A Computational Signal Algebra Framework For Image Interferometry Processing Applications

This work deals with the development of a computational signal algebra framework for the modeling and simulation of signals interferometry processing applications. The signal algebra is constructed by using the binary two-dimensional cyclic convolution as the product operation that turns a vectorial space of two-dimensional finite discrete signals into an algebra. Matrix representations of two-dimensional cyclic convolution operations are represented as block circulant matrices with circulant blocks when finite discrete signals object arrays, serving as inputs in the unary operation representation of the cyclic convolution are transformed into one-dimensional column vectors using, both, lexicographic and anti-lexicographic ordering. Special attention is given to the algebra of cyclic correlations which is related to the algebra of cyclic convolutions through the index reversal or reflection operator. The numeric computation and scientific visualization package MATLABRTM is used as an environment for the modeling and simulation. Special attention is given to radar interferometry applications. Radar interferometry, as a correlation technique between two signals, is used to detect Earth surface changes produced by phenomena such as landslides, earthquakes, and flash floods.