The book contains twenty-two original scienti?c research articles that address the state-of-the-art in using partial di?erential equations for image and signal processing. The articles arose from presentations given at the inter- tional conference on PDE-Based Image Processing and Related Inverse Pr- lems, held at the Centre of Mathematics for Applications, University of Oslo, Norway, August 8-12, 2005. The purpose of the conference was to bring together international - searchers to present various aspects of new developments in using numerical techniques for partial di?erential equations to analyse and process digital - ages. Various aspects of new trends and techniques in this ?eld were discussed in the conference, covering the following topics: - Level set methods and applications - Total variation regularization and other nonlinear ?lters - Noise analysis and removal - Image inpainting - Image dejittering - Optical ?ow estimation - Image segmentation - Image registration - Analysis and processing of MR images and brain mapping - Image construction techniques - Level set methods for inverse problems Inverse problems for partial di?erential equations have large areas of app- cations. Although image analysis and PDE inverse problems seem to be - related at a ?rst glance, there are many techniques used in one of these two areas that are useful for the other. One goal of the conference was to highlight some of the recent e?orts in merging some of the techniques for these two research areas.

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