Determination of the Scaling Parameters of Affine Fractal Interpolation Functions with the Aid of Wavelet Analysis

Fractal interpolation functions have become popular after the works of M.Barnsley and his co-authors on iterated function systems and their applications to data compression. We consider here the following problem: given a set of values of a fractal interpolation function, determine the contractive affine mappings generating this function. The suggested solution is based on the connection, which is established in the work, between the maxima skeleton of wavelet transform of the function and the locations of fixed points of the affine mappings in question.