Fractal representation of images via the discrete wavelet transform

Fractal representation of images is based on mappings between similar regions within an image (also known as IFS). Such a representation can be applied to image coding and to increase image resolution. One of the main drawbacks of conventional fractal representation is the fact that the mappings are between blocks. As a result, the reconstructed image may suffer from disturbing blockiness. In this work we present a method for mapping similar regions within an image in the wavelet domain. We first show how to use the Haar wavelet transform coefficients to find mappings which are identical to conventional blockwise mappings. The union of these mappings, between sets of wavelet coefficients, can be interpreted as a prediction of higher bands of a signal from its lower band. Changing the mother-wavelet to other than Haar, creates mappings which are between regions which smoothly decay towards their borders, thus reducing the blockiness, as well as improving the PSNR of the reconstructed image.