This article is cited in 3 papers

On phase correction in tomographic research

Ya. Wang^a, A. S. Leonov^b, D. V. Lukyanenko^c, V. D. Shinkarev^c, A. G. Yagola<sup>c

a</sup> Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, P. O. Box 9825, Beijing 100029, P. R. China
^b Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, P.O. Box 9825, Beijing 100029, P.R. China
^c National Research Nuclear University (MEPhI), Kashirskoye sh. 31, Moscow 115409, Russia

Abstract: Under consideration is the problem of improving the contrast of the image obtained by processing tomographic projections with phase distortion. The study is based on the well-known intensity transfer equation. Unlike other works, this equation is solved in a bounded region of variation of the tomographic parameters. In a domain, a boundary value problem is posed for the intensity transfer equation which is then specialized for a three-dimensional parallel tomographic scheme. The case of two-dimensional tomography is also considered, together with the corresponding boundary value problem for the intensity transfer equation. We propose numerical methods for solving the boundary value problems of phase correction. The results are given of the numerical experiments on correction of tomographic projections and reconstruction of the structure of the objects under study (in particular, a slice of a geological sample) by using piecewise uniform regularization.

Keywords: tomography, phase correction, intensity transfer, regularization, ill-posed problem. .

UDC: 519.632.4:519.642

Received: 01.06.2020
Revised: 10.08.2020
Accepted: 10.09.2020

DOI: 10.33048/SIBJIM.2020.23.402

 English version: Journal of Applied and Industrial Mathematics, 2020, 14:4, 802–810

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