Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-10T14:12:15.690Z Has data issue: false hasContentIssue false
  • English
  • Français

An Inverse Problem of Determining Coefficients in a One-Dimensional Radiative Transport Equation

Published online by Cambridge University Press:  03 June 2015

Nobuyuki Higashimori
Nobuyuki Higashimori*
Affiliation:
Faculty of Engineering, Shibaura Institute of Technology, 307 Fukakusa, Minuma, Saitama, Japan
*
Corresponding author. Email: i037200@shibaura-it.ac.jp or higashim@econ.hit-u.ac.jp
Get access

Abstract

We consider an inverse problem of determining unknown coefficients for a one-dimensional analogue of radiative transport equation. We show that some combination of the unknown coefficients can be uniquely determined by giving pulse-like inputs at the boundary and observing the corresponding outputs. Our result can be applied for determination of absorption and scattering properties of an optically turbid medium if the radiative transport equation is appropriate for describing the propagation of light in the medium.

Keywords

35R3035L5035Q9962P10Inverse problemradiative transport equationfirst-order hyperbolic systemoptical tomography
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 4 , August 2014 , pp. 515 - 522
Copyright
Copyright © Global-Science Press 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Arridge, S. R., Optical tomography in medical imaging, Inverse Problems, 15 (1999), pp. R41–R93.CrossRefGoogle Scholar
[2] Arridge, S. R. and Schotland, J. C., Optical tomography: forward and inverse problems, Inverse Problems, 25 (2009), 123010.CrossRefGoogle Scholar
[3] Kress, R., Linear Integral Equations, Second ed., Applied Mathematical Sciences 82, Springer-Verlag, New York, 1999.Google Scholar
[4] Romanov, V. G., Inverse Problems of Mathematical Physics, Translated from the Russian by Yuzina, L. Ya., VNU Science Press, Utrecht, 1987.Google Scholar