An application of Tikhonov regularization to phase retrieval

The phase reconstruction problem consists of recovering a function from absolute values of its Fourier transform. Since this nonlinear problem is ill-posed, some kind of regularization has to be used to solve it. It is shown that Tikhonov regularization is a stable and convergent method to solve the problem if the function to be reconstructed is time-limited, or, more generally, belongs to a specific weighted Hilbert space and convergence rates are provided.