A recurrent neural network for 1-D phase retrieval

In this paper we propose the use of recurrent neural networks for solving the problem of signal restoration from its Fourier spectrum magnitudes. The neural network incorporates the constants related to the real and imaginary parts of the spectrum. We analyze the stability and convergence of the proposed neural network. The solution is provided by the steady state of the neural network. The obtained simulation results demonstrate the high efficiency of our approach.