A Bayesian level set method for geometric inverse problems

A Bayesian level set method for geometric inverse problems

We introduce a level set based approach to Bayesian geometric inverse problems. In these problems the interface between different domains is the key unknown, and is realized as the level set of a function. This function itself becomes the object of the inference. Whilst the level set methodology has been widely used for the solution of geometric inverse problems, the Bayesian formulation that w...

A Level Set Method for Inverse Problems

Level Set Methods for Geometric Inverse Problems in Linear Elasticity

In this paper we investigate the regularization and numerical solution of geometric inverse problems related to linear elasticity with minimal assumptions on the geometry of the solution. In particular we consider the probably severely ill-posed reconstruction problem of a twodimensional inclusion from a single boundary measurement. In order to avoid parameterizations, which would introduce a-p...

A piecewise constant level set method for elliptic inverse problems

We apply a piecewise constant level set method to elliptic inverse problems. The discontinuity of the coefficients is represented implicitly by a piecewise constant level set function, which allows to use one level set function to represent multiple phases. The inverse problem is solved using a variational penalization method with the total variation regularization of the coefficients. An opera...

Parametric Level Set Methods for Inverse Problems

In this paper, a parametric level set method for reconstruction of obstacles in general inverse problems is considered. General evolution equations for the reconstruction of unknown obstacles are derived in terms of the underlying level set parameters. We show that using the appropriate form of parameterizing the level set function results a significantly lower dimensional problem, which bypass...