A phase retrieval framework based on the multigrid method to alleviate the twin-image problem

Abstract

The twin-image problem, a persistent stagnation mode in iterative projection algorithms (IPAs) for coherent diffraction imaging, occurs when the ideal and twin images appear simultaneously in the reconstruction. Presented here is a methodological framework for IPAs termed the half-cycle multigrid (HMG) for use in phase retrieval to alleviate the twin-image problem during the iterative process. HMG reconstructs the low-frequency phase first to reduce the impact of oscillation caused by phase retrieval in the higher-frequency region of Fourier space during the iteration. The higher-frequency Fourier magnitude is then added to the reconstruction stage by stage using the multigrid method. The unification of phase retrieval orientation in the low-frequency region lays the foundation for that in the whole Fourier space. The reconstruction results of simulated and experimental diffraction patterns demonstrate that HMG effectively reduces the probability of the twin-image problem occurring, enhances the accuracy of low-frequency information, and achieves credible and faithful reconstruction results from noisy diffraction patterns. The combination of HMG with the oversampling smoothness framework allows more reliable reconstruction results, proving that the HMG framework has good extensibility. It is expected that HMG can be combined with other IPAs.

Improved fast Fourier solution based on transport of intensity equation

“…In 2022, Xie et al [15] performed phase recovery by solving the transport of the intensity equation using membrane vibration modes. In 2023, Ou [16] et al solved the dual-image problem in the multigrid method using half-period multi-networks. These methods have been proven to be effective solutions, but there are problems such as computational complexity in these methods.…”