@conference {esser2015EAGElcs,
	title = {A lifted $\ell_1/\ell_2$ constraint for sparse blind deconvolution},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2015},
	note = {(EAGE, Madrid)},
	month = {06},
	abstract = {We propose a modification to a sparsity constraint based on the ratio of $\ell_1$ and $\ell_2$ norms for solving blind seismic deconvolution problems in which the data consist of linear convolutions of different sparse reflectivities with the same source wavelet. We also extend the approach to the Estimation of Primaries by Sparse Inversion (EPSI) model, which includes surface related multiples. Minimizing the ratio of $\ell_1$ and $\ell_2$ norms has been previously shown to promote sparsity in a variety of applications including blind deconvolution. Most existing implementations are heuristic or require smoothing the $\ell_1/\ell_2$ penalty. Lifted versions of $\ell_1/\ell_2$ constraints have also been proposed but are challenging to implement. Inspired by the lifting approach, we propose to split the sparse signals 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 without smoothing the $\ell_1$ or $\ell_2$ norms. We show that a method of multipliers implementation of the resulting model can recover source wavelets that are not necessarily minimum phase and approximately reconstruct the sparse reflectivities. Numerical experiments demonstrate robustness to the initialization as well as to noise in the data.},
	keywords = {blind deconvolution, EAGE, EPSI},
	doi = {10.3997/2214-4609.201413420},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/esser2015EAGElcs/esser2015EAGElcs.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/esser2015EAGElcs/esser2015EAGElcs_poster.pdf},
	author = {Ernie Esser and Tim T.Y. Lin and Rongrong Wang and Felix J. Herrmann}
}
@conference {esser2015CAMSAPrsa,
	title = {Resolving scaling ambiguities with the $\ell_1/\ell_2$ norm in a blind deconvolution problem with feedback},
	booktitle = {IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing},
	year = {2015},
	note = {(IEEE CAMSAP Workshop, Canc{\'u}n, Mexico)},
	month = {12},
	pages = {365-368},
	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.},
	keywords = {$\ell_1/\ell_2$, blind deconvolution, CAMSAP, lifting, method of multipliers},
	doi = {10.1109/CAMSAP.2015.7383812},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/CAMSAP/2015/esser2015CAMSAPrsa/esser2015CAMSAPrsa.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/CAMSAP/2015/esser2015CAMSAPrsa/esser2015CAMSAPrsa_poster.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/CAMSAP/2015/esser2015CAMSAPrsa/esser2015CAMSAPrsa_ext.pdf},
	author = {Ernie Esser and Rongrong Wang and Tim T.Y. Lin and Felix J. Herrmann}
}
@conference {esser2014EAGEacp,
	title = {Application of a convex phase retrieval method to blind seismic deconvolution},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2014},
	month = {06},
	abstract = {A classical strategy for blind seismic deconvolution is to first estimate the autocorrelation of the unknown source wavelet from the data and then recover the wavelet by assuming it has minimum phase. However, computing the minimum phase wavelet directly from the amplitude spectrum can be sensitive to even extremely small errors, especially in the coefficients close to zero. Since the minimum phase requirement follows from an assumption that the wavelet should be as impulsive as possible, we propose to directly estimate an impulsive wavelet by minimizing a weighted l2 penalty subject to a constraint on its amplitude spectrum. This nonconvex model has the form of a phase retrieval problem, in this case recovering a signal given only estimates of the magnitudes of its Fourier coefficients. Following recent work on convex relaxations of phase retrieval problems, we propose a convex semidefinite program for computing an impulsive minimum phase wavelet whose amplitude spectrum is close to a given estimate, and we show that this can be robustly solved by a Douglas Rachford splitting method for convex optimization.},
	keywords = {blind deconvolution, convex phase retrieval, EAGE, source wavelet estimation},
	doi = {10.3997/2214-4609.20141590},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/esser2014EAGEacp/esser2014EAGEacp.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/esser2014EAGEacp/esser2014EAGEacp_poster.pdf},
	author = {Ernie Esser and Felix J. Herrmann}
}
