Source encoding of images for efficient transmission

Abstract

A set of recursive rules which generate unitary transforms with a fast algorithm are presented. For each rule, simple relations give the number of elementary operations required by the fast algorithm. The common Fourier, Walsh-Hadamard, Slant, and Haar transforms are expressed with these rules. The framework developed allows the introduction of generalized transforms which include all common transforms in a large class of identical computation transforms. A systematic and unified view is provided for unitary transforms which have appeared in the literature and for a number of new transforms of potential interest. Generalization to complex and multidimensional unitary transforms is considered.