TIGRA an iterative algorithm for regularizing nonlinear ill-posed problems

Abstract

We report on a new iterative method for regularizing a nonlinear operator equation in Hilbert spaces. The proposed TIGRA algorithm is a combination of Tikhonov regularization and a gradient method for minimizing the Tikhonov functional. Under the assumptions that the operator F is twice continuous Fréchet differentiable with a Lipschitz-continuous first derivative and that the solution of the equation F (x) = y fulfils a smoothness condition, we will give a convergence rate result. Finally we present some applications and a numerical result for the reconstruction of the activity function in single-photon-emission computed tomography.