A new improved collage theorem with applications to multiresolution fractal image coding

Abstract

The paper presents an improved collage theorem, valid for a class of signal mappings called affine blockwise average (ABA) mappings. The ABA structure is exploited to form a bound depending on norms of collage error signals at several resolutions. Compared to previously published collage theorems, the new theorem provides a much tighter bound on the maximum distance between the original signal (real world image) and the decoder attractor, given the distance between the original and the «collage» optimized by the encoder. This is achieved without contractivity constraints on the ABA mapping parameters. Finally, an encoding method in which one attempts to minimize the upper bound directly is suggested. © 1994 IEEE.