Generalized Minkowski sets for the regularization of inverse problems

TitleGeneralized Minkowski sets for the regularization of inverse problems
Publication TypeConference
Year of Publication2019
AuthorsBas Peters, Felix J. Herrmann
Conference NameSIAM Conference on Mathematical and Computational Issues in the Geosciences
KeywordsIntersections, Inverse problems, Minkowski set, Projections, Sets

We present a new algorithm to compute projections onto the intersection of constraint sets, designed particularly for multiple sets because we exploit similarities between constraint sets. When we do not know projections onto the individual sets in closed form, as is the case for total-variation constraints, our algorithm does not need other optimization algorithms to solve sub-problems. This a significant advantage in terms of computational cost and number of tuning parameters and stopping conditions, compared to classical algorithms to compute projections onto the intersection, such as Dykstra's algorithm. The proposed algorithm is suitable for problems with a large number of model parameters such as full-waveform inversion because it exploits coarse and fine-grained parallelism, and we also present a multilevel accelerated version. The corresponding software is open-source and implemented in Julia. We present strategies to use projections onto multiple constraints to regularize full-waveform inversion for models with salt domes or sedimentary geology.



Citation Keypeters2019SIAMGEOgmrip