Ambiguities in one-dimensional phase retrieval from magnitudes of a linear canonical transform

TL;DR

This paper explores ambiguities in one-dimensional phase retrieval problems when signals are reconstructed from magnitudes of linear canonical transforms, extending classical Fourier phase retrieval insights to more general transforms.

Contribution

It generalizes the understanding of phase retrieval ambiguities from Fourier to linear canonical transforms, providing new characterizations of solution sets.

Findings

Identifies ambiguities specific to linear canonical transform phase retrieval.

Transfers classical Fourier phase retrieval characterizations to the linear canonical transform case.

Provides a framework for analyzing phase retrieval ambiguities in broader transform settings.

Abstract

Phase retrieval problems occur in a wide range of applications in physics and engineering. Usually, these problems consist in the recovery of an unknown signal from the magnitudes of its Fourier transform. In some applications, however, the given intensity arises from a different transformation such as the Fresnel or fractional Fourier transform. More generally, we here consider the phase retrieval of an unknown signal from the magnitudes of an arbitrary linear canonical transform. Using the close relation between the Fourier and the linear canonical transform, we investigate the arising ambiguities of these phase retrieval problems and transfer the well-known characterizations of the solution sets from the classical Fourier phase retrieval problem to the new setting.