Several approaches to signal reconstruction from spectrum magnitudes

The problem of reconstructing a one-dimensional (1D) signal from only the magnitude of its Fourier transform emerges when the phase of a signal is apparently lost or impractical to measure. Previous solutions usually employed an iterative Fourier transform (IFT) algorithm applied on a discrete approximation of a signal. The utilization of these algorithms is seriously limited by the unpredictability of their convergence. We propose several solutions to the phase retrieval problem. The first two proposed solutions uses relationships between the phase and the gain differences (GD), or gain samples (GS), in nepers. The last proposed solution uses a neural network NN for solving the problem. The NN incorporates a combination of the maximum entropy estimation algorithm with some additional nonlinear constraints. We compare our solutions by using some numerical examples. The performances under noisy conditions are also considered