• DOI:10.1002/zamm.201600137
• Corpus ID: 5764732

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}
}

• R. Beinert
• Published 15 June 2016
• Physics
• ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik

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.