G. E. Øien, Z. Baharav, S. Lepsøy, D. Malah, E. Karnin. A new improved collage theorem with applications to multiresolution fractal image coding. In Proceedings of ICASSP-1994 IEEE International Conference on Acoustics, Speech and Signal Processing, Volume 5, Adelaide, 1994.
The paper presents an improved collage theorem, valid for a class of signal mappings called Affine Blockwise Averaging (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 decoded 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.
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@InProceedings{OBLMK94,
Author = {Øien, G. E. and Baharav, Z. and Lepsøy, S. and Malah, D. and Karnin, E.},
Title = {A new improved collage theorem with applications to multiresolution fractal image coding},
BookTitle = {Proceedings of ICASSP-1994 IEEE International Conference on Acoustics, Speech and Signal Processing},
Volume = {5},
Address = {Adelaide},
Year = {1994}
}