Splitting methods in image processing [Elektronische Ressource] / vorgelegt von Simon Setzer

SPLITTING METHODS IN IMAGE PROCESSINGInauguraldissertationzur Erlangung des akademischen Gradeseines Doktors der Naturwissenschaftender Universit¨at Mannheimvorgelegt vonDipl.-Math. Simon Setzeraus HeidelbergMannheim, September 2009Dekan: Professor Dr. Felix Freiling, Universit¨at MannheimReferent: Professor Dr. Gabriele Steidl, Universit¨at MannheimKorreferent: Professor Dr. Christoph Schn¨orr, Universit¨at HeidelbergTag der mu¨ndlichen Pru¨fung: 9. Dezember 2009AcknowledgmentsForemost, I would like to express my sincere gratitude to my thesis supervisor GabrieleSteidl for here guidance, support and constant encouragement. Many thanks go to TanjaTeuber whom I had the great pleasure to work with in the last two years. I also thankall my other collaborators: I am indebted to Raymond Chan (Chinese University of HongKong) for his fruitful collaboration and his invitation to the workshop in Singapore lastyear. My thanks alsogotoBernhard Burgeth(SaarlandUniversity), Stephan Didas(Saar-land University, now Fraunhofer-Institut, Kaiserslautern), Guido Morkoette (University ofMannheim) and Bj¨orn Popilka for the constructive and inspiring collaboration.Finally, I want to express my deep gratitude to my family, to the Gerner family andespecially to Yela for everything they have have done for me.iiiSummaryIt is often necessary to restore digital images which are affected by noise (denoising), blur(deblurring), or missing data (inpainting).