Parametric Level Set Methods for Inverse Problems

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...

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...

On multiple level-set regularization methods for inverse problems

We analyze a multiple level-set method for solving inverse problems with piecewise constant solutions. This method corresponds to an iterated Tikhonov method for a particular Tikhonov functional Gα based on TV–H 1 penalization. We define generalized minimizers for our Tikhonov functional and establish an existence result. Moreover, we prove convergence and stability results of the proposed Tikh...

Levenberg-Marquardt Level Set Methods for Inverse Obstacle Problems

The aim of this paper is to construct Levenberg-Marquardt level set methods for inverse obstacle problems, and to discuss their numerical realization. Based on a recently developed framework for the construction of level set methods, we can define LevenbergMarquardt level set methods in a general way by varying the function space used for the normal velocity. In the typical case of a PDE-constr...

A Level Set Method for Inverse Problems