Robust inversion, dimensionality reduction, and randomized sampling

TitleRobust inversion, dimensionality reduction, and randomized sampling
Publication TypeJournal Article
Year of Publication2012
AuthorsAleksandr Y. Aravkin, Michael P. Friedlander, Felix J. Herrmann, Tristan van Leeuwen
JournalMathematical Programming
KeywordsFWI, Inverse problems, Optimization, Robust estimation, Seismic inversion, Stochastic optimization

We consider a class of inverse problems in which the forward model is the solution operator to linear ODEs or PDEs. This class admits several dimensionality-reduction techniques based on data averaging or sampling, which are especially useful for large-scale problems. We survey these approaches and their connection to stochastic optimization. The data-averaging approach is only viable, however, for a least-squares misfit, which is sensitive to outliers in the data and artifacts unexplained by the forward model. This motivates us to propose a robust formulation based on the Student's t-distribution of the error. We demonstrate how the corresponding penalty function, together with the sampling approach, can obtain good results for a large-scale seismic inverse problem with 50 % corrupted data.

Citation KeyAravkin11TRridr