L'uso dell'ottimizzazione non lineare nella procedura di compressione di immagini con IFS

Using nonlinear optimization techniques in fractal image compression. Fractal image compression generally seeks to express an image as a union of spatially contracted and greyscale modified copies of subsets of itself. Most practical as well as theoretical works in image processing and mathematical imaging consider images as real-valued functions u: X->R where X denotes the base or pixel space over which the images are defined. After all, at a particular point x in a (for simplicity) greyscale image I, we observe a pixel with a well defined intensity value, which we denote as u(x). Various function spaces F(X) may be considered. It has been found that an image u may be very well approximated by a union of shrunken and distorted copies of subsets of itself. This has been the basis of the so called "inverse problem" for fractal image compression which, after some transformations, can be reduced to a nonlinear optimization problem.