Phaseless Signal Recovery in Infinite Dimensional Spaces Using Structured Modulations
- 229 Downloads
This paper considers the recovery of continuous signals in infinite dimensional spaces from the magnitude of their frequency samples. It proposes a sampling scheme which involves a combination of oversampling and modulations with complex exponentials. Sufficient conditions are given such that almost every signal with compact support can be reconstructed up to a unimodular constant using only its magnitude samples in the frequency domain. Finally it is shown that an average sampling rate of four times the Nyquist rate is enough to reconstruct almost every time-limited signal.
KeywordsBernstein spaces Interpolation Phase retrieval Sampling Signal reconstruction
Mathematics Subject ClassificationPrimary 30D10 94A20 Secondary 42C15 94A12
This work was partly supported by the German Research Foundation (DFG) under Grant PO 1347/2-1 and BO 1734/22-1.
- 5.Bodmann, B.G., Hammen, N.: Stable phase retrieval with low-redundancy frames. Adv. Comput. Math. (2014). doi: 10.1007/s10444-014-9359-y
- 14.Goodman, J.W.: Introduction to Fourier Optics. McGraw-Hill Comp, New York (1996)Google Scholar
- 15.Hayes, M.H., Lim, J.S., Oppenheim, A.V: Signal reconstruction from phase or magnitude. IEEE Trans. Acoust. Speech Signal Process. ASSP-28, 6, 672–680 (1980)Google Scholar
- 17.Jaming, P.: The phase retrieval problem for the radar ambiguity function and vice versa. IEEE International Radar Conference, May 2010Google Scholar
- 22.Lu, Y.M., Vetterli, M.: Sparse spectral factorization: unicity and reconstruction algorithms. Proceedings 36th International Conference on Acoustics, Speech, and Signal Processing (ICASSP), May 2011, pp. 5976–5979Google Scholar
- 28.Pohl, V., Yang, F., Boche, H.: Phase retrieval from low-rate samples. Sampl. Theory Signal Image Process. (2014). arXiv:1311.7045
- 29.Pohl, V., Yapar, C., Boche, H., Yang, F.: A phase retrieval method for signals in modulation-invariant spaces. Proceedings of 39th International Conference on Acoustics, Speech, and Signal Processing (ICASSP), May 2014Google Scholar
- 30.Rabiner, L., Juang, B.-H.: Fundamentals of Speech Recognition. Prentice Hall Inc, Englewood Cliffs (1993)Google Scholar
- 34.Vladimirov, V.S.: Equations of Mathematical Physics. Marcel Dekker Inc, New York (1971)Google Scholar
- 36.Yang, F., Pohl, V., Boche, H.: Phase retrieval via structured modulations in Paley–Wiener spaces. Proceedings of 10th International Conference on Sampling Theory and Applications (SampTA), July 2013.Google Scholar