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
KeywordsAcquisition, Geophysics, Optimization, Pareto, Processing, SLIM

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.

Citation Keyhennenfent2008GEOPnii