A Bayesian approach to nonlinear inversion.

Abstract

Iterated linear inversion theory can often solve nonlinear inverse problems. Also, linear inversion theory provides convenient error estimates and other interpretive measures. But are these interpretive measures valid for nonlinear problems? This question is addressed in terms of the joint probability density function of the estimated parameters. Linear inversion theory will be valid if the observations are linear functions of the parameters within a reasonable (say, 95%) confidence region about the optimal estimate, if the optimal estimate is unique. Bayes' rule is used to show how prior information can improve the uniqueness of the optimal estimate, while stabilizing the iterative search for this estimate. -from Authors