Abstract
This paper surveys animportant class of methods that combine iterative projection methods and variational regularization methods for large-scale inverse problems. Iterative methods such as Krylov subspace methods are invaluable in the numerical linear algebra community and have proved important in solving inverse problems due to their inherent regularizing properties and their ability to handle large-scale problems. Variational regularization describes abroad and important class of methods that are used to obtain reliable solutions to inverse problems, whereby one solves a modified problem that incorporates prior knowledge. Hybrid projection methods combine iterative projection methods with variational regularization techniques in a synergistic way, providing
researchers with a powerful computational framework for solving very large inverse problems. Although the idea of a hybrid Krylov method for linear inverse problems goes back to the 1980s, several recent advances on new regularization frameworks and methodologies have made this field ripe for extensions, further analyses, and new applications. In this paper, we provide a practical and accessible introduction to hybrid projection methods in the context of solving large (linear) inverse problems.
researchers with a powerful computational framework for solving very large inverse problems. Although the idea of a hybrid Krylov method for linear inverse problems goes back to the 1980s, several recent advances on new regularization frameworks and methodologies have made this field ripe for extensions, further analyses, and new applications. In this paper, we provide a practical and accessible introduction to hybrid projection methods in the context of solving large (linear) inverse problems.
Original language | English |
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Pages (from-to) | 205-284 |
Number of pages | 80 |
Journal | Siam Review |
Volume | 66 |
Issue number | 2 |
Early online date | 9 May 2024 |
DOIs | |
Publication status | Published - 31 May 2024 |
Funding
The work of the first author was partially supported by the National Science Foundation (NFS) under grants DMS-1654175 and DMS-1723005. The work of the second author was partially supported by the Engineering and Physical Sciences Research Council (EPSRC) under grant EP/T001593/1.
Funders | Funder number |
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National Science Foundation | |
Nebraska Forest Service | DMS-1723005, DMS-1654175 |
Engineering and Physical Sciences Research Council | EP/T001593/1 |
Keywords
- Krylov methods
- Tikhonov regularization
- computed tomography
- image deconvolution
- inverse problems
- projection methods
- regularization
- variational regularization
ASJC Scopus subject areas
- Theoretical Computer Science
- Computational Mathematics
- Applied Mathematics