# A semi-implicit relaxed Douglas-Rachford algorithm (sir-DR) for Ptychograhpy

## TL;DR

The paper introduces a semi-implicit relaxed Douglas-Rachford algorithm (sir-DR) that accelerates convergence and improves reconstruction quality in ptychography, especially with sparse data, outperforming existing methods like ePIE and rPIE.

## Contribution

The paper presents a novel semi-implicit relaxed Douglas-Rachford algorithm for ptychography, demonstrating improved convergence and reconstruction with sparse data, and provides open-source implementation.

## Key findings

- sir-DR converges faster than ePIE and rPIE.
- sir-DR achieves higher reconstruction quality.
- sir-DR successfully reconstructs images with sparse measurements.

## 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.