@conference {aravkin2012SEGST,
title = {On non-uniqueness of the {Student{\textquoteright}s} t-formulation for linear inverse problems},
booktitle = {SEG Technical Program Expanded Abstracts},
volume = {31},
year = {2012},
month = {11},
pages = {1-5},
publisher = {SEG},
organization = {SEG},
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{\textquoteright}s t is the potential for non-uniqueness, and we present a simple example where the Student{\textquoteright}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{\textquoteright}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{\textquoteright}s t is able to recover a velocity perturbation from data contaminated by a very peculiar artifact {\textendash}- data from a different velocity perturbation. The performance of Student{\textquoteright}s t inversion is investigated empirically for different values of the degrees of freedom parameter, and different initial conditions.},
keywords = {non-convex, robust, SEG, student{\textquoteright}s t, uniqueness},
doi = {10.1190/segam2012-1558.1},
url = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/SEG/2012/aravkin2012SEGST/aravkin2012SEGST.pdf},
author = {Aleksandr Y. Aravkin and Tristan van Leeuwen and Kenneth Bube and Felix J. Herrmann}
}