Using Artificial Neural Networks for Fractal Interpolation Approach in 3D

In this paper, we introduce a new method for fractal interpolation, herein called Neural Network Algorithm (NNA), which is based on Iterated Functions Systems (IFS); proposed to self-affine signals interpolation with error of expected interpolation. Experiments on theoretical data show that the proposed interpolation schemes can obtain the expected point value and work with great precision in rebuilding the specified data profile, which leads to a significant advantage over other interpolation methods.

A HYBRID ALGORITHM FOR THE SOLUTION OF THE INVERSE PROBLEM IN FRACTAL INTERPOLATION

A new algorithm for the solution of the inverse problem concerning interpolatory iterated functions systems (IFS) is presented. It combines the advantages of the greedy least squares approach of Mazel and Hayes, and the self-affinity in the wavelet scalogram. Thus, the algorithm is computationally cheap and yields results with high accuracy.

FRACTAL APPROACHES IN SIGNAL PROCESSING

Some recent advances in the application of fractal tools for studying complex signals are presented. The first part of the paper is devoted to a brief description of the theoretical methods used. These essentially consist of generalizations of previous techniques that allow us to efficiently handle real signals. We present some results dealing with the multifractal analysis of sequences of Choquet capacities, and the possibility of constructing such capacities with prescribed spectrum. Related results concerning the pointwise irregularity of a continuous function at each point are given in the frame of iterated functions systems. Finally, some results on a particular stochastic process are sketched: the multifractional Brownian motion, which is a generalization of the classical fractional Brownian motion, where the parameter H is replaced by a function. The second part consists of the description of selected applications of current interest, in the fields of image analysis, speech synthesis and road traffic modeling. In each case we try to show how a fractal approach provides new means to solve specific problems in signal processing, sometimes with greater success than classical methods.