A Super Resolution Phase Retrieval Method for Sparse Signals with Arbitrary Scattering Function

Abstract

The phase retrieval problem studies the recovery of the original signal from its phaseless Fourier intensity measurement. Unlike traditional phase retrieval algorithms that only recover the discrete approximation of the original signal, the recently proposed super resolution phase retrieval theories first realize continuous-domain phase retrieval of sparse signals. However, these current methods maintain too strict restriction on the scattering function and there is unnecessary redundancy in the parameter estimation models. This paper proposes a novel super resolution sparse phase retrieval method suitable for arbitrary scattering function and can reduce nearly half of the redundant parameters. First, after a recursive data processing procedure, we use Prony's method to calculate the support intervals. Then, the support of the original signal can be restored through a reordering algorithm. Finally, under the premise of known support, recovering the amplitude is equivalent to solving a series of nonlinear equations, which can be solved by Chebyshev's method. The simulation results verify the effectiveness of the proposed method.