OVER-PARAMETERIZED NETWORK SOLVES PHASE RETRIEVAL EFFECTIVELY

Phase retrieval estimates a complex signal vector from the modulus observation of its linear projections. The problem is the core problem in numerous applications. The phase-less/sign-less observation makes it a nonconvex problem in the gradient flow-based approaches. To enable the convergence to the global solution, an initialization close to the solution is indispensable for these methods. In this paper, we propose using an over-parameterized network to represent the unknown signal to solve the problem. With the help of over-parameterization, a gradient flow-based algorithm enables locating solution with vanishing objective. We show that the introduction of the network in phase retrieval problem benefits the gradient flow method to find the optimal solution. Our proposed method outperforms the existing methods with best recovery performance. Code is publicly accessible at \url{https://github.com/Chilie/PR_Repara}.