Norm retrieval from few spatio-temporal samples

Abstract

Vectors in a real finite-dimensional Hilbert space that accomplish phase and norm retrieval can be characterized. In this article, we consider the cases where an operator A is self adjoint, normal or an operator in Jordan canonical form in a real finite-dimensional Hilbert space. In each case, we give a structure to construct norm-retrievable frame sets that have a dynamical sampling structure. Given that phase retrieval always implies norm retrieval, we particularly concentrate on finding conditions for norm retrieval where phase retrieval is not possible.