Title | New insights into one-norm solvers from the Pareto curve |
Publication Type | Journal Article |
Year of Publication | 2008 |
Authors | Hennenfent G, van den Berg E, Friedlander MP, Herrmann FJ |
Journal | Geophysics |
Volume | 73 |
Pagination | A23-A26 |
Date Published | 07 |
Keywords | acquisition, 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. |
URL | https://www.slim.eos.ubc.ca/Publications/Public/Journals/Geophysics/2008/hennenfent08GEOnii/hennenfent08GEOnii.pdf |
DOI | 10.1190/1.2944169 |