Fourier and wavelets for blind image restoration

This paper describes a technique for the blind deconvolution based on the wavelet domain deconvolution that comprises Fourier-domain followed by wavelet-domain noise suppression, in order to benefit from the advantages of each of them. The algorithm employs regularized Wiener filter, which allows it to operate even when the system is non-invertible. In fact, we model such image to be the result of a convolution of the original image with a point spread function (PSF). This PSF depends mainly on the image formation system. Unfortunately, it is often very difficult to model this PSF from the physical data, for this reason we consider the problem as a blind deconvolution. First, the identification of the blur is based on maximum likelihood and the solution is obtained iteratively by successive estimations of the PSF from the noisy blurred image. We propose a blind restoration by estimating the noise variance, the point spread function (PSF) and the original image from a blurred and noisy observation. Our method is based on regularized Wiener filter and RDWT (redundant discrete wavelet transform). We illustrate the results with simulations on some examples.