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

摘要

We consider constrained ill-posed operator equations. The constraints are such that in one case we restrict the domain to functions which are piecewise constant. In another case we allow only functions that attain values in a certain interval. We use Ginzburg–Landau regularization methods for solving these 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 modified H1-Tikhonov regularization methods.