A neural network approach to magnitude retrieval

Abstract

This paper presents a neural network (NN) approach for constructing time-domain signals from phases of their discrete Fourier transforms, to solve the so-called magnitude retrieval problem. The solution of the magnitude retrieval problem is not unique in general. In this paper, we impose two constraints (non-negativity and not having conjugate reciprocal z-transform zeros) to obtain a unique solution by a neural network. The neural network structure we propose is a multi-layer perceptron (MLP) with sigmoid function and back-propagation learning rule. Using simulation studies, we illustrate the capability of this NN structure in solving the magnitude retrieval problem for discrete signals. The NN approach presented in this paper is fast, always generates a specific solution, i.e., the non-negative solution, and is not sensitive to the observation noise. A combination of the NN approach and a classical approach (alternating projections) can eliminate the deficiencies of both methods.