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ANZIAM J. 46(E) ppC29--C46, 2005.

A fast wavelet algorithm for image deblurring

D. L. Donoho

M. E. Raimondo

(Received 8 October 2004, revised 1 February 2005)

Abstract

We present a nonlinear fully adaptive wavelet algorithm which can recover a blurred image (n×n) observed in white noise with O(n²(logn)²) steps. Our method exploits both the natural representation of the convolution operator in the Fourier domain and the typical characterisation of Besov classes in the wavelet domain. A particular feature of our method includes "cycle-spinning" band-limited wavelet approximations over all circulant shifts. The speed and the accuracy of the algorithm is illustrated with numerical examples of image deblurring. All figures presented in this paper are reproducible using the WaveD software package.

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Authors

D. L. Donoho

Dept. Statistics, Stanford University, Stanford, u.s.a.

M. E. Raimondo

Dept. Maths & Stats, The University of Sydney, Sydney, Australia. mailto:marcr@maths.usyd.edu.au

Published 10 March 2005, amended March 18, 2005. ISSN 1446-8735

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