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Bioluminescence tomography (BLT) aims at the determination of the distribution of a bioluminescent source quantitatively. The mathematical problem involved is an inverse source problem and is ill-posed. With the Tikhonov regularization, an optimization problem is formed for the light source reconstruction and it is usually solved by gradient-type methods. However, such iterative methods are often locally convergent and thus the solution accuracy depends largely on initial guesses. In this paper, we reformulate the reduced regularized optimal problem as a nonlinear equation and apply a homotopy method, which is a powerful tool for solving nonlinear problem due to its globally convergent property, to it. Numerical experiments show that the application of the homotopy technique is feasible and can produce satisfactory approximate solutions for a very large range of initial guesses. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]