IFS-Type Operators on Integral Transforms

Most standard fractal image compression techniques rely on using an IFS operator directly on the image function. Sometimes, however , it is more convenient to work on a faithful representation of the image which, in certain applications, may be a transformed version of the image. For example, if an MRI image is scanned in as frequency data it may be more natural to work on the Fourier transform of the image rather than on the image itself. After a brief introduction to frac-tal transforms and classical fractal image compression, we discuss some generalities of IFS operators on transform spaces. We then illustrate with examples from Fourier, wavelet and Lebesgue transforms. We emphasize that the operations can be done completely in the transform domain. In some applications, e.g. measures, we may not even need or desire to return to the spatial domain.