Fractal image approximation and orthogonal bases

摘要

We are concerned with the fractal approximation of multidimensional functions in L2. In particular, we treat a position-dependent approximation using orthogonal bases of L2 and no search. We describe a framework that establishes a connection between the classic orthogonal approximation and the fractal approximation. The main theorem allows easy and univocal computation of the parameters of the approximating function. From the computational perspective, the result avoids to solve ill-conditioned linear systems that are usually needed in former fractal approximation techniques. Additionally, using orthogonal bases the most compact representation of the approximation is obtained. We discuss the approximation of gray-scale digital images as a direct application of our approximation scheme.