Wavelet Based Approach to Fractals and Fractal Signal Denoising

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In this paper localized fractals are studied by using harmonic wavelets. It will be shown that, harmonic wavelets are orthogonal to the Fourier basis. Starting from this, a method is defined for the decomposition of a suitable signal into the periodic and localized parts. For a given signal, the denoising will be done by simply performing a projection into the wavelet space of approximation. It is also shown that due to their self similarity property, a good approximation of fractals can be obtained by a very few instances of the wavelet series. Moreover, the reconstruction is independent on scale as it should be according to the scale invariance of fractals.

Preliminary results presented at the International Conference on Computational Science and Applications (ICCSA 2008), June 30-July 3, 2008 Perugia (It) .