# On non-uniqueness of the Student's t-formulation for linear inverse problems

Title | On non-uniqueness of the Student's t-formulation for linear inverse problems |

Publication Type | Conference |

Year of Publication | 2012 |

Authors | Aleksandr Y. Aravkin, Tristan van Leeuwen, Kenneth Bube, Felix J. Herrmann |

Conference Name | SEG Technical Program Expanded Abstracts |

Month | 11 |

Publisher | SEG |

Keywords | non-convex, robust, SEG, Student's t, uniqueness |

Abstract | We review the statistical interpretation of inverse problem formulations, and the motivations for selecting non-convex penalties for robust behaviour with respect to measurement outliers or artifacts in the data. An important downside of using non-convex formulations such as the Student's t is the potential for non-uniqueness, and we present a simple example where the Student's t penalty can be made to have many local minima by appropriately selecting the degrees of freedom parameter. On the other hand, the non-convexity of the Student's t is precisely what gives it the ability to ignore artifacts in the data. We explain this idea, and present a stylized imaging experiment, where the Student's t is able to recover a velocity perturbation from data contaminated by a very peculiar artifact –- data from a different velocity perturbation. The performance of Student's t inversion is investigated empirically for different values of the degrees of freedom parameter, and different initial conditions. |

URL | https://slim.gatech.edu/Publications/Public/Conferences/SEG/2012/aravkin2012SEGST/aravkin2012SEGST.pdf |

DOI | 10.1190/segam2012-1558.1 |

Citation Key | aravkin2012SEGST |