Iterative projection algorithms are among the most widely used reconstruction methods for high-performance ptychographic imaging. While flexible and powerful, these algorithms still face problems with convergence and solution uniqueness, as real measurements are always degraded by noise. Here, we present a generalized method termed Wirtinger projections (WP), which rectifies the inaccuracies inherent in ptychographic models and is capable of improving imaging performance in the presence of noise. This is made possible by integrating maximum likelihood principles, high-order nonlinear optimization with Wirtinger Hessian calculus, and highly parallel set-projection phase retrieval strategies. We derive the theory and algorithms of WP and demonstrate significant imaging performance gains in the signal-to-noise ratio and convergence on both simulated and experimental ptychography datasets. In addition, we showcase that WP outperforms conventional methods when dealing with diffraction patterns that contain significant background noise. WP enables high-resolution, robust ab initio ptychographic imaging from noisy datasets and potentially allows decreasing the exposure or dose required to achieve a certain reconstruction quality. Moreover, it provides additional flexibility to balance multiple key aspects that affect imaging performance, including phase retrieval efficiency, convergence stability, and noise tolerance, compared with conventional approaches.
Dong et al. (Sun,) studied this question.