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Fourier ptychographic microscopy enables gigapixel-scale imaging, with bothlarge field-of-view and high resolution. Using a set of low-resolution imagesthat are recorded under varying illumination angles, the goal is tocomputationally reconstruct high-resolution phase and amplitude images. Toincrease temporal resolution, one may use multiplexed measurements where thesample is illuminated simultaneously from a subset of the angles. In thispaper, we develop an algorithm for Fourier ptychographic microscopy with suchmultiplexed illumination. Specifically, we consider gradient descent typeupdates and propose an analytical step size that ensures the convergence of theiterates to a stationary point. Furthermore, we propose an accelerated versionof our algorithm (with the same step size) which significantly improves theconvergence speed. We demonstrate that the practical performance of ouralgorithm is identical to the case where the step size is manually tuned.Finally, we apply our parameter-free approach to real data and validate itsapplicability.

Accelerated Wirtinger Flow for Multiplexed Fourier Ptychographic Microscopy