Recovery of Compactly Supported Functions from Spectrogram Measurements via Lifting

Abstract

A novel phase retrieval method, motivated by ptychographic imaging, is proposed for the approximate recovery of a compactly supported specimen function $f:\mathbb{R}\to \mathbb{C}$ from its continuous short time Fourier transform (STFT) spectrogram measurements. The method, partially inspired by the well known PhaseLift 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.

arXiv comment2017 International Conference on Sampling Theory and Applications (SampTA2017)