Pseudopassive two‐dimensional recursive digital filters for image processing

Abstract

SUMMARYThis paper describes the theory of two-dimensional digital filters that are pseudopassive with respect to the &-norm of the state vector. As the classical pseudopassive digital filters are a subclass of these filters, the respective theorems referred to stability are also generalized. It is shown that this theory is useful for the two-dimensional filters that answer with non-negative-valued responses to non-negative-valued excitations. Such systems are especially suitable for image processing. The synthesis of the It-pseudolossless systems is proposed as a tool to guarantee stability of such filters. A technique to obtain local state-space models for such two-dimensional Il-pseudolossless recursive filters with prescribed spatial responses is given. A 'Gaussian filter' design illustrates the technique and shows that the proposed two-dimensional Il-pseudolossless filters are able to match useful spatial responses.