Our numerical experiments suggest that the approximation by sinc functions coupled with the Tikhonov regularization technique is an effective restoration method. For images satisfying the band limited hypothesis underlying the sampling theorem restoration on finer grids can be obtained without an appreciable overload.
The multiresolution analysis coupled with the Tikhonov regularization brings a remarkable improvement of the accuracy. However it is not clear how this method performs in smoothing images affected by Poisson noise. We feel it will be possible to refine this smoothing method in order to obtain the same accuracy of the most popular restoration techniques (mainly the Richardson-Lucy one) but characterized by a much lower computational effort.
We are grateful to A. Innocenti (CRS4) for helping us in using WAVE II. The work of the second author (F. Maggio) was supported by Sardinian Regional Authorities.