Iterative Algorithms for Ptychography

In computational imaging, ptychography is a cutting-edge technique that has garnered significant attention for its ability to address the challenge of the phase problem in the microscope. At its core, ptychography involves breaking the imaging process into a series of overlapping measurements. Instead of capturing the entire image at once, ptychography acquires diffraction patterns from overlapping regions of the specimen. This approach allows for the recovery of both amplitude and phase information with high accuracy. With the development of ptychography, various phase retrieval algorithms have been proposed in the recent decades. These different algorithms can be categorized as direct ptychography and iterative ptychography. Furthermore, iterative ptychography can also be subdivided into two types: sequential projection methods and set projection methods. All of these different categories will be discussed and analyzed in this thesis. The direct ptychography will be introduced in the Chapter 4, while the iterative ptychography will be in the Chapter 5. Further contributions in this thesis are two new blind ptychographic solutions. The first is generalizing the set projection methods to a standard form and introducing the Bayesian Optimization to tune the parameters automatically. The other is a novel approach called Weighted Average of Sequential Projections (WASP), which combines the advantages of both sequential projection methods and set projection methods. This thesis aims to find novel and effective ptychographic approaches, based on evaluating and comparing the existing algorithms. All the different approaches will be tested with different simulations and real-world ptychography experiments to verify their performance in different contexts and provide a deep understanding of different types of ptychographic solutions for future research.