Phase Retrieval from Linear Canonical Transforms

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 (fractional) Fourier transform and a wide range of engineering applications such as optics and quantum mechanism. In this paper, we consider the linear canonic phase retrieval problem of determining a function from the magnitudes of the linear canonic transforms. We show that a compactly supported function f can be determined, up to a global phase, from the magnitudes of multiple linear canonic transforms, where is a class of real unimodular matrices. It generalizes the results of phase retrieval from multiple fractional Fourier transforms. On the other hand, we show that a compactly supported function f can be determined, up to a global phase, from the interference linear canonic magnitudes and where Moreover, if the ambiguity of conjugate reflection is taken into account, the compactly supported function f can be determined, up to a rotation and conjugate reflection, from the linear canonic magnitudes and