Recovery of Compactly Supported Functions from Spectrogram Measurements via Lifting
For researchers in phase retrieval and ptychographic imaging, this offers a new method, but it is incremental as it adapts existing ideas (PhaseLift) to a new setting.
The paper proposes a novel phase retrieval method for recovering compactly supported functions from STFT spectrogram measurements, using a lifted formulation. Numerical experiments show the approach is promising.
A novel phase retrieval method, motivated by ptychographic imaging, is proposed for the approximate recovery of a compactly supported specimen function $f:\mathbb{R}\rightarrow\mathbb{C}$ 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.