Fourier phase retrieval with random phase illumination
Tuesday, August 15, 2017 - 10:30am - 11:00am
Fourier phase retrieval is the problem of recovering images from their Fourier intensity data. The standard Fourier phase retrieval (without a mask) is known to have non-trivial ambiguity, and standard phasing algorithms often stagnate at a local minimum, which produces wrong or inaccurate solutions. In this talk Fourier phase retrieval is studied with the introduction of a randomly fabricated mask. We prove uniqueness if the mask information is exactly known, and show superior numerical performance of the standard phasing algorithms, including rapid convergence, significantly reduced data and noise stability. In applications exact knowledge of the mask may not be available. We next consider the case that only rough information about the mask is known. Uniqueness is proved with an exponentially high probability in terms of the mask uncertainty. New phasing algorithms alternating between the object update and the mask update are demonstrated to have the capability of recovering both the image and the mask (within the object support) simultaneously, which is consistent with our uniqueness result.