The extended one-dimensional discrete phase retrieval problem

It has been known for decades that the iterative methods are perhaps the most popular approaches to solve the phase retrieval problem. Unfortunately the iterative methods often stagnate. This happens also in the case of the 1-D Discrete Phase Retrieval (1-D DPhR) problem. Recently it has been shown that some requirements in the input magnitude data might be one of the reasons why the direct method cannot solve the 1-D DPhR Problem. In this work we present some difficulties that can be encountered when one has to implement the iterative method for finding a solution of 1-D DPhR problem. We shall formulate the extended form of 1-D DPhR problem. Simulations indicate the conjecture to be true.