FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2149171671> ?p ?o ?g. }

• W2149171671 endingPage "1605" @default.
• W2149171671 startingPage "1578" @default.
• W2149171671 abstract "The imaging problem of elastography is an inverse problem. The nature of an inverse problem is that it is ill-conditioned. We consider properties of the mathematical map which describes how the elastic properties of the tissue being reconstructed vary with the field measured by magnetic resonance imaging (MRI). This map is a nonlinear mapping, and our interest is in proving certain conditioning and regularity results for this operator which occurs implicitly in this problem of imaging in elastography. In this treatment we consider the tissue to be linearly elastic, isotropic, and spatially heterogeneous. We determine the conditioning of this problem of function reconstruction, in particular for the stiffness function. We further examine the conditioning when determining both stiffness and density. We examine the Fréchet derivative of the nonlinear mapping, which enables us to describe the properties of how the field affects the individual maps to the stiffness and density functions. We illustrate how use of the implicit function theorem can considerably simplify the analysis of Fréchet differentiability and regularity properties of this underlying operator. We present new results which show that the stiffness map is mildly ill-posed, whereas the density map suffers from medium ill-conditioning. Computational work has been done previously to study the sensitivity of these maps, but our work here is analytical. The validity of the Newton–Kantorovich and optimization methods for the computational solution of this inverse problem is directly linked to the Fréchet differentiability of the appropriate nonlinear operator, which we justify." @default.
• W2149171671 created "2016-06-24" @default.
• W2149171671 creator A5003906979 @default.
• W2149171671 creator A5067257016 @default.
• W2149171671 creator A5086469747 @default.
• W2149171671 date "2011-01-01" @default.
• W2149171671 modified "2023-09-26" @default.
• W2149171671 title "On an Inverse Problem from Magnetic Resonance Elastic Imaging" @default.
• W2149171671 cites W1574943236 @default.
• W2149171671 cites W1600485280 @default.
• W2149171671 cites W1963847255 @default.
• W2149171671 cites W1968148995 @default.
• W2149171671 cites W1969583173 @default.
• W2149171671 cites W1973174656 @default.
• W2149171671 cites W1979287287 @default.
• W2149171671 cites W1980034166 @default.
• W2149171671 cites W1980124656 @default.
• W2149171671 cites W1981131286 @default.
• W2149171671 cites W2007752234 @default.
• W2149171671 cites W2008633227 @default.
• W2149171671 cites W2020596016 @default.
• W2149171671 cites W2022237755 @default.
• W2149171671 cites W2026786928 @default.
• W2149171671 cites W2031795410 @default.
• W2149171671 cites W2034712897 @default.
• W2149171671 cites W2036291324 @default.
• W2149171671 cites W2037550710 @default.
• W2149171671 cites W2038345553 @default.
• W2149171671 cites W2048686704 @default.
• W2149171671 cites W2053619386 @default.
• W2149171671 cites W2056554708 @default.
• W2149171671 cites W2057557783 @default.
• W2149171671 cites W2060819023 @default.
• W2149171671 cites W2061510103 @default.
• W2149171671 cites W2069854011 @default.
• W2149171671 cites W2072338864 @default.
• W2149171671 cites W2076970569 @default.
• W2149171671 cites W2081090472 @default.
• W2149171671 cites W2083039650 @default.
• W2149171671 cites W2083610112 @default.
• W2149171671 cites W2083789485 @default.
• W2149171671 cites W2084022716 @default.
• W2149171671 cites W2091027394 @default.
• W2149171671 cites W2091106302 @default.
• W2149171671 cites W2092835007 @default.
• W2149171671 cites W2094979113 @default.
• W2149171671 cites W2107649622 @default.
• W2149171671 cites W2115115308 @default.
• W2149171671 cites W2116302790 @default.
• W2149171671 cites W2119785679 @default.
• W2149171671 cites W2123397541 @default.
• W2149171671 cites W2124986897 @default.
• W2149171671 cites W2133836163 @default.
• W2149171671 cites W2144719117 @default.
• W2149171671 cites W2152072871 @default.
• W2149171671 cites W2153683847 @default.
• W2149171671 cites W2318845040 @default.
• W2149171671 cites W2482439325 @default.
• W2149171671 cites W284076903 @default.
• W2149171671 cites W567453437 @default.
• W2149171671 cites W638618906 @default.
• W2149171671 doi "https://doi.org/10.1137/110832082" @default.
• W2149171671 hasPublicationYear "2011" @default.
• W2149171671 type Work @default.
• W2149171671 sameAs 2149171671 @default.
• W2149171671 citedByCount "9" @default.
• W2149171671 countsByYear W21491716712014 @default.
• W2149171671 countsByYear W21491716712015 @default.
• W2149171671 countsByYear W21491716712016 @default.
• W2149171671 countsByYear W21491716712017 @default.
• W2149171671 countsByYear W21491716712023 @default.
• W2149171671 crossrefType "journal-article" @default.
• W2149171671 hasAuthorship W2149171671A5003906979 @default.
• W2149171671 hasAuthorship W2149171671A5067257016 @default.
• W2149171671 hasAuthorship W2149171671A5086469747 @default.
• W2149171671 hasBestOaLocation W21491716712 @default.
• W2149171671 hasConcept C104317684 @default.
• W2149171671 hasConcept C118335899 @default.
• W2149171671 hasConcept C121332964 @default.
• W2149171671 hasConcept C132954091 @default.
• W2149171671 hasConcept C134306372 @default.
• W2149171671 hasConcept C135252773 @default.
• W2149171671 hasConcept C14036430 @default.
• W2149171671 hasConcept C143753070 @default.
• W2149171671 hasConcept C158448853 @default.
• W2149171671 hasConcept C158622935 @default.
• W2149171671 hasConcept C17020691 @default.
• W2149171671 hasConcept C184050105 @default.
• W2149171671 hasConcept C185592680 @default.
• W2149171671 hasConcept C202615002 @default.
• W2149171671 hasConcept C24890656 @default.
• W2149171671 hasConcept C2777690781 @default.
• W2149171671 hasConcept C2779124084 @default.
• W2149171671 hasConcept C28826006 @default.
• W2149171671 hasConcept C33923547 @default.
• W2149171671 hasConcept C55493867 @default.
• W2149171671 hasConcept C62520636 @default.
• W2149171671 hasConcept C78458016 @default.

• next