Sparse Fast Trigonometric Transforms

Abstract

This thesis is the result of the work I did in the last three years, during which I had the opportunity to work at the Institute for Numerical and Applied Mathematics at the University of Göttingen.First of all I owe my deepest thanks to my adviser Gerlind Plonka-Hoch for introducing me to the world of signal and image processing. I could not imagine a more interesting and inspiring topic of research. Furthermore, I would like to thank her, and my coadviser Russell Luke, for their constantly open doors and their continued support during all stages of my PhD. My sincere thanks also go to the co-referees of my thesis, Daniel Potts and Felix Krahmer. I am particularly grateful to Felix Krahmer for inviting me to Munich in May 2016 to meet Mark Iwen. The collaboration initiated by that visit and finalized during a two-week research stay at Michigan State University in February 2017 resulted in Chapter 3 of my thesis. For the invitation to MSU and also for his support during our collaboration I would like to thank Mark Iwen as well.Furthermore, I gratefully acknowledge the financial support of the German Research Foundation (DFG) in the framework of the Research Training Group (RTG) 2088 "Discovering structure in complex data: Statistics meets Optimization and Inverse Problems". For the whole duration of my PhD I was either a member or an associated member of this RTG, enabling me to attend many conferences and workshops for broadening my scientific horizon, but also giving me the opportunity to improve my soft skills.I am particularly indebted to my wonderful colleagues, former colleagues and friends from the "Mathematical Signal and Image Processing" group for the incredible working environment and their emotional support. I would especially like to thank Hanna Knirsch, Inge Keller and Markus Petz for proofreading this thesis.I am eternally grateful to my family and all my friends for their unconditional support, advice and patience with me during the past three years. This thesis would not exist without you. Finally, I want to express my deepest gratitude to Daniel H.