Theoretical and numerical analysis on multispectral bioluminescence tomography

Recently, molecular imaging has been rapidly developed to study physiological and pathological processes in vivo at the cellular and molecular levels. Among molecular imaging modalities, optical imaging has attracted a major attention for its unique advantages. In this paper, we establish a mathematical framework for multispectral bioluminescence tomography (BLT) that allows simultaneous studies of multiple optical reporters. We show solution existence, uniqueness and continuous dependence on data as well as the limiting behaviours when the regularization parameter approaches zero or when the penalty parameter approaches infinity. Then, we propose two numerical schemes for multispectral BLT and derive error estimates for the corresponding solutions.