Mathematical theory and numerical analysis of bioluminescence tomography

Molecular imaging is widely recognized as the main stream in the next generation of biomedical imaging. Bioluminescence tomography (BLT) is a rapidly developing new area of molecular imaging. The goal of BLT is to provide quantitative three-dimensional reconstruction of a bioluminescent source distribution within a small animal from optical signals on the surface of the animal body. In this paper, a mathematical framework is established for BLT. Solution existence and uniqueness are established. Continuous dependence of the solution is demonstrated with respect to data. Stable BLT schemes are studied, leading to error estimates and convergence of the methods. A numerical example is presented to illustrate the algorithmic performance.

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