Phase retrieval via Lagrange programming neural network

In this paper, the problem of phase retrieval is addressed. Its solution is based on the Lagrange programming neural network (LPNN), which is an analog neural computational technique for solving nonlinear constrained optimization problems according to the Lagrange multiplier theory. The local stability of the proposed algorithm is also investigated. Furthermore, we extend the LPNN based approach to more challenging array signal processing applications, namely, when multiple vector signals with full column rank or other constraints are required to be recovered from measured magnitudes. One of the key difficulties for these challenges is pairing the separately estimated parameters, while the parameters estimated by the extended method are automatically paired. The performance of the developed algorithms is demonstrated via computer simulations.