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Robust inversion, dimensionality reduction, and randomized sampling

Aleksandr Aravkin(saravkin***at***eos.ubc.ca)
Michael P. Friedlander(mpf***at***cs.ubc.ca)
Felix Herrmann(fherrmann***at***eos.ubc.ca)
Tristan van Leeuwen(tleeuwen***at***eos.ubc.ca)

Abstract: 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.

Keywords: inverse problems, seismic inversion, stochastic optimization, robust estimation

Category 1: Nonlinear Optimization

Category 2: Stochastic Programming

Category 3: Applications -- Science and Engineering (Basic Sciences Applications )


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Entry Submitted: 11/17/2011
Entry Accepted: 11/17/2011
Entry Last Modified: 11/17/2011

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