2-D Spectral Distribution Parameter Estimation

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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.