Robust inversion, dimensionality reduction, and randomized sampling

• 成果类型: Article
• 署名作者: Aravkin, Aleksandr; Friedlander, Michael P.; Herrmann, Felix J.; van Leeuwen, Tristan
• 署名单位: University of British Columbia; University of British Columbia
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-012-0571-6
• 发表日期: 2012
• 页码: 101-125
• 关键词: hybrid l(1)/l(2); tomography; algorithms

摘要

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.