A Bayesian approach for neutral particles source estimation

References

• Gao H, Zhao H. Multilevel bioluminescence tomography based on radiative transfer equation part 1: l1 regularization. Opt Express. 2010;18(3):1854–1871.
   Google Scholar
• Dorn O. Scattering and absorption transport sensitivity functions for optical tomography. Opt Express. 2000;7(13):492–506.
   Google Scholar
• Kauati AT, Silva Neto AJ, Roberty NC. A source-detector methodology for the construction and solution of the one-dimensional inverse transport equation. Inverse Probl Eng. 2001;9(1):45–66.
   Google Scholar
• Haltmeier M, Neumann L, Rabanser S. Single-stage reconstruction algorithm for quantitative photoacoustic tomography. Inverse Probl. 2015;31(6):1–24.
   Google Scholar
• Asllanaj F, Addoum A, Roche JR. Fluorescence molecular imaging based on the adjoint radiative transport equation. Inverse Probl. 2018;34:1–28.
   Google Scholar
• Hykes JM, Azmy YY. Radiation source reconstruction with known geometry and materials using the adjoint. International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C); 2011 May 8–12; Rio de Janeiro, Brazil.
   Google Scholar
• Miller KA, Charlton WS. An inverse transport approach to radiation source location for border security. Proceedings of the 29th Annual Meeting of the European Safeguards Research and Development Association; 2007 May 22–24; Aix-en-Provence, France.
   Google Scholar
• Sugaya S, Endo T, Yamamoto A. Inverse estimation of unknown radioactive source using detection probability and adjoint calculation. International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C); 2017 Apr 16–20; Jeju, Korea.
   Google Scholar
• Siewert CE. An inverse source problem in radiative transfer. J Quant Spectrosc Radiat Transf. 1993;50(6):603–609.
   Google Scholar
• Siewert CE. A radiative-transfer inverse-source problem for a sphere. J Quant Spectrosc Radiat Transf. 1994;52(2):157–160.
   Google Scholar
• Tao Z, McCormick NJ, Sanchez R. Ocean source and optical property estimation from explicit and implicit algorithms. Appl Opt. 1994;33(15):3265–3275.
   Google Scholar
• Bledsoe KC, Favorite JA. Using the Levenberg-Marquardt method for the solution of inverse transport problems with scattering. Joint International Conference on Mathematics and Computation (M&C) and Supercomputing in Nuclear Applications (SNA); 2007 Apr 15–19; Monterey, California, USA.
   Google Scholar
• Curbelo JP, Barros RC. Application of the adjoint spectral Green's function–constant nodal method for one–speed xy–geometry discrete ordinates source-detector problems. International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C); 2017 Apr 16–20; Jeju, Korea.
   Google Scholar
• Pazinatto CB, Cromianski SR, Barros RC, Barichello LB. An analytical discrete ordinates solution for one-speed slab geometry adjoint transport problems with isotropic scattering. Joint International Conference on Mathematics and Computation (M&C), Supercomputing in Nuclear Applications (SNA) and the Monte Carlo (MC) Method; 2015 Apr 19-23; Nashville, Tennessee, USA.
   Google Scholar
• Pazinatto CB. Formulação ADO para o problema adjunto de transporte unidimensional e aplicação em um problema inverso de reconstrução de fonte [master's thesis]. [Porto Alegre, RS, Brazil]: Universidade Federal do Rio Grande do Sul; 2015. Portuguese.
   Google Scholar
• Pazinatto CB, Barros RC, Barichello LB. Analytical adjoint discrete ordinates formulation for monoenergetic slab-geometry source-detector calculations. Int J Nucl Energ Sci Tech. 2016;10(2):107–122.
   Google Scholar
• Barichello LB, Siewert CE. A discrete-ordinates solution for a non-grey model with complete frequency redistribution. J Quant Spectrosc Radiat Transf. 1999;62(6):665–675.
   Google Scholar
• Chandrasekhar S. Radiative transfer. New York (NY): Dover Publications; 1960.
   Google Scholar
• Siewert CE. A discrete-ordinates solution for multigroup transport theory with upscattering. J Quant Spectrosc Radiat Transf. 2000;64(3):255–273.
   Google Scholar
• Pazinatto CB, Barichello LB. Energy dependent source reconstructions via explicit formulations of the adjoint particles flux. J Comput Theor Trans. 2018;47:58–83.
   Google Scholar
• Kaipio J, Somersalo E. Statistical and computational inverse problems. New York (NY): Springer; 2005.
   Google Scholar
• Pazinatto CB, Barichello LB. On the use of the adjoint operator for source reconstruction in particle transport problems. Inverse Probl Sci Eng. 2018;27(4):513–539.
   Google Scholar
• Beck JV, Arnold KJ. Parameter estimation in engineering and science. New York (NY): John Wiley & Sons; 1977.
   Google Scholar
• Lewis E, Miller W. Computational methods of neutron transport. New York (NY): John Wiley & Sons; 1984.
   Google Scholar
• Bell GI, Glasstone S. Nuclear reactor theory. New York (NY): Van Nostrand Reinhold Company; 1970.
   Google Scholar
• Prinja AK, Larsen EW. General principles of neutron transport. Chapter 5 in handbook of nuclear engineering. New York (NY): Springer; 2010. (Nuclear engineering fundamentals; vol. 1).
   Google Scholar
• Somasundaram E, Palmer T. Application of variational variance reduction for source-detector problems in nuclear non-proliferation. J Comput Theor Trans. 2016;45(7):554–557.
   Google Scholar
• Barros RC, Larsen EW. A numerical method for multigroup slab-geometry discrete ordinates problems with no spatial truncation error. Transp Theory Stat Phys. 1991;20(5–6):441–462.
   Google Scholar
• Siewert CE. A spherical harmonics method for multi-group or non-gray radiation transport. J Quant Spectrosc Radiat Transf. 1993;49(2):95–106.
   Google Scholar
• Barichello LB, Picoloto CB, da Cunha RD. The ADO-nodal method for solving two-dimensional discrete ordinates transport problems. Ann Nucl Energy. 2017;108:376–385.
   Google Scholar