Data based regularization for discrete deconvolution problems

We focus on the solution of discrete deconvolution problems to recover the original information from blurred signals in the presence of Gaussian white noise more accurately. For a certain class of blur operators and signals we develop a diagonal preconditioner to improve the reconstruction quality, both for direct and iterative regularization methods. In this respect, we incorporate the variation of the signal data during the construction of the preconditioner. Embedding this method in an outer iteration may yield further improvement of the solution. Numerical examples demonstrate the effect of the presented approach.