TY - JOUR A1 - Göppel, Simon A1 - Frikel, Jürgen A1 - Haltmeier, Markus T1 - Regularization of Inverse Problems with Translation Invariant Frames JF - Proceedings of the 20th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM-2022), 2022, Heraklion (Crete, Greece) N2 - In various fields of applications, inverse problems are characterized by their sensitivity to data perturbations which can cause severe reconstruction errors. Hence, regularization procedures are employed in order to ensure stability and reconstruction quality. To overcome limitations of classical approaches such as the filtered singular value decomposition (SVD), frame based diagonalization methods have been studied in the recent years, e.g., wavelet-vagulette (WVD) decomposition. While these methods can be well adapted to the problem at hand, it is well-known, that the lack of translation invariance in multiscale systems can cause specific artifacts in the recovered object. Thus, to overcome these drawbacks we use the translation invariant diagonal frame decomposition (TI-DFD) of linear operators. For illustration, we construct a TI-WVD for one-dimensional integration operator, and confirm our theoretical findings by numerical simulations. Y1 - 2023 PB - AIP Publishing ER -