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In this paper, we consider an infinite-dimensional phase retrieval problem to reconstruct real-valued signals living in a shift-invariant space from their phaseless samples taken either on the whole line or on a discrete set with finite sampling density. We characterize all phase retrievable signals in a real-valued shift-invariant space using their nonseparability. For nonseparable signals generated by some function with support length L, we show that they can be well approximated, up to a sign, from their noisy phaseless samples taken on a discrete set with sampling density 2L-1 . In this paper, we also propose an algorithm with linear computational complexity to reconstruct nonseparable signals in a shift-invariant space from their phaseless samples corrupted by bounded noises.more » « less
