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dc.contributor.authorIsakov, Victor
dc.identifier.citationIsakov V. (2017) Chapter 7. Integral Geometry and Tomography. In: Inverse Problems for Partial Differential Equations. Applied Mathematical Sciences, vol 127. Springer, Cham, pp.241-268.en_US
dc.descriptionClick on the DOI link to access the article (may not be free).en_US
dc.description.abstractThe problems of integral geometry are to determine a function given (weighted) integrals of this function over a “rich” family of manifolds. These problems are of importance in medical applications (tomography), and they are quite useful for dealing with inverse problems in hyperbolic differential equations (integrals of unknown coefficients over ellipsoids or lines can be obtained from the first terms of the asymptotic expansion of rapidly oscillating solutions and an information about first-arrival times of a wave). There has been significant progress in the classical Radon problem when manifolds are hyperplanes and the weight function is the unity; there are interesting results in the plane case when a family of curves is regular (resembling locally the family of straight lines) or in case of the family of straight lines with an arbitrary regular attenuation. Still there are many interesting open questions about the problem with local data and simultaneous recovery of density of a source and of attenuation. We give a brief review of this area, referring for more information to the books of Natterer [Nat] and Sharafutdinov [Sh].en_US
dc.relation.ispartofseriesApplied Mathematical Sciences;v.127
dc.titleIntegral Geometry and Tomographyen_US
dc.typeBook chapteren_US
dc.rights.holder© Springer International Publishing AG 2017en_US

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