Geodesic
The statement and numerical solution of an optimization problem in X-ray tomography
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 1, pp. 18-25

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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. 
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D. S. Anikonov; I. V. Prokhorov. The statement and numerical solution of an optimization problem in X-ray tomography. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 1, pp. 18-25. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_1_a3/