Published November 2016
| public
Book Section - Chapter
Ambiguities on convolutions with applications to phase retrieval
Chicago
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Abstract
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.
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.Additional details
- Eprint ID
- 74928
- DOI
- 10.1109/ACSSC.2016.7869569
- Resolver ID
- CaltechAUTHORS:20170308-150241370
- Deutsche Forschungsgemeinschaft (DFG)
- JU 2795/3
- Deutsche Forschungsgemeinschaft (DFG)
- WA 3390/1
- Created
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2017-03-08Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field