# One-norm regularized inversion: learning from the Pareto curve

Title | One-norm regularized inversion: learning from the Pareto curve |

Publication Type | Report |

Year of Publication | 2008 |

Authors | Gilles Hennenfent, Felix J. Herrmann |

Document Number | TR-EOAS-2008-5 |

Institution | UBC Earth and Ocean Sciences Department |

Keywords | 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. 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 performance of Fourier and curvelet reconstructions with sparsity promoting inversion. |

URL | https://slim.gatech.edu/Publications/Public/TechReport/2008/hennenfent08TRori/hennenfent08TRori.pdf |

Citation Key | hennenfent08TRori |