Hierarchical Bayesian Level Set Inversion

Andrew Stuart
University of Warwick

I will begin by overviewing the Bayesian approach

to the reconstruction of fields from indirect

and noisy (possibly nonlinear) measurement functionals [1].

I will then explain the basic Bayesian level set approach to reconstructing piecewise constant fields [2].

Finally I will demonstrate how the method can be enhanced

by means of a hierarchical multiscale approach in which the

charateristic length scale of interface separation is

learned from the data, along with the geometry of interfaces themselves.

[1] M. Dashti and A.M. Stuart. The Bayesian approach to inverse problems.

To appear in Handbook of Uncertainty Quantification, Springer, 2016.


[2] M.A. Iglesias, Y. Lu, A.M. Stuart, "A level-set approach to Bayesian

geometric inverse problems", submitted.


Joint work with Matt Dunlop (Warwick) and Marco Iglesias (Nottingham)

Presentation (PDF File)

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