Phaseless Rcovery using Gauss-Newton Method
It provides a provably fast and sample-efficient algorithm for the phase retrieval problem, which is important in imaging and optics.
The paper develops a Gauss-Newton algorithm for phase retrieval that achieves quadratic convergence with nearly minimal random measurements, outperforming existing methods in numerical experiments.
In this paper, we develop a concrete algorithm for phase retrieval, which we refer to as Gauss-Newton algorithm. In short, this algorithm starts with a good initial estimation, which is obtained by a modified spectral method, and then update the iteration point by a Gauss-Newton iteration step. We prove that a re-sampled version of this algorithm quadratically converges to the solution for the real case with the number of random measurements being nearly minimal. Numerical experiments also show that Gauss-Newton method has better performance over the other algorithms.