Multiresolution approximation of fractal transforms and its applications

To generate a fractal by using an iterated function system (IFS) (Barnsley, 1988) is a very efficient and economic way. This led Barnsley to suggest the use of IFSs for data compression. However, the attractor of an IFS is self-affine but real data are not always self-affine. The real break-through for this problem was made in 1988 by Barnsley (Barnsley and Hurd, 1993) who generalized IFS to local IFS which resulted in so-called fractal transform (FT) for the iteration of functions. The coding of real data by fractal transform has generally achieved high-compression ratio with high-fidelity to the data