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)

The book sets out pragmatically and sensibly to introduce to the fast field of mathematical techniques in solving many specific problems in image processing Covers also more recent methods based on PDE and variational methods Has the virtues of a good an handy reference manual

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.