Numerical approximation of bioluminescence tomography based on a new formulation

Cheng, Xinbin; Gong, Rongfang; Han, Weimin

doi:10.1007/s10665-008-9246-y

Cited by 3 publications

(2 citation statements)

References 36 publications

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“…A common way to overcome the ill-posed property is the regularization. The Tikhonov regularization strategy is usually used [7,8,9,10,11,12,13,14,15,16,17,18,19,20]. Given a suitable regularization parameter, the Tikhonov method can get excellent results.…”

Section: Introductionmentioning

confidence: 99%

A trust region method in adaptive finite element framework for bioluminescence tomography

et al. 2010

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Bioluminescence tomography (BLT) is an effective molecular imaging (MI) modality. Because of the ill-posedness, the inverse problem of BLT is still open. We present a trust region method (TRM) for BLT source reconstruction. The TRM is applied in the source reconstruction procedure of BLT for the first time. The results of both numerical simulations and the experiments of cube phantom and nude mouse draw us to the conclusion that based on the adaptive finite element (AFE) framework, the TRM works in the source reconstruction procedure of BLT. To make our conclusion more reliable, we also compare the performance of the TRM and that of the famous Tikhonov regularization method after only one step of mesh refinement of the AFE framework. The conclusion is that the TRM can get faster and better results after only one mesh refinement step of AFE framework than the Tikhonov regularization method when handling large scale data. In the TRM, all the parameters are fixed, while in the Tikhonov method the regularization parameter needs to be well selected.

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Section: Introductionmentioning

confidence: 99%

A trust region method in adaptive finite element framework for bioluminescence tomography

et al. 2010

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“…A comprehensive theoretical and numerical analysis of the BLT problem is performed in [9]. More theoretical investigations and numerical solutions of the BLT problem are reported in [11,8,2,3]. A further step along the direction of BLT development is multi-spectral bioluminescence tomography (MBT) that uses multi-spectral measurement data in reconstructing the bioluminescent source distribution.…”

Section: Introductionmentioning

confidence: 99%

Studies of a mathematical model for temperature-modulated bioluminescence tomography

Han

Shen

Kazmi

et al. 2009

Applicable Analysis

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Abstract. We introduce and study a mathematical model for temperature-modulated bioluminescence tomography (TBT). The model is capable of self-adjusting values of experimental parameters that are used in the formulation. Major theoretical results of the paper include: solution existence of the model, convergence of numerical solutions, an iterative scheme based on linearization, studies of the solution limiting behaviors when normalized total energy function and/or some or all the energy percentages in individual spectral bands are known exactly. Several numerical examples are included to illustrate the improvement of the accuracy of the reconstructed bioluminescent source distribution due to the employment of measurements from multiple temperature distributions.

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Source sparsity based primal-dual interior-point method for three-dimensional bioluminescence tomography

Zhang

Zhao

Chen

et al. 2011

Optics Communications

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Numerical approximation of bioluminescence tomography based on a new formulation

Cited by 3 publications

References 36 publications

A trust region method in adaptive finite element framework for bioluminescence tomography

A trust region method in adaptive finite element framework for bioluminescence tomography

Studies of a mathematical model for temperature-modulated bioluminescence tomography

Source sparsity based primal-dual interior-point method for three-dimensional bioluminescence tomography

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