Application of Wavelets to Filtering of Noisy Data

Abstract

I discuss approaches to optimally remove noise from images. A generalization of Wiener filtering to Non-Gaussian distributions and wavelets is described, as well as an approach to measure the errors in the reconstructed images. We argue that the wavelet basis is highly advantageous over either Fourier or real space analysis if the data is intermittent in nature, i.e. if the filling factor of objects is small.

13 pages, submitted to Philosophical Transactions of the Royal Society Series A, 5 high res grayscale images available as jpg files. Full PS file available at http://www.cita.utoronto.ca/~pen/download/royalsoc/proc2.ps.gz

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