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

arXiv: https://arxiv.org/abs/1906.01875 · HTML: https://mlsanity.com/paper/1906.01875/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2019.

## Built on by (most cited first, 1 of 1)

- [Learning neural representations for X-ray ptychography reconstruction with unknown probes](https://mlsanity.com/paper/2509.04402/) (2025)

## Abstract (arXiv)

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.