If a signal generator satisfies a new zero-set condition, causal signals in complex-generated shift-invariant spaces can be recovered from three random magnitude samples per unit interval, with probability one.
Conjugate Phase Retrieval in Paley-Wiener Space
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abstract
We consider the problem of conjugate phase retrieval in Paley-Wiener space $PW_{\pi}$. 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 $\overline{f(t)}$ are not necessarily distinguishable from the available data. We show that conjugate phase retrieval can be accomplished in $PW_{\pi}$ by sampling only on the real line by using structured convolutions. We also show that conjugate phase retrieval can be accomplished in $PW_{\pi}$ by sampling both $f$ and $f^{\prime}$ only on the real line. Moreover, we demonstrate experimentally that the Gerchberg-Saxton method of alternating projections can accomplish the reconstruction from vectors that do conjugate phase retrieval in finite dimensional spaces. Finally, we show that generically, conjugate phase retrieval can be accomplished by sampling at three times the Nyquist rate, whereas phase retrieval requires sampling at four times the Nyquist rate.
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2019 1verdicts
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Random phaseless sampling for causal signals in shift-invariant spaces: a zero distribution perspective
If a signal generator satisfies a new zero-set condition, causal signals in complex-generated shift-invariant spaces can be recovered from three random magnitude samples per unit interval, with probability one.