Title

Inverse Source Problems In Transport Equations

Keywords

Attenuated Radon transform; Optical molecular imaging; Scattering

Abstract

This paper proposes an iterative technique to reconstruct the source term in transport equations, which account for scattering effects, from boundary measurements. In the two-dimensional setting, the full outgoing distribution in the phase space (position and direction) needs to be measured. In three space dimensions, we show that measurements for angles that are orthogonal to a given direction are sufficient. In both cases, the derivation is based on a perturbation of the inversion of the two-dimensional attenuated Radon transform and requires that (the anisotropic part of) scattering be sufficiently small. We present an explicit iterative procedure, which converges to the source term we want to reconstruct. Applications of the inversion procedure include optical molecular imaging, an increasingly popular medical imaging modality. © 2007 Society for Industrial and Applied Mathematics.

Publication Date

12-1-2007

Publication Title

SIAM Journal on Mathematical Analysis

Volume

39

Issue

1

Number of Pages

57-76

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1137/050647177

Socpus ID

39449123875 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/39449123875

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