Uniqueness of the Short-Time Linear Canonical Transform Phase Retrieval

TL;DR

This paper investigates the phase retrieval problem for the Short-Time Linear Canonical Transform (STLCT), demonstrating unique recovery under certain sampling conditions and providing counterexamples and solutions for band-limited functions.

Contribution

It establishes conditions for unique phase retrieval from STLCT measurements and addresses limitations and solutions for different lattice sampling schemes.

Findings

Unique recovery of functions from phaseless STLCT sampling on square-root lattices.

Counterexamples showing non-uniqueness on uniform lattices in L2(R).

Phase retrieval is possible for band-limited functions on uniform lattices.

Abstract

In this paper, we focus on the problem of phase retrieval from intensity measurements of the Short-Time Linear Canonical Transform (STLCT). Specifically, we show that the STLCT allows for the unique recovery of any square-integrable function through phaseless STLCT sampling on rectangular square-root lattices. When turning to the uniform lattices, we establish counterexamples about the STLCT phase retrieval problems in L2(R). Nevertheless, for functions in band-limited function spaces, phase retrieval results on uniform lattices can still be accomplished.