Conjugate Phase Retrieval in Paley-Wiener Space

We consider the problem of conjugate phase retrieval in Paley-Wiener space PW
_π
. The goal of conjugate phase retrieval is to recover a signal f from the magnitudes of linear measurements up to unknown phase factor and unknown conjugate, meaning f(t) and $\overline {f\left( t \right)} $ are not necessarily distinguishable from the available data. We show that conjugate phase retrieval can be accomplished in PW
_π
by sampling only on the real line by using structured convolutions. We also show that conjugate phase retrieval can be accomplished in PW
_π
by sampling both f and f
^'
only on the real line. Finally, we show that generically, conjugate phase retrieval can be accomplished by sampling at 3 times the Nyquist rate, whereas phase retrieval requires sampling at 4 times the Nyquist rate.