2-D Spectral Distribution Parameter Estimation

这个项目将利用Francos的COPI最近的理论发现，这些发现导致了一种改进的二维均匀随机场的谱分布函数的估计程序(这也可以被称为估计二维混合谱的问题)。通过对离散(规则)随机场施加总顺序并对均匀随机场使用新的二维类Wold分解，原始随机场可以被分解成纯确定性分量，该分量被建模为具有随机幅度和相位的二维调和分量的和，由其频谱分布属性表征的广义消逝分量，以及由2-D AR过程建模的纯不确定分量。拟议研究的目的是开发一种联合检测/估计程序，用于检测确定性分量--纯确定性分量和广义消逝分量--的存在，并估计在原始分解中被认为存在的分量的必要参数。

This project will exploit recent theoretical findings by the coPI, Francos, which lead to an improved estimation procedure for the spectral distribution function of a 2-D homogeneous random field (which can also be referred to as a problem in estimating a 2-D mixed spectrum). By imposing a total order on the discrete (regular) random field and using a new 2-D Wold-like decomposition for homogeneous random fields, the original random field can be decomposed into a purely-deterministic component, modelled as a sum of 2-D harmonic components with random amplitude and phase, a generalized evanescent component which is characterized by its spectral distribution attributes, and a purely-indeterministic component which is modelled by a 2-D AR process. The purpose of the proposed research is to develop a combined detection/estimation procedure for detecting the presence of the deterministic components - the purely-deterministic and generalized evanescent components, and for estimating the necessary parameters of the components which are deemed present in the original decomposition.