A Provably Accurate Algorithm for Recovering Compactly Supported Smooth Functions from Spectrogram Measurements

We present an algorithm which is closely related to direct phase retrieval methods that have been shown to work well empirically [1], [2] and prove that it is guaranteed to recover (up to a global phase) a large class of compactly supported smooth functions from their spectrogram measurements. As a result, we take a first step toward developing a new class of practical phaseless imaging algorithms capable of producing provably accurate images of a given sample after it is masked by just a few shifts of a fixed periodic grating.