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Abstract: We are concerned with the fractal approximation of multidimensional functions in L 2 . In particular, we treat a position-dependent approximation with no search using orthogonal bases of L 2 . 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... (Update)
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BibTeX entry: (Update)
@article{ lonardi99fractal,
author = "S. Lonardi and P. Sommaruga",
title = "Fractal Image Approximation and Orthogonal Bases",
journal = "Signal Processing: Image Communication",
volume = "15",
number = "4",
publisher = "Elsevier",
pages = "413--423",
year = "1999",
url = "citeseer.ist.psu.edu/lonardi99fractal.html" }
Citations (may not include all citations):508 The Fractal Geometry of Nature (context) - Mandelbrot - 1982
375 Fractals Everywhere (context) - Barnsley - 1988
173 Image coding based on a fractal theory of iterated contracti.. (context) - Jacquin - 1992
128 Fractal Image Compression (context) - Barnsley, Hurd - 1993
48 Image compression: A study of the iterated transform method (context) - Jacobs, Fisher et al. - 1992
48 The science of fractal images (context) - Peitgen, Saupe - 1988
44 A fractal theory of iterated Markov operators with applicati.. (context) - Jacquin - 1989
33 Fractal approximations of image blocks (context) - Monro, Dudbridge - 1992
33 Fractal block coding of images (context) - Monro, Dudbridge - 1992
24 A novel fractal block-coding technique for digital images (context) - Jacquin - 1990
23 A inner product space approach to image coding by contractiv.. (context) - ien, Lepsoy et al. - 1991
22 A wavelet-based analysis of fractal image compression - Davis - 1996
21 Fractal representation of images via the discrete wavelet tr.. (context) - Krupnik, Malah et al. - 1995
19 Optimal attractor image coding with fast decoder convergence (context) - ien - 1993
15 Inverse problem methods for generalized fractal transform - Forte, Vrscay - 1996
[Article contains additional citations not shown here]
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