Convolutional computations for  local Bayesian approximations in linear inverse problems

Presenter: Odd Kolbjørnsen, Aker BP/UiO

Joint work with Charlotte Semin Sanchis

Abstract:

We discuss uncertainty assessment in linear inverse problems  with  a  latent target property.

Many problems of indirect measurements fit into this framework. In x-ray  tomography, the data are line integrals of the absorption, whereas the latent target property is tissue type or density. For seismic data, the  interest might be the rock type or the porosity, but the physics is  related to intermediate properties such as sound velocity and density.  The hierarchical structure of the problem and the multiple levels of  uncertainty makes the problem well-suited for a Bayesian formulation.  However, the general solution to Bayesian inference through McMC  sampling is, in general, too time-consuming for large-scale problems. We present an approximate computation which provides a sampling-free  Bayesian inversion based on the principles of expectation propagation.  The approach is valid for a large class of inverse problems. Going from  a global problem, we build on the likelihood principle to provide an  approximate likelihood which is suited for local inference. We show  examples from CT images of rock and seismic amplitude inversion.

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