# Recovery of Compactly Supported Functions from Spectrogram Measurements via Lifting

## TL;DR

This paper introduces a new phase retrieval technique inspired by ptychography, enabling the approximate reconstruction of compactly supported functions from spectrogram data using a lifted formulation and numerical validation.

## Contribution

It presents a novel phase retrieval method based on lifting for spectrogram measurements, extending phaseLift ideas to infinite-dimensional functions with practical truncation.

## Key findings

- Numerical experiments show promising reconstruction results.
- The method effectively handles infinite-dimensional spectrogram data.
- The approach offers a new avenue for phase retrieval in imaging applications.

## Abstract

A novel phase retrieval method, motivated by ptychographic imaging, is proposed for the approximate recovery of a compactly supported specimen function $f:\mathbb{R}\rightarrow\mathbb{C}$ 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.