On the Phase Retrievable Sequences

TL;DR

This paper characterizes phase retrievable sequences of bounded linear operators on Hilbert spaces, especially finite-dimensional complex spaces, and explores methods for constructing such sequences and their relation to frames.

Contribution

It provides a new characterization of phase retrievability for sequences of operators and introduces approaches for constructing phase retrievable sequences, extending the understanding of phase retrieval in Hilbert spaces.

Findings

Characterization of phase retrievable sequences on Hilbert spaces.

Methods for constructing phase retrievable sequences.

Analysis of phase retrieval properties for g-frames and frames.

Abstract

In this paper, we study phase retrievable sequences and give a characterization of phase retrievability of a sequence of bounded linear operators on a Hilbert space $H$; in particular, for $H=\ell_2^d(\Bbb{C})$. We also give several approaches for constructing phase retrievable sequences. Then, we investigate the property of phase retrieval for $g$-frames and frames.