G. Davis. Self-quantized wavelet subtrees: A wavelet-based theory for fractal image compression. In Proceedings DCC'95 Data Compression Conference, J. A. Storer, M. Cohn (eds.), March 1995.
We describe a novel adaptive wavelet-based compression scheme for image which takes advantage of image redundancy across scales. As with standard wavelet transform coders, our compressed image representation consists of a set quantized wavelet coefficients and quantized wavelet subtrees. Instead of having a fixed subtree codebook, however, we construct a codebook from the image being compressed. Subtrees are quantized to locally smooth regions and locally straight edges. We prove that this self-quantization enables us to recover the fine scale wavelet coefficients of an image given ist coarse scale coefficients. We show that this self-quantization algorithm is equivalent to a fractal image compression scheme when the wavelet basis is the Haar basis. The wavelet framework greatly simplifies the analysis of fractal compression schemes and places compression in the context of existing wavelet subtree coding schemes. We obtain a simple convergence proof which strengthens existing fractal compression results, we describe a new reconstruction algorithm which requires O(N) operations for an N pixel image, and we derive an improved means of estimating the error incurred in decoding fractal compressed images. We show the effect of self-quantization for a test image.
@InProceedings{Davi95a,
Author = {Davis, G.},
Title = {Self-quantized wavelet subtrees: A wavelet-based theory for fractal image compression},
BookTitle = {Proceedings DCC'95 Data Compression Conference},
editor = {Storer, J. A. and Cohn, M.},
Publisher = {IEEE Computer Society Press},
Month = {March},
Year = {1995}
}