极化目标分解方法的量子力学诠释及其统一

To extract scattering information regarding complex terrain from high-resolution fully polarimetric radar data using polarimetric decomposition for target recognition and classification is one of the highly-focused topics in geoscience and remote sensing research. During the past forty-eight-year’s vigorous development a lot of polarimetric decomposition methods have been proposed, which can be broadly attributed into three categories, i.e. the phenomenological decompositions, the eigenvector-based decompositions, and the model-based decompositions. However, what is the relationship among the three? This is still an open question. The famous polarimetrists Huynen and Cloude viewed them as competitive methods, and the Huynen-Cloude controversy on decomposition uniqueness was then posed. Such controversy enriches the different understandings of the polarimetric decomposition methods, however, it also aggravates the splitting among the three categories. By applying principles of quantum mechanics to interpreting the polarimetric decomposition techniques, we reconsider the relationship of the three categories as noncompetitive, and the unification of them is thus possible. This project is dedicated to formulate the general paradigms and principles on polarimetric decomposition by investigating the related mathematical essence and the underlying physical constraints. Based on which, a tree-like multivariable fusion model is then developed to unify the phenomenological decompositions, the eigenvector-based decompositions, and the model-based decompositions into a whole. By integrating the diversified scattering preference features provided by the unified decomposition and constructing the generalized decomposition diagram, an unsupervised and refined classification scheme of complex terrain is finally proposed. The study of unified polarimetric decomposition method is hoped to inaugurate a new hot topic in this field and promote the related research progress in China.

利用极化分解从高分辨率全极化雷达数据中提取复杂地物目标散射信息用于识别和分类是地球遥感科学的研究热点。极化分解经过48年的蓬勃发展主要形成了唯象分解、特征分解和模型分解等三类方法。但三者间有何本质关系？这仍是个开放问题。著名极化理论学家Huynen和Cloude曾视之为竞争关系，从而引发了Huynen-Cloude分解唯一性争论。争论虽丰富了对分解方法的认识，但也割裂了三者间的联系。通过运用量子力学基本理论对极化分解方法的诠释，使我们认识到三者实为非竞争性关系，因此存在可统一性。本项目拟通过挖掘极化分解的数学本质和物理约束，归纳极化分解的一般原则和通用范式，提出树状多元融合模型实现唯象分解、特征分解和模型分解的统一。整合统一分解多样性散射偏好特征、构建极化分解广义模式图，据此研究面向复杂地物目标的非监督精细分类方案。统一极化分解方法研究有望开拓新的热点，提升我国在极化遥感领域的研究水平。

极化分解在复杂目标解译识别中发挥着重要作用。自1970年首个极化分解提出至今，该方向逐渐形成了以唯象分解、特征分解和模型分解为代表的三类方法。通过挖掘量子力学与雷达极化学之间的对应关系，我们发现极化分解也存在类似于量子测量的观测者效应，其体现为每种分解都携带着提出者的不同偏好，提供了对目标的多样性认识。故在Bohr互补性原理启发下，我们放弃了雷达极化学家Huynen和Cloude的分解唯一性争论，而是从物理和数学角度去探索三类分解方法的统一之路。我们发现，极化分解的本质就是在物理可实现条件下对目标相干矩阵的逐级降秩。由此归纳出极化分解的物理可实现降秩（P3R）原理，并推导出极化分解所应满足的优先性、不相容和对应性等原则。在这些原理和原则指导下，我们针对唯象分解发展出广义Huynen分解，发现其为一种半正定约束的Wedderburn过程，并通过完善修正矩阵的Moore-Penrose逆理论，对支撑该分解的数学机理开展了严格论证。在特征分解方面，我们将广义Cloude分解由特征值分解拓展为面向任意矩阵的斜奇异值分解，证明了其与广义Huynen分解之间的等价性。在模型分解方面，我们给出了基于P3R的体散射功率解析表达，推导了多分量分解中各新增分量的功率上限，挖掘了标准Huynen分解在表面和二面散射分量提取上的重要价值，提出了一个无缠绕极化取向角估计算法，并基于笛卡尔、极化、椭球和球面几何开展了面向一般椭球粒子3D定向的广义体散射建模。根据这些我们发展出广义模型分解，并通过自适应秩选择实现了其与广义Huynen分解和广义Cloude分解的最终统一。从代数角度研究了与P3R相关的矢量空间分解与投影，揭示了构筑于任意方阵矢量空间之上的投影关系。设计了一个广义目标分解树状模式图，并定义了一个散射偏好度参数，用以实现对极化分解观测者效应的定量刻画。通过以对应性原则对这些散射偏好进行排列组合，我们发展出一个自适应模型分类方法。其完全由标准散射模型所驱动，并以独特的符号语言有效避免了类别解译上的语义模糊。在复杂地物目标非监督精细分类、地震/海啸损伤监测评估以及极化雷达陡峭地形反演等应用中，我们验证了所提分解和分类方法的优异性能。统一极化目标分解研究打破了现有三大类方法割裂的局面，从方法论角度提供了一个关于极化分解的全景认识，实现了量子力学与雷达极化学的有益交叉。