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

@article{Beinert2016AmbiguitiesIO, title={Ambiguities in one‐dimensional phase retrieval from magnitudes of a linear canonical transform}, author={Robert Beinert}, journal={ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift f{\"u}r Angewandte Mathematik und Mechanik}, year={2016}, volume={97} }

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…

## 3 Citations

### One-Dimensional Discrete-Time Phase Retrieval

- Mathematics
- 2020

This section studies the structure of the arising ambiguities of the phase retrieval problem and shows how they can be characterized using the given Fourier intensity, and considers the assumption of non-negativity of the solution signal, additional magnitudes or phases of some signal components in time domain, or additional intensities of interference measurements in frequency domain.

### Phase Retrieval from Linear Canonical Transforms

- MathematicsNumerical Functional Analysis and Optimization
- 2022

Abstract The classical phase retrieval problem aims to recover an unknown function from the Fourier magnitudes. The linear canonical transform has a more generalized form of the well-known…

### Sparse Phase Retrieval of One-Dimensional Signals by Prony's Method

- MathematicsFront. Appl. Math. Stat.
- 2017

In this paper, we show that sparse signals f representable as a linear combination of a finite number N of spikes at arbitrary real locations or as a finite linear combination of B-splines of order m…

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