Transport equation and tomography

zbMath1042.45009MaRDI QIDQ1412158

I. V. Prokhorov, D. S. Anikonov, Andrey E. Kovtanyuk

Publication date: 6 November 2003

Published in: Inverse and Ill-Posed Problems Series (Search for Journal in Brave)

zbMATH Keywords

textbooknumerical algorithmsuniqueness resultsLinear transport equationsrecovering unknown surfacestomography problemsuniqueness for inverse problemswell-posedness of direct problems

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) Biomedical imaging and signal processing (92C55) Transport processes in time-dependent statistical mechanics (82C70) Numerical methods for inverse problems for integral equations (65R32) Inverse problems for integral equations (45Q05) Research exposition (monographs, survey articles) pertaining to integral equations (45-02)

Related Items (27)

Using a derivative-free optimization method for multiple solutions of inverse transport problems ⋮ Solvability of a Two Dimensional Coefficient Inverse Problem for Transport Equation and a Numerical Method ⋮ Method of hyperplanes in the problem of identification of an unknown substance ⋮ Localization the discontinuity lines of bottom scattering coefficient according to acoustic sounding data ⋮ Estimation of the calculation accuracy in the problem of partial identification of a substance ⋮ On a problem of reconstruction of discontinuities of a function by its attenuated ray transform along geodesics ⋮ An underdetermined problem of integral geometry for the generalized radon transform ⋮ Unnamed Item ⋮ Method of singular value decomposition at the problem of determining the chemical composition of a medium ⋮ Modeling and simulation of Compton scatter image formation in positron emission tomography ⋮ Generalized stability estimates in inverse transport theory ⋮ Layerwise sensing in X-ray tomography in the polychromatic case ⋮ A method for studying singular integral equations ⋮ Formula for Solving a Mixed Problem for a Hyperbolic Equation ⋮ Numerical Reconstruction of Radiative Sources in an Absorbing and Nondiffusing Scattering Medium in Two Dimensions ⋮ The Cauchy problem for the non-stationary radiative transfer equation with Compton scattering ⋮ Recovery of coefficients in the linear Boltzmann equation ⋮ A Fourier approach to the inverse source problem in an absorbing and anisotropic scattering medium ⋮ An inverse problem for the linear Boltzmann equation with a time-dependent coefficient ⋮ Determination of Discontinuities of a Function in a Domain with Refraction from Its Attenuated Ray Transform ⋮ Determination of the attenuation coefficient for the nonstationary radiative transfer equation ⋮ An integrodifferential indicator for the problem of single beam tomography ⋮ Initial-boundary value problem for a radiative transfer equation with generalized matching conditions ⋮ The use of resonance effect in \(X\)-ray tomography ⋮ Unnamed Item ⋮ Initial boundary value problem for the radiative transfer equation with diffusion matching conditions ⋮ Recovery of the absorption coefficient in radiative transport from a single measurement

This page was built for publication: Transport equation and tomography