Journal Article

An optimal finite element error estimate for an inverse problem in multispectral bioluminescence tomography

Rongfang Gong and Xiaoliang Cheng

in IMA Journal of Applied Mathematics

Volume 80, issue 1, pages 115-134
Published in print February 2015 | ISSN: 0272-4960
Published online June 2013 | e-ISSN: 1464-3634 | DOI: http://dx.doi.org/10.1093/imamat/hxt031
An optimal finite element error estimate for an inverse problem in multispectral bioluminescence tomography

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Inspired by the paper (Gong, W., Li, R., Yan, N. N. & Zhao, W. B. (2008) An improved error analysis for finite element approximation of bioluminescence tomography. J. Comput. Math., 26, 1–13), we consider an optimal finite element error estimate for an inverse problem in multispectral bioluminescence tomography. Different from achromatic or monochromatic measurements, hyperspectral or multispectral data can reduce the ill-posedness of the inverse problem and yield improved depth reconstruction. Compared with Gong et al. (2008, An improved error analysis for finite element approximation of bioluminescence tomography. J. Comput. Math., 26, 1–13), which just improved the error order of piecewise constant light source function, error order in this paper is optimal and all error estimates here are valid for a general smooth domain rather than a polyhedral/polygonal one. Moreover, under a boundedness assumption for the admissible source set, the constants in our error estimates do not depend on the regularization parameter, and therefore are bounded.

Keywords: multispectral bioluminescence tomography; finite element methods; error estimates

Journal Article.  0 words. 

Subjects: Applied Mathematics

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