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Stable Blind Deconvolution over the Reals from Additional Autocorrelations

Walk, Philipp and Hassibi, Babak (2017) Stable Blind Deconvolution over the Reals from Additional Autocorrelations. . (Unpublished)

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Recently the one-dimensional time-discrete blind deconvolution problem was shown to be solvable uniquely, up to a global phase, by a semi-definite program for almost any signal, provided its autocorrelation is known. We will show in this work that under a sufficient zero separation of the corresponding signal in the z−domain, a stable reconstruction against additive noise is possible. Moreover, the stability constant depends on the signal dimension and on the signals magnitude of the first and last coefficients. We give an analytical expression for this constant by using spectral bounds of Vandermonde matrices.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Walk, Philipp0000-0002-8476-3464
Additional Information:The authors would like to thank Ahmed Douik, Richard Kueng and Peter Jung for many helpful discussions. The work of Philipp Walk was supported by the German Research Foundation (DFG) under the grant WA 3390/1 and the one of Babak Hassibi was supported in part by the National Science Foundation under grants CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by a grant from Qualcomm Inc., by NASA’s Jet Propulsion Laboratory through the President and Director’s Fund, by King Abdulaziz University, and by King Abdullah University of Science and Technology.
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)WA 3390/1
JPL President and Director's FundUNSPECIFIED
King Abdulaziz UniversityUNSPECIFIED
King Abdullah University of Science and Technology (KAUST)UNSPECIFIED
Record Number:CaltechAUTHORS:20190402-102240889
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:94360
Deposited By: Tony Diaz
Deposited On:02 Apr 2019 17:25
Last Modified:09 Mar 2020 13:19

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