Fractal-based image compression: a fast algorithm using wavelet transform
Yonghong Tang, William G. Wee · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1994
Deterministic fractals have been successfully applied to gray-level image compression. In this approach, an image is represented by a set of affine transforms, each of which maps one subimage to another subimage. The affine transforms are found by exhaustive searching over all the collection of subimages and is very time-consuming. The objectives of this paper are to demonstrate the applicability of wavelet transform (WT) in the searching process and to show a time saving in using WT as compared to exhaustive searching. The wavelet transform provides a multiscale description of an image based on local `detail signals' at each resolution scale. We propose a fast algorithm that takes the advantage of the structural information of the subimages by searching through the wavelet coefficient space instead of the gray-level space. The wavelet transform is computed only once, and can be done very rapidly by using short FIR filters. We have experimentally shown here that the approach is applicable, and there is a time saving of 77% over the exhaustive searching method.