Frame decompositions of bounded linear operators in Hilbert spaces with applications in tomography
Open Access
- 12 February 2021
- journal article
- research article
- Published by IOP Publishing in Inverse Problems
- Vol. 37 (5), 055001
- https://doi.org/10.1088/1361-6420/abe5b8
Abstract
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and ill-posedness of the problem and can be used as the basis for the design and implementation of efficient numerical solution methods. In contrast to the singular-value decomposition, the presented frame decompositions can be derived explicitly for a wide class of operators, in particular for those satisfying a certain stability condition. In order to show the usefulness of this approach, we consider different examples from the field of tomography.Keywords
Funding Information
- Austrian Science Fund (F6805-N36)
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