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Volume 29, Issue 5
Inversion of Electron Tomography Images Using $L^2$-Gradient Flows — Computational Methods

Guoliang Xu, Ming Li, Ajay Gopinath, & Chandrajit L. Bajaj

DOI: 10.4208/jcm.1106-m3302

J. Comp. Math., 29 (2011), pp. 501-525.

Published online: 2011-10

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  • Abstract

In this paper, we present a stable, reliable and robust method for reconstructing a three dimensional density function from a set of two dimensional electric tomographic images. By minimizing an energy functional consisting of a fidelity term and a regularization term, an $L^2$-gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and an explicit Euler scheme in temporal direction. The experimental results show that the proposed method is efficient and effective.

  • Keywords

Computational Inversion, Reconstruction, Electric Tomography.

  • AMS Subject Headings

65D17.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-29-501, author = {Guoliang Xu, Ming Li, Ajay Gopinath, and Chandrajit L. Bajaj}, title = {Inversion of Electron Tomography Images Using $L^2$-Gradient Flows — Computational Methods}, journal = {Journal of Computational Mathematics}, year = {2011}, volume = {29}, number = {5}, pages = {501--525}, abstract = {

In this paper, we present a stable, reliable and robust method for reconstructing a three dimensional density function from a set of two dimensional electric tomographic images. By minimizing an energy functional consisting of a fidelity term and a regularization term, an $L^2$-gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and an explicit Euler scheme in temporal direction. The experimental results show that the proposed method is efficient and effective.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1106-m3302}, url = {http://global-sci.org/intro/article_detail/jcm/8491.html} }
TY - JOUR T1 - Inversion of Electron Tomography Images Using $L^2$-Gradient Flows — Computational Methods AU - Guoliang Xu, Ming Li, Ajay Gopinath, & Chandrajit L. Bajaj JO - Journal of Computational Mathematics VL - 5 SP - 501 EP - 525 PY - 2011 DA - 2011/10 SN - 29 DO - http://doi.org/10.4208/jcm.1106-m3302 UR - https://global-sci.org/intro/article_detail/jcm/8491.html KW - Computational Inversion, Reconstruction, Electric Tomography. AB -

In this paper, we present a stable, reliable and robust method for reconstructing a three dimensional density function from a set of two dimensional electric tomographic images. By minimizing an energy functional consisting of a fidelity term and a regularization term, an $L^2$-gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and an explicit Euler scheme in temporal direction. The experimental results show that the proposed method is efficient and effective.

Guoliang Xu, Ming Li, Ajay Gopinath, and Chandrajit L. Bajaj. (2011). Inversion of Electron Tomography Images Using $L^2$-Gradient Flows — Computational Methods. Journal of Computational Mathematics. 29 (5). 501-525. doi:10.4208/jcm.1106-m3302
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