Span of regularization for solution of inverse problems with application to magnetic resonance relaxometry of the brain
We present a new regularization method for the solution of the Fredholm integral equation (FIE) of the first kind, in which we incorporate solutions corresponding to a range of Tikhonov regularizers into the end result. This method identifies solutions within a much larger function space, spanned by...
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Published in | Scientific reports Vol. 12; no. 1; p. 20194 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
London
Nature Publishing Group UK
23.11.2022
Nature Portfolio |
Subjects | |
Online Access | Get full text |
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Summary: | We present a new regularization method for the solution of the Fredholm integral equation (FIE) of the first kind, in which we incorporate solutions corresponding to a range of Tikhonov regularizers into the end result. This method identifies solutions within a much larger function space, spanned by this set of regularized solutions, than is available to conventional regularization methods. An additional key development is the use of dictionary functions derived from noise-corrupted inversion of the discretized FIE. In effect, we combine the stability of solutions with greater degrees of regularization with the resolution of those that are less regularized. The span of regularizations (SpanReg) method may be widely applicable throughout the field of inverse problems. |
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Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
ISSN: | 2045-2322 2045-2322 |
DOI: | 10.1038/s41598-022-22739-3 |