Sampling Density for Gabor Phase Retrieval

TL;DR

This paper investigates the minimal sampling densities required for successful Gabor phase retrieval from discrete samples across various lattice configurations, providing optimal conditions for accurate signal reconstruction.

Contribution

It introduces the concept of optimal sampling densities for Gabor phase retrieval on different lattice structures, extending understanding of sampling requirements in this context.

Findings

Optimal densities identified for square root lattice sampling

Optimal densities established for intersecting line sampling

Optimal densities determined for parallel line sampling

Abstract

Gabor phase retrieval stands for recovering a square integrable function up to a global phase from absolute values of its Gabor transform. In this paper, we study Gabor phase retrieval from discrete samples. We consider three types of sampling sequences, which include square root lattices, square root sequences on two intersecting lines and on three parallel lines respectively. In all cases we give the optimal sampling density for a sequence to do Gabor phase retrieval.