Recovery of compactly supported functions from spectrogram measurements via lifting

A novel phase retrieval method, motivated by ptychographic imaging, is proposed for the approximate recovery of a compactly supported specimen function f : ℝ → ℂ from its continuous short time Fourier transform (STFT) spectrogram measurements. The method, partially inspired by the well known PhaseLift [1] algorithm, is based on a lifted formulation of the infinite dimensional problem which is then later truncated for the sake of computation. Numerical experiments demonstrate the promise of the proposed approach.