Phase retrieval of complex and vector-valued functions

The phase retrieval problem in the classical setting is to reconstruct real/complex functions from magnitudes of their Fourier/frame measurements. In this paper, we consider a new paradigm vector-valued setting, which motivated by complex conjugate vectors range space real matrix and Paley-Wiener space, also determination vector field defined on graph relative between neighboring vertices. provide several characterizations determine complex/vector-valued f linear S (in)finite dimensions, up trivial ambiguity, ??(f)? measurements ?(f),???, apply for recovery shift-invariant phaseless evaluations fields absolute at vertices discuss affine quaternion setting.