Explicit link between local fractal transform and multiresolution transform

Much research is currently being carried out in the field of fractal coding of images. Fractal models try to identify and represent, self-similarity relationships within images through the use of spatial transformations of the signal associated with shrinking, translation, symmetries and scaling. These transformations are particularly suited to an interpretation in the multiresolution decomposition space of the functions. We study the expression of a particular fractal transform within the orthogonal multiresolution context. Conclusions drawn from the results show that the fractal transformation can be decoupled in two terms, one serves to interpolate the high frequency coefficients from one resolution layer to the next while the other is a constant term containing low pass information. A fractal transformation taking these elements into account is defined and it is shown that the parameters can be estimated only on the basis of the multiresolution decomposition coefficients. A method of applying these results to images is then envisaged