Constrained networks for fractal image compression.

摘要

A new method for fractal image compression is proposed. The method replaces the contractive affine maps used by Barnsley, Jacquin, and others with a constrained network that looks for (strictly) contractive nonaffine mappings between sets of input/output data obtained from (local) portions of a given image. To identify these mappings, first a neural network with embedded constraints (NNEC) is proposed. Since the NNEC has high time complexity and slow due to numerical integration, instead a new wavelet network with constraints (WNWC) is proposed. The WNWC links the theory of multiresolution analysis (MRA) with iterated function systems (IFS) theory. This not only provides a local time-frequency analysis on (the partitions of) the image using multiresolution representation but also an iterative construction of the same (partitions of the) image using IFS and fixed point theory. When this is done such that the whole image is covered, an Iterated Function System (IFS) code for that image is obtained. It is shown and proven that the constrained network can identify any contractive map, and simulations suggest that the "closest" contractive approximation to noncontractive training set of input/output data can be obtained. The fractal code obtained via constrained network requires no search or classification of the domain blocks. A set of experiments, simulations, and analysis is proposed that will show whether the IFS code obtained via the constrained network can provide a competitive method for image compression and more efficient storage of multimedia data.