  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.
