@article {lin2013GEOPrepsi,
	title = {Robust estimation of primaries by sparse inversion via one-norm minimization},
	journal = {Geophysics},
	volume = {78},
	number = {3},
	year = {2013},
	month = {05},
	pages = {R133-R150},
	abstract = {A recently proposed method called estimation of primaries by sparse inversion (EPSI) avoids the need for adaptive subtraction of approximate multiple predictions by directly inverting for the multiple-free subsurface impulse response as a collection of band-limited spikes. Although it can be shown that the correct primary impulse response is obtained through the sparsest possible solution, the original EPSI algorithm was not designed to take advantage of this result, and instead it relies on a multitude of inversion parameters, such as the level of sparsity per gradient update. We proposed and tested a new algorithm, named robust EPSI, in which we make obtaining the sparsest solution an explicit goal. Our approach remains a gradient-based approach like the original algorithm, but it is derived from a new biconvex optimization framework based on an extended basis-pursuit denoising formulation. Furthermore, because it is based on a general framework, robust EPSI can recover the impulse response in transform domains, such as sparsifying curvelet-based representations, without changing the underlying algorithm. We discovered that the sparsity-minimizing objective of our formulation enabled it to operate successfully on a variety of synthetic and field marine data sets without excessive tweaking of inversion parameters. We also found that recovering the solution in alternate sparsity domains can significantly improve the quality of the directly estimated primaries, especially for weaker late-arrival events. In addition, we found that robust EPSI produces a more artifact-free impulse response compared to the original algorithm.},
	keywords = {algorithm, biconvex, EPSI, multiples, Optimization, Pareto, sparsity, waveform inversion},
	doi = {10.1190/geo2012-0097.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2013/lin2013GEOPrepsi/lin2013GEOPrepsi.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
@article {hennenfent2008GEOPnii,
	title = {New insights into one-norm solvers from the Pareto curve},
	journal = {Geophysics},
	volume = {73},
	number = {4},
	year = {2008},
	month = {07},
	pages = {A23-A26},
	abstract = {Geophysical inverse problems typically involve a trade off between data misfit and some prior. Pareto curves trace the optimal trade off between these two competing aims. These curves are commonly used in problems with two-norm priors where they are plotted on a log-log scale and are known as L-curves. For other priors, such as the sparsity-promoting one norm, Pareto curves remain relatively unexplored. We show how these curves lead to new insights in one-norm regularization. First, we confirm the theoretical properties of smoothness and convexity of these curves from a stylized and a geophysical example. Second, we exploit these crucial properties to approximate the Pareto curve for a large-scale problem. Third, we show how Pareto curves provide an objective criterion to gauge how different one-norm solvers advance towards the solution.},
	keywords = {Acquisition, Geophysics, Optimization, Pareto, Processing, SLIM},
	doi = {10.1190/1.2944169},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2008/hennenfent08GEOnii/hennenfent08GEOnii.pdf},
	author = {Gilles Hennenfent and Ewout van den Berg and Michael P. Friedlander and Felix J. Herrmann}
}
