Resolving scaling ambiguities with the $\ell_1/\ell_2$ norm in a blind deconvolution problem with feedback

TitleResolving scaling ambiguities with the $\ell_1/\ell_2$ norm in a blind deconvolution problem with feedback
Publication TypeConference
Year of Publication2015
AuthorsErnie Esser, Rongrong Wang, Tim T.Y. Lin, Felix J. Herrmann
Conference NameIEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing
Page365-368
Month12
Keywords$\ell_1/\ell_2$, blind deconvolution, CAMSAP, lifting, method of multipliers
Abstract

Compared to more mundane blind deconvolution problems, blind deconvolution in seismic applications involves a feedback mechanism related to the free surface. The presence of this feedback mechanism gives us an unique opportunity to remove ambiguities that have plagued blind deconvolution for a long time. While beneficial, this feedback by itself is insufficient to remove the ambiguities even with $\ell_1$ constraints. However, when paired with an $\ell_1/\ell_2$ constraint the feedback allows us to resolve the scaling ambiguity under relatively mild assumptions. Inspired by lifting approaches, we propose to split the sparse signal into positive and negative components and apply an $\ell_1/\ell_2$ constraint to the difference, thereby obtaining a constraint that is easy to implement. Numerical experiments demonstrate robustness to the initialization as well as to noise in the data.

Notes

(IEEE CAMSAP Workshop, Cancún, Mexico)

URLhttps://www.slim.eos.ubc.ca/Publications/Public/Conferences/CAMSAP/2015/esser2015CAMSAPrsa/esser2015CAMSAPrsa.pdf
DOI10.1109/CAMSAP.2015.7383812
Presentation

https://www.slim.eos.ubc.ca/Publications/Public/Conferences/CAMSAP/2015/...

URL1

https://www.slim.eos.ubc.ca/Publications/Public/Conferences/CAMSAP/2015/...

Citation Keyesser2015CAMSAPrsa