A fast wavelet algorithm for image deblurring

Abstract

We present a nonlinear fully adaptive wavelet algorithm which can recover a blurred image (n?n) observed in white noise with O(n 2 (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.