Mathematical Signal and Image Processing
Welcome to the lecture Mathematical Signal and Image Processing
Course Description
Signals and images are the most widely used types of data with numerous applications. The area of mathematical signal and image processing aims to develop methods for their acquisition and analysis, which arise from and allow a deep mathematical understanding. Of particular interest in this area are also inverse problems, which aim to recover signals or images from measurements in the sense of inverting the measurement operator. Intriguingly, various of the methods which were developed to solve such problems led in turn to deep mathematical theories, such as wavelet systems in the realm of approximation theory and functional analysis. Finally, a recent development also connects the area of mathematical signal and image processing with artificial intelligence, in particular, deep neural networks.
This lecture will provide an introduction into this exciting and rich research area. Some of the topics, which we will discuss, are:
- Compressed Sensing
- Frame Theory
- Inverse Problems
- Wavelet and Shearlet Theory
- Deep Neural Networks
Schedule and Venue
This course is very likely to be virtual. The registered participants will be informed about the decision until 11.4. on this webpage as well as in an email to the registered participants on moodle. If presence would be possible, the lectures would take place in room C 123.
In case of a virtual course, which seems currently the most likely format, the course will be organized as follows:
| Introductory Event Prof. Dr. Gitta Kutyniok |
April 13, 10-12 |
| Lectures Prof. Dr. Gitta Kutyniok |
The lectures will be provided as videos on moodle, which each registered participant can access. Also written material will be provided. |
| Discussions/Questions Prof. Dr. Gitta Kutyniok |
In the spirit of the concept of a flipped classroom, we will offer frequent meetings for discussion of the material and possible questions. Those meetings will take place during Tu, 10-12. |
| Exercise Classes Adalbert Fono |
The exercise classe will take place as live session on Zoom during Thur, 10-12. The required information will be provided via moodle. |
| Tutorials Adalbert Fono, Jago Silberbauer |
TBA |
| Office Hours Adalbert Fono, Mariia Seleznova |
Thur, 16-18, for help with practical exercises by Mariia Seleznova. |
Registration
We ask all participants to enroll in the course in moodle.
Exam
Information about the exam will be announced in the first lecture and also posted here.
Requirements
This course is targeted at Bachelor and Master students from mathematics, business mathematics, or financial mathematics, but also interested students from computer science and statistics are welcome. The course requires knowledge of the topics from the course “Maßtheorie und Integralrechnung mehrerer Variablen” and “Stochastics”. Moreover, basics of functional analysis are helpful, but not required.