Fourier-Laplace structure of  the inverse scattering  problem for the radiative transport equation

John C. Schotland; Vadim A. Markel

doi:10.3934/ipi.2007.1.181

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2007, Volume 1, Issue 1: 181-188. Doi: 10.3934/ipi.2007.1.181

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Fourier-Laplace structure of the inverse scattering problem for the radiative transport equation

John C. Schotland^1, and
Vadim A. Markel^2,

1.
Department of Bioengineering, University of Pennsylvania, Philadelphia, PA
2.
Department of Radiology, University of Pennsylvania, Philadelphia, PA

Received: September 30, 2006

Published: January 2007

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Abstract

We consider the inverse scattering problem for the radiative transport equation. We show that the linearized form of this problem can be formulated in terms of the inversion of a suitably defined Fourier-Laplace transform. This generalizes a previous result obtained within the diffusion approximation to the radiative transport equation.

Keywords:

Inverse scattering,
radiative transport.

Mathematics Subject Classification: Primary: 34A55; Secondary: 85A25.

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