Kovtanyuk, A. E.; Mun, V. M.; Nazarov, V. G.; Prokhorov, I. V.; Yarovenko, I. P. \(X\)-ray and optical tomography problems. (Russian. English summary) Zbl 1299.65295 Sib. Èlektron. Mat. Izv. 5, 483-498 (2008). Summary: We address the problems of \(X\)-ray and optical tomography. We propose a method for the determination of the chemical composition of a substance which is based on the use of \(X\)-ray irradiation results. We prove the uniqueness of the solution for the problem of the attenuation coefficient determination for the vector transfer equation in the case of a special external radiation source. The problems of determination of the refraction indices and optical thicknesses for a layered medium are also studied. A computer verification of the proposed numerical algorithms is carried out. MSC: 65R10 Numerical methods for integral transforms 85A25 Radiative transfer in astronomy and astrophysics 65R32 Numerical methods for inverse problems for integral equations 92C55 Biomedical imaging and signal processing 78A40 Waves and radiation in optics and electromagnetic theory Keywords:radiation transfer theory; inverse problem; \(X\)-ray and optical tomography; radiation; refraction indices; optical thicknesses; layered medium; numerical algorithms PDFBibTeX XMLCite \textit{A. E. Kovtanyuk} et al., Sib. Èlektron. Mat. Izv. 5, 483--498 (2008; Zbl 1299.65295) Full Text: Link