Wavelet and Fractal Transforms for Image Compression

The main idea behind all fractal coding algorithms is to exploit the similarities present within many natural images: one block of an image is represented by an affine transform of another larger block taken from the image itself [1, 2, 3]. The characteristic property of fractal coders is to exploit similarities between different scales. Wavelet transforms perform multiresolution decompositions of images, i.e, decompositions of the original images into subimages at different scales. The translation of the fractal property in the wavelet transform domain is straightforward: multiresolution decompositions through wavelet transforms of fractal coded images reveal strong relationships between subimages at different scales. These relationships limit the frequency content. Multiresolution fractal coders introduce degrees of freedom on these constraints.