An inverse source problem for linearly anisotropic radiative sources in absorbing and scattering medium

References

• Cercignani C. The boltzmann equation and its applications. Berlin: Springer-Verlag; 1988.
   Google Scholar
• Chandrasekhar S. Radiative transfer. New York: Dover Publ; 1960.
   Google Scholar
• Anikonov DS, Kovtanyuk AE, Prokhorov IV. Transport equation and tomography. Brill Academics; 2002. (Inverse and Ill-Posed Problems Series; 30).
   Google Scholar
• Choulli M, Stefanov P. An inverse boundary value problem for the stationary transport equation. Osaka J Math. 1999;36:87–104. https://projecteuclid.org/journals/osaka-journal-of-mathematics/volume-36/issue-1/An-inverse-boundary-value-problem-for-the-stationary-transport-equation/ojm/1200788449.pdf
   Web of Science ®Google Scholar
• Dautray R, Lions J-L. Mathematical analysis and numerical methods for science and technology. Vol. 4. Berlin: Springer-Verlag; 1990.
   Google Scholar
• Mokhtar-Kharroubi M. Mathematical topics in neutron transport theory. Singapore: World Scientific; 1997.
   Google Scholar
• Stefanov P, Uhlmann G. An inverse source problem in optical molecular imaging. Anal PDE. 2008;1(1):115–126. doi: 10.2140/apde
   Web of Science ®Google Scholar
• Fujiwara H, Sadiq K, Tamasan A. A two dimensional source reconstruction method in radiative transport using boundary data measured on an arc. Inverse Probl. 2021;37:115005. doi: 10.1088/1361-6420/ac2d75
   Web of Science ®Google Scholar
• Egger H, Schlottbom M. An Lp theory for stationary radiative transfer. Appl Anal. 2014;93(6):1283–1296. doi: 10.1080/00036811.2013.826798
   Web of Science ®Google Scholar
• Klibanov MV, Li J, Nguyen LH, et al. Convexification numerical method for a coefficient inverse problem for the radiative transport equation. SIAM J Img Sci Comput. 2023;16:35–63. doi: 10.1137/22M1509837
   Web of Science ®Google Scholar
• Smirnov AV, Klibanov MV, Nguyen LH. On an inverse source problem for the full radiative transfer equation with incomplete data. SIAM J Sci Comput. 2019;41(5):B929–B952. doi: 10.1137/19M1253605
   Web of Science ®Google Scholar
• Bal G, Tamasan A. Inverse source problems in transport equations. SIAM J Math Anal. 2007;39:57–76. doi: 10.1137/050647177
   Web of Science ®Google Scholar
• Sharafutdinov VA. Integral geometry of tensor fields. Utrecht: VSP; 1994.
   Google Scholar
• Tamasan A. Tomographic reconstruction of vector fields in variable background media. Inverse Probl. 2007;23:2197–2205. doi: 10.1088/0266-5611/23/5/022
   Web of Science ®Google Scholar
• Fujiwara H, Sadiq K, Tamasan A. A Fourier approach to the inverse source problem in an absorbing and anisotropic scattering medium. Inverse Probl. 2019;36(1):015005. doi: 10.1088/1361-6420/ab4d98
   Web of Science ®Google Scholar
• Monard F, Bal G. Inverse source problems in transport via attenuated tensor tomography, arXiv:1908.06508v1.
   Google Scholar
• Bukhgeim AL. Inversion formulas in inverse problems, chapter in linear operators and Ill-posed problems by Lavrentiev MM, and Savalev LY. New York: Plenum; 1995.
   Google Scholar
• Natterer F. The mathematics of computerized tomography. New York: Wiley; 1986.
   Google Scholar
• Natterer F, Wübbeling F. Mathematical methods in image reconstruction. SIAM monographs on mathematical modeling and computation. Philadelphia, PA: SIAM; 2001.
   Google Scholar
• Sparr G, Stråhlén K, Lindström K, et al. Doppler tomography for vector fields. Inverse Probl. 1995;11:1051–1061. doi: 10.1088/0266-5611/11/5/009
   Web of Science ®Google Scholar
• Han W, Eichholz JA, Huang J. RTE-based bioluminescence tomography: a theoretical study. Inverse Probl Sci Eng. 2011;19(4):435–459. doi: 10.1080/17415977.2010.500383
   Web of Science ®Google Scholar
• Klose AD, Ntziachristos V, Hielscher AH. The inverse source problem based on the radiative transfer equation in optical molecular imaging. J Comput Phys. 2005;202:323–345. doi: 10.1016/j.jcp.2004.07.008
   Web of Science ®Google Scholar
• Yi HC, Sanchez R, McCormick NJ. Bioluminescence estimation from ocean in situ irradiances. Appl Opt. 1992;31:822–830. doi: 10.1364/AO.31.000822
   PubMed Web of Science ®Google Scholar
• Arbuzov EV, Bukhgeim AL, Kazantsev SG. Two-dimensional tomography problems and the theory of A-analytic functions. Siberian Adv Math. 1998;8:1–20.
   Google Scholar
• Finch DV. The attenuated x-ray transform: recent developments, In: Inside out: inverse problems and applications, Math. Sci. Res. Inst. Publ., 47, Cambridge: Cambridge Univ. Press; 2003. p. 47–66.
   Google Scholar
• Sadiq K, Tamasan A. On the range of the attenuated radon transform in strictly convex sets. Trans Amer Math Soc. 2015;367(8):5375–5398. doi: 10.1090/tran/2015-367-08
   Web of Science ®Google Scholar
• Sadiq K, Scherzer O, Tamasan A. On the X-ray transform of planar symmetric 2-tensors. J Math Anal Appl. 2016;442(1):31–49. doi: 10.1016/j.jmaa.2016.04.018
   Web of Science ®Google Scholar
• Muskhelishvili NI. Singular integral equations. New York: Dover; 2008.
   Google Scholar
• Sadiq K, Tamasan A. On the range characterization of the two dimensional attenuated Doppler transform. SIAM J Math Anal. 2015;47(3):2001–2021. doi: 10.1137/140984282
   Web of Science ®Google Scholar
• Adam R. Sobolev spaces. New York: Academic Press; 1975.
   Google Scholar