A piecewise constant level set method for elliptic inverse problems

Abstract

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 operator splitting scheme is used to get efficient and robust numerical schemes for solving the obtained problem. Numerical experiments show that the method can recover coefficients with rather complicated geometry of discontinuities under a moderate amount of noise in the observation data.