S. Lonardi, P. Sommaruga. Fractal Image Approximation and Orthogonal Bases. Image Communication (Elsevier), 15(4):413-423, 1999.
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, we can avoid to solve linear systems often suffering from ill conditioning and needed in former fractal approximation techniques. Moreover, using orthogonal bases we obtain the most compact representation of the approximation. As a direct application we show some results on the compression of gray scale digital images.
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@article{LoSo99,
Author = {Lonardi, S. and Sommaruga, P.},
Title = {Fractal Image Approximation and Orthogonal Bases},
Journal = {Image Communication (Elsevier)},
Volume = {15},
Number = {4},
Pages = {413--423},
Year = {1999}
}