Theoretical and numerical analysis on multispectral bioluminescence tomography |
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| Authors: | Han Weimin; Wang Ge |
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| Institution: |
1 Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA, 2 Division of Biomedical Imaging, Virginia Tech—Wake Forest University School of Biomedical Engineering and Sciences, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
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| Abstract: | Recently, molecular imaging has been rapidly developed to studyphysiological and pathological processes in vivo at the cellularand molecular levels. Among molecular imaging modalities, opticalimaging has attracted a major attention for its unique advantages.In this paper, we establish a mathematical framework for multispectralbioluminescence tomography (BLT) that allows simultaneous studiesof multiple optical reporters. We show solution existence, uniquenessand continuous dependence on data as well as the limiting behaviourswhen the regularization parameter approaches zero or when thepenalty parameter approaches infinity. Then, we propose twonumerical schemes for multispectral BLT and derive error estimatesfor the corresponding solutions. |
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| Keywords: | multispectral bioluminescence tomography optical molecular imaging multiple optical reporters well-posedness numerical solution convergence error estimates |
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