Improved Recovery Guarantees for Phase Retrieval from Coded Diffraction Patterns

摘要

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