Affiliation:
1. School of Mathematics, Statistics and Mechanics Beijing University of Technology Beijing China
Abstract
Recently, quaternionic Fourier analysis has received increasing attention due to its applications in signal analysis and image processing. This paper addresses quaternionic generalized phase retrieval (QGPR) problem in quaternion Euclidean spaces
. We introduce the concept of QGPR which aims to reconstruct a signal
in
from the quadratic measurements
, where each
is an
self‐adjoint quaternion matrix. We characterize QGPR sequences in terms of their real Jacobian matrices, prove that the set of QGPR sequences is an open set in some sense, and present some phaselift‐based sufficient conditions on QGPR which gives a method to construct QGPR sequences.
Funder
National Natural Science Foundation of China