Regularization methods for nonlinear ill-posed problems with applications to phase reconstruction

This paper is concerned with regularizing algorithms for nonlinear ill-posed operator equations F(x)=y and with their application to phase retrieval problems. We consider nonlinear Tikhonov regularization as well as iterative methods, especially iterations derived from Newton's method, and give convergence and convergence rates results both for calculation with exact data and for the case that the data y are contaminated by noise. Finally, we apply some of these methods to a problem appearing in medical imaging and nondestructive testing, namely the reconstruction of the phase of a function from intensity measurements of its Fourier transform.