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Ambiguities on convolutions with applications to phase retrieval

Walk, Philipp and Jung, Peter and Pfander, Götz and Hassibi, Babak (2016) Ambiguities on convolutions with applications to phase retrieval. In: 50th Asilomar Conference on Signals, Systems and Computers. IEEE , Piscataway, NJ, pp. 1228-1234. ISBN 978-1-5386-3954-2.

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In this work we characterize all ambiguities of the convolution on two fixed finite-dimensional complex vector spaces. It will be shown that the convolution ambiguities correspond to factorization ambiguities in the z-domain, which are generated by swapping their zeros. We use this polynomial description to show a deterministic version of a recently introduced masked Fourier phase retrieval design. A semidefinite program can be used to recover exactly the noise-free input signals if they share no common factors. Then, we reformulate the problem as a deterministic blind deconvolution with knowledge of their autocorrelations. Moreover, numerically simulations show robustness against additive noise.

Item Type:Book Section
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Walk, Philipp0000-0002-8476-3464
Additional Information:© 2016 IEEE. We would like to thank Kishore Jaganathan, Fariborz Salehi and Michael Sandbichler for helpful discussions. This work was partially supported by the DFG grant JU 2795/3 and WA 3390/1. We also like to thank the Hausdorff Institute of Mathematics for providing for some of the authors resources at the Trimester program in spring 2016 on “Mathematics of Signal Processing” where part of the work have been prepared.
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)JU 2795/3
Deutsche Forschungsgemeinschaft (DFG)WA 3390/1
Record Number:CaltechAUTHORS:20170308-150241370
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Official Citation:P. Walk, P. Jung, G. Pfander and B. Hassibi, "Ambiguities on convolutions with applications to phase retrieval," 2016 50th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA, 2016, pp. 1228-1234. doi: 10.1109/ACSSC.2016.7869569
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:74928
Deposited By: Kristin Buxton
Deposited On:08 Mar 2017 23:09
Last Modified:15 Nov 2021 16:29

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