Pseudopassive two‐dimensional recursive digital filters for image processing

摘要

AbstractThis paper describes the theory of two‐dimensional digital filters that are pseudopassive with respect to thelp‐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 thel1‐pseudolossless systems is proposed as a tool to guarantee stability of such filters. A technique to obtain local state‐space models for such two‐dimensionall1‐pseudolossless recursive filters with prescribed spatial responses is given. A ‘Gaussian filter’ design illustrates the technique and shows that the proposed two‐dimensionall1‐pseudolossless filters are able to m