Phase retrieval revisited

Abstract

The main conclusion of this paper is the necessary and sufficient condition of the phase retrieval problem in general real normed space. The main tool is to prove

$\{\|x+\varphi_{n}\|, \|x-\varphi_{n}\|\}=\{\|y+\varphi_{n}\|, \|y-\varphi_{n}\|\}$

holds and equivalent conditions of the above equation. So we can find the equivalent condition of phase retrieval.