One-norm regularized inversion: learning from the Pareto curve

TitleOne-norm regularized inversion: learning from the {Pareto} curve
Publication TypeConference
Year of Publication2008
AuthorsGilles Hennenfent, Felix J. Herrmann
Conference NameSEG Technical Program Expanded Abstracts
OrganizationSEG
KeywordsSEG
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. First, we show how these curves provide an objective criterion to gauge how robust one-norm solvers are when they are limited by a maximum number of matrix-vector products that they can perform. Second, we use Pareto curves and their properties to define and compute one-norm compressibilities. We argue this notion is key to understand one-norm regularized inversion. Third, we illustrate the correlation between the one-norm compressibility and the perfor- mance of Fourier and curvelet reconstructions with sparsity promoting inversion.

URLhttps://www.slim.eos.ubc.ca/Publications/Public/Conferences/SEG/2008/hennenfent08SEGonri/hennenfent08SEGonri.pdf
Citation Keyhennenfent2008SEGonri