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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Bibliographic Details
Published inScientific reports Vol. 12; no. 1; p. 20194
Main Authors Bi, Chuan, Ou, M. Yvonne, Bouhrara, Mustapha, Spencer, Richard G.
Format Journal Article
LanguageEnglish
Published London Nature Publishing Group UK 23.11.2022
Nature Portfolio
Subjects
639/705/1041
639/705/1042
Algorithms
Brain - diagnostic imaging
Humanities and Social Sciences
Magnetic Resonance Imaging
Magnetic Resonance Spectroscopy
multidisciplinary
Science
Science (multidisciplinary)
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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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ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-022-22739-3