Variable tree size fractal compression for wavelet pyramid image coding

Pyramidal wavelet decomposition provides a hierarchical data structure for image representation which is suitable for further quantization and compression. Through discrete wavelet transform, image signals are decomposed into multi-resolution and multi-frequency subbands with a set of tree-structured coefficients. The coefficients which have the same spatial location but with different resolution and different orientation can be organized into wavelet subtree. This efficient representation of image signals has achieved superior coding performance in wavelet-based image compression. In this paper, a novel variable tree partition algorithm is introduced which can efficiently split the wavelet subtrees according to the local details. Then a new variable size wavelet-subtree-based fractal coding algorithm is proposed to obtain a good trade-off between image quality and compression ratio. The self-similarities among wavelet subtrees are successfully exploited in the fractal coding method by predicting the coefficients at finer scales from those at coarser scales through proper affine transformation. Experimental results show a gain over JPEG of 5-6 dB in PSNR with even a slightly higher compression ratio (around 60 : 1 to 70 : 1). A slight gain in terms of coding efficiency is also achieved when compared to a method proposed by Davis, which also applies variable tree size wavelet fractal coding, but the complexity has been significantly reduced by avoiding iterative optimization procedures. © 1999 Elsevier Science B.V. All rights reserved.