Phase reconstruction from magnitude of band-limited multidimensional signals
In this paper, the problem of phase reconstruction from magnitude of multidimensional band-limited functions is considered. It is shown that any irreducible band-limited function \(f(z_ 1,...,z_ n)\), \(z_ i\in {\mathbb{C}}\), \(i=1,...,n\), is uniquely determined from the magnitude of \(f(x_ 1,...,x_ n):\) \(| f(x_ 1,...,x_ n)|\), \(x_ i\in {\mathbb{R}}\), \(i=1,...,n\), except for (1) linear shifs: \(e^{i(\alpha_ 1z_ 1+...+\alpha_ nz_ n+\beta)}\), \(\alpha_ i\in {\mathbb{R}}\), \(i=1,...,n\); and (2) conjugation: \(f^*(z^*_ 1,...,z^*_ n)\).
scientific article; zbMATH DE number 3944489