Multilevel regularization for image deblurring problems
Marco Donatelli · PAMM · 2007
Abstract We consider the de‐blurring problem of noisy and blurred signals/images in the case of space invariant point spread functions. The use of appropriate boundary conditions leads to linear systems with structured coefficient matrices related to space invariant operators like Toeplitz, circulants, trigonometric matrix algebras etc. We combine an algebraic multigrid (which is designed ad hoc for structured matrices) with the low‐pass projectors typical of the classical geometrical multigrid for elliptic partial differential equations. The smoother is any iterative regularizing method, while the projector is chosen in order to maintain the same algebraic structure at each recursion level and having a low‐pass filter property, which is very useful in order to reduce the noise effects. In this way, we obtain a better restored image with a flatter restoration error curve and also in less time than the auxiliary method used as smoother. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)