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Sampled Tikhonov Regularization for Large Linear Inverse Problems by Slagel, J. Tanner; Chung, Julianne; Chung, Matthias; Kozak, David; Tenorio, Luis is a scholarly article available to read on EtoBox.

What is Sampled Tikhonov Regularization for Large Linear Inverse Problems about?

In this paper, we investigate iterative methods that are based on sampling of the data for computing Tikhonov-regularized solutions. We focus on very large inverse problems where access to the entire data set is not possible all at once (e.g., for problems with streaming or massive datasets). Row-access methods provide an ideal framework for solving such problems, since they only require access to "blocks" of the data at any given time. However, when using these iterative sampling methods to solve inverse problems, the main challenges include a proper choice of the regularization parameter, appropriate sampling strategies, and a convergence analysis. To address these challenges, we first describe a family of sampled iterative methods that can incorporate data as they become available (e.g., randomly sampled). We consider two sampled iterative methods, where the iterates can be characterized as solutions to a sequence of approximate Tikhonov problems. The first method requires the regularization parameter to be fixed a priori and converges asymptotically to an unregularized solution for randomly sampled data. This is undesirable for inverse problems. Thus, we focus on the second met

Author

Slagel, J. Tanner; Chung, Julianne; Chung, Matthias; Kozak, David; Tenorio, Luis

Published

2018

Language

EN