Improved Recovery Guarantees for Phase Retrieval from Coded Diffraction Patterns

Abstract: In this work we analyze the problem of phase retrieval from Fourier measurements with random diffraction patterns. To this end, we consider the recently introduced PhaseLift algorithm, which expresses the problem in the language of convex optimization. We provide recovery guarantees which require O(log^2 d) different diffraction patterns, thus improving on recent results by Candes et al. [arXiv:1310.3240], which require O(log^4 d) different patterns.