Reconstruction of Bandlimited Functions from Unsigned Samples

Abstract

We consider the recovery of real-valued bandlimited functions from the absolute values of their samples, possibly spaced nonuniformly. We show that such a reconstruction is always possible if the function is sampled at more than twice its Nyquist rate, and may not necessarily be possible if the samples are taken at less than twice the Nyquist rate. In the case of uniform samples, we also describe an FFT-based algorithm to perform the reconstruction. We prove that it converges exponentially rapidly in the number of samples used and examine its numerical behavior on some test cases.

Cited by in corpus (20)

• Uniqueness of STFT phase retrieval for bandlimited functions
• Injectivity of Gabor phase retrieval from lattice measurements
• Phase Retrieval via Structured Modulations in Paley-Wiener Spaces
• Non-uniqueness theory in sampled STFT phase retrieval
• Phase retrieval of bandlimited functions for the wavelet transform
• Phase Retrieval of Real-Valued Signals in a Shift-Invariant Space
• Stable Phase Retrieval in Infinite Dimensions
• Random phaseless sampling for causal signals in shift-invariant spaces: a zero distribution perspective
• Stable Gabor phase retrieval in Gaussian shift-invariant spaces via biorthogonality
• Stable Phase Retrieval from Locally Stable and Conditionally Connected Measurements
• Phaseless Sampling and Linear Reconstruction of Functions in Spline Spaces
• Phaseless Signal Recovery in Infinite Dimensional Spaces using Structured Modulations
• Phaseless Sampling and Reconstruction of Real-Valued Signals in Shift-Invariant Spaces
• Conjugate Phase Retrieval on ${\mathbb{C}}^M$ by real vectors
• Undersampled windowed exponentials and their applications
• The discrete sign problem: uniqueness, recovery algorithms and phase retrieval applications
• Conjugate Phase Retrieval in Paley-Wiener Space
• Compressive phase retrieval of sparse bandlimited signals
• Phase Retrieval for $L^2([-\pi ,\pi ])$ via the Provably Accurate and Noise Robust Numerical Inversion of Spectrogram Measurements
• Phaseless Reconstruction from Space-Time Samples