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Alexandru Bogdan. The Fractal Pyramid with Applications to Image Coding. In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'95), Detroit, MI, May 1995.

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We extend the iterated transformation theory (ITT) fractal image coding algorithm proposed by A. Jacquin [1] to generate a pyramid image representation. An ITT-coded image is modeled as the solution of a second kind functional equation. This representation is iterated to form an ITT-chain of functional equations which can serve as the framework for a multi-scale 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. We use this decomposition to build an ITT-pyramid representation for gray-tone images as well as for RGB color images

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   Author = {Bogdan, Alexandru},
   Title = {The Fractal Pyramid with Applications to Image Coding},
   BookTitle = {IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'95)},
   Address = {Detroit, MI},
   Month = {May},
   Year = {1995}

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