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\(X\)-ray and optical tomography problems. (Russian. English summary) Zbl 1299.65295

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
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