Two dimensional phase retrieval using neural networks

The object of the 2D phase retrieval problem is to reconstruct an image from its spectral magnitude alone. This problem emerges when the phase of the 2D signal is apparently lost or is impractical to measure. For 2D spatially-limited non-negative objects characterized by an analytic spectrum, the solution is unique. In this paper, we propose the use of a neural network for solving the 2D phase retrieval problem. The neural network incorporates a combination of the maximum entropy estimation algorithm with some additional nonlinear constraints. These constraints make use of additional unknowns that are related to the real and imaginary parts of the image spectrum. The solution is provided by the steady state of the neural network, then it is verified and eventually improved with an iterative Fourier transform algorithm. The obtained simulation results demonstrate the high efficiency of the proposed approach.