Solving constraint ill-posed problems using Ginzburg–Landau regularization functionals

Abstract

Abstract. We consider constraint ill-posed operator equations such that we restrict the domain to functions, which in the first case are piecewise constant and in the second case attain values in a certain interval. We use Ginzburg-Landau regularization methods for solving this equations. In our numerical examples we consider the inverse conductivity problem which has applications in electrical impedance tomography. We present a numerical implementation along with some results and compare them with standard H 1 -Tikhonov regularization.