1-D multiplierless phase retrieval using recurrent neural networks

The phase retrieval problem arises when the phase of a signal is apparently lost or impractical to measure and must be reconstructed from only the magnitude of its Fourier transform. In this paper we propose a multiplierless recurrent neural network for solving this problem. The recurrent 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 effectiveness of our solution is illustrated with some numerical examples