Mathematical Image Processing

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) Front Matter ....Pages i-xiii Introduction (Kristian Bredies, Dirk Lorenz)....Pages 1-13 Mathematical Preliminaries (Kristian Bredies, Dirk Lorenz)....Pages 15-53 Basic Tools (Kristian Bredies, Dirk Lorenz)....Pages 55-108 Frequency and Multiscale Methods (Kristian Bredies, Dirk Lorenz)....Pages 109-170 Partial Differential Equations in Image Processing (Kristian Bredies, Dirk Lorenz)....Pages 171-250 Variational Methods (Kristian Bredies, Dirk Lorenz)....Pages 251-443 Back Matter ....Pages 445-473