Phaseless Signal Recovery in Infinite Dimensional Spaces using Structured Modulations

This paper considers the recovery of continuous signals in infinite dimensional spaces from the magnitude of its frequency samples. It proposes a sampling scheme which involves a combination of oversampling and specific structured modulations. This allows for almost every signal with finite support to be reconstructed from its magnitude samples in the frequency domain up to a unimodular constant. Sufficient conditions on the signal and the sampling system are given such that signal recovery is possible, and it is shown that an average sampling rate of four times the Nyquist rate is enough to reconstruct almost every time limited signal.