  This paper is concerned with the numerical solution of nonlinear ill-posed
operator equations involving convex constraints. We study a Newton-type method
which consists in applying linear Tikhonov regularization with convex
constraints to the Newton equations in each iteration step. Convergence of this
iterative regularization method is analyzed if both the operator and the right
hand side are given with errors and all error levels tend to zero. Our study
has been motivated by the joint estimation of object and phase in 4Pi
microscopy, which leads to a semi-blind deconvolution problem with
nonnegativity constraints. The performance of the proposed algorithm is
illustrated both for simulated and for three-dimensional experimental data.
