Semi-implicit relaxed Douglas-Rachford algorithm (sDR) for ptychography

Abstract

Alternating projection based methods, such as ePIE and rPIE, have been used widely in ptychography. However, they only work well if there are adequate measurements (diffraction patterns); in the case of sparse data (i.e. fewer measurements) alternating projection underperforms and might not even converge. In this paper, we propose semi-implicit relaxed Douglas Rachford (sir-DR), an accelerated iterative method, to solve the classical ptychography problem. Using both simulated and experimental data, we show that sir-DR improves the convergence speed and the reconstruction quality relative to ePIE and rPIE. Furthermore, in certain cases when sparsity is high, sir-DR converges while ePIE and rPIE fail. To facilitate others to use the algorithm, we post the Matlab source code of sir-DR on a public website (www.physics.ucla.edu/research/imaging/sir-DR). We anticipate that this algorithm can be generally applied to the ptychographic reconstruction of a wide range of samples in the physical and biological sciences.

Deep neural networks in single-shot ptychography

“…In this work we compare SspNet with two different iterative reconstruction algorithms: ePIE [2] and sDR [10]. These algorithms belong to different classes: ePIE is an alternate projection algorithm while sDR is based on both projection and reflection [10].…”

“…Importantly, in contrast to all current ptychographic reconstruction algorithms (single-shot and scanning based, iterative and DNN), our DNN does not receive the connections between the DPs and their associated central coordinates on the object or any other information about the microscopic system. We find that the network handles experimental noise and artifacts better than currently standard single-shot ptychographic reconstruction algorithms, extended Ptychographic Iterative Engine (ePIE) [1,2] and Semi-implicit relaxed Douglas-Rachford (sDR) [10] which is a generalized version of the Difference Map (DM) algorithm [11], giving rise to higher spatial resolution and improved reconstructions, especially with poorly aligned system.…”

Cramér-Rao lower bound and maximum-likelihood estimation in ptychography with Poisson noise

“…Our conclusions suggest that more illumination power should be given to the part of object which is of most interest, although this may be difficult to realize in a practical ptychography experiment. As next steps of research, the performance of other ptychographic denoising algorithm [19,35,37,38,47] deserve further investigation. Investigating the CRLB and the statistic properties of the two algorithms for Gaussian noise and the mixed Poisson-Gaussian noise is also an interesting topic for further research.…”

“…Another popular choice is the difference map algorithm, which can be formulated in terms of finding the intersection of two constraint sets [14,34]. Based on the augmented Lagrangian methods for solving the conventional * x.wei-2@tudelft.nl constrained optimization problems, several interesting ptychographic algorithms have been developed during the past 10 years [35][36][37][38].…”

“…On the one hand, ambiguities due to a constant scaling factor, a global phase shift, and raster grid pathology, occur in particular when the probe is unknown [39]. Although many algorithms have been presented to enhance the robustness of ptychography [19,35,37,38], a good starting point and proper parameter settings (e.g., update step size, regularization factor, etc.) are needed in general.…”