Existence, uniqueness and convergence properties of a linear optimization technique for two-dimensional signal and system modeling with rational functions

A two-dimensional (2D) signal or image can be represented by a rational complex function. Also, a two-dimensional, linear and shift invariant system can be modeled by a two-dimensional auto-regressive, moving-averaging (ARMA) process. A recently proposed linear technique for image or 2D system representation, by using a rational function, is briefly presented. This method, which is based on the recursive like structure or equationary model, can approximate the unknown 2D system transfer function, or the transform of an image, in the frequency domain in the least-square sense. The authors discuss the important existence, uniqueness and convergence properties associated with this technique. In addition, design examples are also given to show the excellent performance of the algorithm