Convergence analysis of error-reduction algorithm for solving of the extended one-dimensional discrete phase retrieval problem

The iterative methods are well-known approaches to solve the one-dimensional phase retrieval problem. Amongst them, the error-reduction algorithm is often used since it can easily implement support constraints. Unfortunately this method often stagnates. Recently we have formulated the extended form of the one-dimensional discrete phase retrieval problem and we have assumed that the stagnation can be avoided by oversampling. Simulations have indicated that the conjecture is true. In this work we prove the convergence of the error-reduction algorithm in the proposed extended one-dimensional discrete phase retrieval framework.