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The statement and numerical solution of an optimization problem in X-ray tomography |
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| Authors: | D S Anikonov I V Prokhorov |
| Institution: | (1) Sobolev Institute of Mathematics, Siberian Division, Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090, Russia;(2) Institute of Applied Mathematics, Far East Division, Russian Academy of Sciences, ul. Radio 7, Vladivostok, 690041, Russia |
| Abstract: | A nonclassical problem is considered for the transport equation with coefficients depending on the energy of radiation. The task is to find the discontinuity surfaces for the coefficients of the equation from measurements of the radiation flux leaving the medium. For this tomography problem, an optimization problem is stated and numerically analyzed. The latter consists in determining the radiation energy that ensures the best reconstruction of the unknown medium. A simplified optimization problem is solved analytically. |
| Keywords: | radiation transfer equation tomography optimization problems |
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