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

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