Abstract

The phase retrieval problem is of wide interest because it appears in a number of interesting application areas in physics. Several kinds of phase retrieval problems appeared in laser optics over the past decade. In this paper we consider the numerical solution of two phase retrieval problems for an unknown smooth function f with compact support. We approximate f by a linear spline. The corresponding spline coefficients are iteratively determined by local Gauss-Newton methods, where convenient initial guesses are constructed by a multilevel strategy. We close with some numerical tests which illustrate our method.