The article addresses the following problem: reconstruct domain boundaries from knowledge of a trace of photon density. The solution relies on the integro-differential transport equation (of Boltzmann type) derived and studied in the book by D. S. Anikonov, A. E. Kovtanyuk and I. V. Prokhorov [Transport equation and tomography, Inverse Ill-posed Probl. Ser., VSP, Utrecht, 2002; MR2010670]
Crosta, G. (2016). Mathematical Review MR3379234 Anikonov, D. S.; Nazarov, V. G.; Prokhorov, I. V. An integro-differential indicator for a problem in single-beam tomography. (Russian) Sib. Zh. Ind. Mat. 17 (2014), no. 2, 3--10; translation in J. Appl. Ind. Math. 8 (2014), no. 3, 301–306 (Reviewer: Giovanni Franco Crosta) 94A08 (35Q20 35R09 35R30) [Altro].
Mathematical Review MR3379234 Anikonov, D. S.; Nazarov, V. G.; Prokhorov, I. V. An integro-differential indicator for a problem in single-beam tomography. (Russian) Sib. Zh. Ind. Mat. 17 (2014), no. 2, 3--10; translation in J. Appl. Ind. Math. 8 (2014), no. 3, 301–306 (Reviewer: Giovanni Franco Crosta) 94A08 (35Q20 35R09 35R30)
Crosta, GF
2016
Abstract
The article addresses the following problem: reconstruct domain boundaries from knowledge of a trace of photon density. The solution relies on the integro-differential transport equation (of Boltzmann type) derived and studied in the book by D. S. Anikonov, A. E. Kovtanyuk and I. V. Prokhorov [Transport equation and tomography, Inverse Ill-posed Probl. Ser., VSP, Utrecht, 2002; MR2010670]
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