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

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 (sDR), an accelerated iterative method, to solve the classical ptychography problem. Using both simulated and experimental data, we show that sDR improves the convergence speed and the reconstruction quality relative to extended ptychographic iterative engine (ePIE) and regularized ptychographic iterative engine (rPIE). Furthermore, in certain cases when sparsity is high, sDR converges while ePIE and rPIE fail or encounter slow convergence. To facilitate others to use the algorithm, we post the Matlab source code of sDR on a public website (www.physics.ucla.edu/research/imaging/sDR/index.html). 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.