Weighted Phase Retrieval of Fourier Measurement with Outliers: Measurement Structure and Reconstruction Algorithm

Phaseless measurement is widely used in various fields, and phase retrieval is a key step in signal reconstruction of phaseless measurement. The occurrence of outliers will cause the optimal solution of the traditional phase retrieval objective function to deviate from the original signal, thereby reducing the reconstruction accuracy. This article modifies the objective function by introducing a weight vector so that its optimal solution will still approximate the original signal when outliers appear and proposes a specific implementation strategy for this idea under the background of Fourier phase retrieval. For the weight vector, we design a two-channel measurement structure using a discrete Fourier transform frequency-domain cyclic shift theorem and mask technique to obtain a weight vector. For the improved objective function, we use the majorization-minimization framework to derive an iterative algorithm to get an optimal solution. Extensive simulation and hardware experiments show that the proposed method can effectively suppress the adverse effects of outliers.