The fractal pyramid with applications to image coding

Extends the iterated transformation theory (ITT) fractal image coding algorithm proposed by A. Jacquin [1993] to generate a pyramid image representation. An ITT-coded image is modeled as the solution of a second type functional equation. This representation is iterated to form an ITT-chain of functional equations which can serve as the framework for a multiscale signal decomposition. This formalism can be extended to accommodate hybrid ITT representations and, in the limit, ITT-coded signals as a solution of a homogeneous functional equation. Existence of the ITT-chain signal representation is shown to be connected to the eigen-structure of the linear operators of the associated functional equations. At each level of the ITT-chain representation, the signal is decomposed into two parts which are not orthogonal. The authors use this decomposition to build an ITT-pyramid representation for gray-tone images as well as for RGB color images