Undersampled Dynamic Fourier Ptychography via Phaseless PCA

In recent work, we studied the phaseless PCA (low rank phase retrieval) problem and developed a provably correct and fast alternating minimization (AltMin) solution for it called AltMinLowRaP. In this work, we develop a modification of AltMinLowRaP, called AltMinLowRaP-Ptych, that is designed for reducing the sample complexity (number of measurements required for accurate recovery) for dynamic Fourier ptychographic imaging. Fourier ptychography is a computational imaging technique that enables high-resolution microscopy using multiple low-resolution cameras. Via exhaustive experiments on real image sequences with simulated ptychographic measurements, we show the power of our algorithm for reducing the number of samples required for accurate recovery.