含冗余噪声成分。 基于光谱线性混合模型, 提出一种改进的p范数纯像元辨识算法。 主要利用光谱数据具有近似于低维流形的特性, 首先采用正交投影的原理, 将提取的端元扩充至正交投影算子中, 然后分析投影后各个像元向量的p范数值, 最终将p范数值高于阈值的向量个数作为材料种类数目。 对实测碎片常用材料和美国地质勘测局数据库分别进行仿真实验, 实验结果表明: 提出的方法在估计材料种类数目的同时, 还能提取出目标所包含的材料光谱, 这在一定程度上提高混合光谱分解过程的自动化程度; 相对于现有的一些主流算法, 该方法有较强的鲁棒性, 并且在信噪比不高的情况下仍能正确地估计空间碎片材料种类数目。

For a long time, the United States and other military powers have been committed to develop their space situational awareness (SSA). The monitoring system of ground space target is an important part of the space situational awareness. Monitoring and identifying of space targets are mainly due to a large number of space debris make the main body of the satellite face some unknown risks. To avoid the space junk and enhance the ability of the satellite identifying the space objects, it is very important to ensure safety of the spacecraft in orbit. In the observation of space debris, because of the compact structure, complex material, and spatial resolution of ground observation equipments, a variety of materials are in the same pixel usually, namely “mixed pixel”. The current researches on mixed pixel mainly focus on obtaining pure components of mixed pixels and the corresponding abundance, but they often neglect that hyperspectral data for determining the number of pure substances is very important for mixed pixels without any prior information analysis. If the estimated number is too small, the extracted endmembers are still mixed pixels; if the number of endmembers is too large, the extracted endmembers may still contain noise components. Based on the spectral linear mixture model, this paper proposes an improved p norm pure pixel identification algorithm. The method is mainly based on the characteristics of spectral data which are similar with those of low dimensional manifolds. Firstly, according to the principle of orthogonal projection, the extracted endmembers are extended to the orthogonal projection operator. By analyzing the p norm of each projected pixel vector, the number of the p norm value higher than the threshold in the vectors is considered to be the number of pure materials. The simulation experiments are carried out by using the commonly used space materials data and the United State Geological Survey database. The experimental results show that the proposed method can not only estimate the number of pure materials, but also extract spectra of the pure materials in the target, which improves the automation of spectral unmixing process to a certain extent. Compared with some existing algorithms, this method has strong robustness and can estimate the correct number of space debris in the case of low SNR. Therefore, the proposed algorithm can greatly improve the feasibility in determining the type and number of materials according to the space debris spectrum.