Bioluminescence tomography for media with spatially varying refractive index

Abstract

Biomedical imaging has developed into the level of molecular imaging. Bioluminescence tomography (BLT), as an optical imaging modality, is a rapidly developing new and promising field. So far, much of the theoretical analysis of BLT is based on a diffusion approximation equation for media with constant refractive index. In this article, we study the BLT problem for media with spatially varying refractive index. We introduce a general framework with Tikhonov regularization for this purpose, present its well-posedness and establish the error bounds for its numerical solution by the finite element method. Numerical results are reported on simulations of the BLT problem for media with spatially varying refractive index.

Keywords:

• bioluminescence tomography
• spatially varying refractive index
• inverse problem
• well-posedness
• numerical solution
• error estimate

AMS Subject Classifications:

• 92C55
• 34K29
• 49K40
• 34K28
• 65N15

Acknowledgements

This work was supported by the National Science Foundation of China under Grant No. 10871179 and the National Basic Research Programme of China under Grant No. 2008CB717806.