{"database":"biostudies-literature","file_versions":[],"scores":null,"additional":{"omics_type":["Unknown"],"volume":["12(1)"],"submitter":["Bi C"],"funding":["This work was supported by the Intramural Research Program of the National Institute on Aging of the National Institutes of Health."],"pubmed_abstract":["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."],"journal":["Scientific reports"],"pagination":["20194"],"full_dataset_link":["https://www.ebi.ac.uk/biostudies/studies/S-EPMC9684479"],"repository":["biostudies-literature"],"pubmed_title":["Span of regularization for solution of inverse problems with application to magnetic resonance relaxometry of the brain."],"pmcid":["PMC9684479"],"pubmed_authors":["Bi C","Ou MY","Bouhrara M","Spencer RG"],"additional_accession":[]},"is_claimable":false,"name":"Span of regularization for solution of inverse problems with application to magnetic resonance relaxometry of the brain.","description":"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.","dates":{"release":"2022-01-01T00:00:00Z","publication":"2022 Nov","modification":"2024-12-04T03:45:21.144Z","creation":"2024-12-04T03:45:21.144Z"},"accession":"S-EPMC9684479","cross_references":{"pubmed":["36418516"],"doi":["10.1038/s41598-022-22739-3"]}}