Foreword

This script accompanies the course Mathematical Image Processing in the summer semester 2026 at FAU Erlangen-Nürnberg. The script is mainly based on a lecture, which I created and held in the summer semester 2016 together with Dr. Camille Sutour and which was based only on few handwritten notes.

In this lecture we discuss various image processing tasks and how to tackle them using a selected set of mathematical methods. These methods are chosen based on my personal research interests and cover tools from various mathematical fields, e.g., convex analysis, calculus of variations, and numerical methods for partial differential equations. Note that these methods represent only a small fraction of all the possibilities to solve image processing problems.

The goal is to extend and revise this script continuously during the course of this lecture. If you notice any errors in the mathematical content or language while studying this script, please let me know by sending an email to daniel.tenbrinck@fau.de.  
I wish you success and lots of fun in this lecture!  
Prof. Dr. Daniel Tenbrinck Erlangen, 14.04.2026