Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published April 2, 2019 | Submitted
Report Open

Stable Blind Deconvolution over the Reals from Additional Autocorrelations

Abstract

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.

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.

Attached Files

Submitted - 1710.07879.pdf

Files

1710.07879.pdf
Files (534.1 kB)
Name Size Download all
md5:7b6e8a564ba66387d345c2c5a81807e7
534.1 kB Preview Download

Additional details

Created:
August 19, 2023
Modified:
March 5, 2024