Modifications of Prony's Method for the Reconstruction of Structured Functions

Abstract

First and foremost I would like to thank my supervisor Gerlind Plonka-Hoch. Not only did she introduce me to the field of image and signal processing. Without her guidance and continuous support this thesis would not exist. Moreover, my sincere thanks goes to Jürgen Prestin, who did not hesitate to agree when asked if he would be a referee for this thesis. I would also like to thank my co-supervisors Russell Luke and Thorsten Hohage for always having a sympathetic ear during these years. Furthermore, I would like to gratefully acknowledge the financial support of the German Research Foundation (DFG) in the framework of the Research Training Group 2088 (GRK 2088) Discovering structure in complex data: Statistics meets Optimization and Inverse Problems. Being a member of the RTG during my doctoral studies enabled me to attend many conferences and workshops and helped to broaden my scientific and professional horizon, but also gave me the opportunity to improve my soft skills. Moreover, I would like to thank my amazing current and former colleagues and friends from the Mathematical Signal and Image Processing group for the incredible working environment and the enormous support. In particular, I would like to thank Sina Bittens, Wolfgang Keller, Hanna Knirsch, Markus Petz and Max Pentzlin for proofreading this thesis. My very special gratitude goes to my family for their unconditional support and in particular, to my brothers Wilfried and Wolfgang, who are and always will be a big source of inspiration for me. I am eternally grateful to my friends for their tremendous support and patience with me throughout the last years and especially during pandemic times. Last but not least I would like to thank Max for his unconditional support, love and for always helping me turn on the light even if times seemed dark. v Contents Notation ix