This book addresses the mathematical aspects of modern image processing methods, with a special emphasis on the underlying ideas and concepts. It discusses a range of modern mathematical methods used to accomplish basic imaging tasks such as denoising, deblurring, enhancing, edge detection and inpainting. In addition to elementary methods like point operations, linear and morphological methods, and methods based on multiscale representations, the book also covers more recent methods based on partial differential equations and variational methods. Review of the German Edition: The overwhelming impression of the book is that of a very professional presentation of an appropriately developed and motivated textbook for a course like an introduction to fundamentals and modern theory of mathematical image processing. Additionally, it belongs to the bookcase of any office where someone is doing research/application in image processing. It has the virtues of a good and handy reference manual. (zbMATH, reviewer: Carl H. Rohwer, Stellenbosch)

Autorentext

Dirk Lorenz is professor at TU Braunschweig, Institute for Analysis and Algebra. His research areas are: Inverse Problemes and Mathematical Image Processing. Kristian Bredies is professor at Karl-Franzens-Universität Graz. His research interests include mathematical imaging, variational methods and numerical optimization.

Inhalt

Introduction.- Mathematical preliminaries.- Basic tools.- Frequency and multiscale methods.- Partial differential equations in image processing.- Variational methods.