2019/10/28 by Chun‐Kit Lai, Lai, Chun-Kit, Friedrich Littmann +3 · 3 citations
Earth and Planetary Sciences · Physics and Astronomy · #30D15 #42C15 #46C05 #94A20 #Advanced X-ray Imaging Techniques #Complex Variables (math.CV) #Digital Holography and Microscopy #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.1910.12975
openalex publication_date 2019/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We consider the problem of conjugate phase retrieval in Paley-Wiener space PWπ. 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 f(t) are not necessarily distinguishable from the available data. We show that conjugate phase retrieval can be accomplished in PWπ by sampling only on the real line by using structured convolutions. We also show that conjugate phase retrieval can be accomplished in PWπ by sampling both f and f′ 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.