Statistical Modelling 13 (5&6) (2013), 481–507

Experimental design in the context of Tikhonov regularized inverse problems

L Tenorio
Applied Mathematics and Statistics,
Colorado School of Mines,
Golden,
CO
e-mail: ltenorio@mines.edu

C Lucero
Applied Mathematics and Statistics, Colorado School of Mines,
Golden,
CO


V Ball
Hess Corporation,
Houston,
TX


L Horesh
IBM T J Watson Research Center,
Yorktown Heights,
NY


Abstract:

The method of Tikhonov regularization is commonly used to obtain regularized solutions of ill-posed linear inverse problems. We use its natural connection to optimal Bayes estimators to determine optimal experimental designs that can be used with Tikhonov regularization; they are designed to control a measure of total relative efficiency. We present an iterative/semidefinite programming hybrid method to explore the configuration space efficiently. Two examples from geophysics are used to illustrate the type of applications to which the methodology can be applied.

Keywords:

Experimental design; inverse problems; regularization; equivalence theorems
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