-

 

 

 




Optimization Online





 

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 )

Citation:

Download: [PDF]

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

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society