Maaß, PeterFernsel, PascalPascalFernsel2022-04-222022-04-222022-03-07https://media.suub.uni-bremen.de/handle/elib/587010.26092/elib/1493This work is devoted to the application-oriented design of Nonnegative Matrix Factorization (NMF) models along with the development of solution algorithms, their application to real-world problems and the analysis of some theoretical aspects. The thesis is divided into two main parts and additionally contains a short introduction in the beginning, which includes a description of the thesis, the featured research papers and the contributions of the author of this thesis. The first part of this work contains preliminary information on basic concepts of inverse problems and NMF as well as a short overview of solution strategies for NMF and the considered applications. The second part contains the five research papers to which the author contributed.enCC BY 4.0 (Attribution)https://creativecommons.org/licenses/by/4.0/nonnegative matrix factorizationNMForthogonal NMFlow-rank approximationinverse problemsvariational methodsmulti-parameter regularizationalgorithm developmentmedical imaging510Dissertationurn:nbn:de:gbv:46-elib58700