Sparse Phase Retrieval of One-Dimensional Signals by Prony's Method

@article{Beinert2017SparsePR,
  title={Sparse Phase Retrieval of One-Dimensional Signals by Prony's Method},
  author={Robert Beinert and Gerlind Plonka-Hoch},
  journal={CoRR},
  year={2017},
  volume={abs/1701.08947}
}
In this paper, we show that sparse signals f representable as a linear combination of a finite number N of spikes at arbitrary real locations or as a finite linear combination of B-splines of order m with arbitrary real knots can be almost surely recovered from O(N2) intensity measurements ∣F [f ] (ω) ∣∣2 up to trivial ambiguities. The constructive proof consists of two steps, where in the first step Prony’s method is applied to recover all parameters of the autocorrelation function and in the… CONTINUE READING
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