New insights into one-norm solvers from the Pareto curve

TitleNew insights into one-norm solvers from the {Pareto} curve
Publication TypeJournal Article
Year of Publication2008
AuthorsGilles Hennenfent, Ewout van den Berg, Michael P. Friedlander, Felix J. Herrmann
JournalGeophysics
Volume73
Number4
PageA23-A26
Month07
KeywordsAcquisition, Geophysics, Optimization, Pareto, Processing, SLIM
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.

URLhttps://slim.gatech.edu/Publications/Public/Journals/Geophysics/2008/hennenfent08GEOnii/hennenfent08GEOnii.pdf
DOI10.1190/1.2944169
Citation Keyhennenfent2008GEOPnii