Compressive Phase Retrieval under Poisson Noise

We present a technique for compressive phase retrieval under Poisson noise using the theory of variance stabilization transforms (VSTs). We modify two existing algorithms using VSTs, and derive worst-case performance bounds for both the algorithms. Our proposed modification allows for easy and very principled parameter tuning. Our estimator is tractable and we also show numerical results on phase recovery of sparse signals for Poisson corrupted measurements, and demonstrate the relative advantage of our modification at low intensities. We also present a comparison of the performance and other theoretical aspects of both the algorithms.