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Volume 8, Issue 3
A Semi-Implicit Binary Level Set Method for Source Reconstruction Problems

C. Liu & S. Zhu

Int. J. Numer. Anal. Mod., 8 (2011), pp. 410-426.

Published online: 2011-08

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  • Abstract

The aim of this paper is to investigate the application of a semi-implicit additive operator splitting scheme based binary level set method to source reconstruction problems. We reformulate the original model to be a new constrained optimization problem under the binary level set framework and solve it by the augmented Lagrangian method. Then we propose an efficient gradient-type algorithm based on the additive operator splitting scheme. The proposed algorithm can create new holes during the evolution. Topological changes can be handled automatically and complex geometry can be recovered under a certain amount of noise in the observation data. Numerical examples are presented to show the effectiveness and efficiency of our method.

  • Keywords

source reconstruction, binary level set method, augmented Lagrangian method, additive operator splitting.

  • AMS Subject Headings

49N45, 65N21

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-8-410, author = {C. Liu and S. Zhu}, title = {A Semi-Implicit Binary Level Set Method for Source Reconstruction Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2011}, volume = {8}, number = {3}, pages = {410--426}, abstract = {

The aim of this paper is to investigate the application of a semi-implicit additive operator splitting scheme based binary level set method to source reconstruction problems. We reformulate the original model to be a new constrained optimization problem under the binary level set framework and solve it by the augmented Lagrangian method. Then we propose an efficient gradient-type algorithm based on the additive operator splitting scheme. The proposed algorithm can create new holes during the evolution. Topological changes can be handled automatically and complex geometry can be recovered under a certain amount of noise in the observation data. Numerical examples are presented to show the effectiveness and efficiency of our method.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/693.html} }
TY - JOUR T1 - A Semi-Implicit Binary Level Set Method for Source Reconstruction Problems AU - C. Liu & S. Zhu JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 410 EP - 426 PY - 2011 DA - 2011/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/693.html KW - source reconstruction, binary level set method, augmented Lagrangian method, additive operator splitting. AB -

The aim of this paper is to investigate the application of a semi-implicit additive operator splitting scheme based binary level set method to source reconstruction problems. We reformulate the original model to be a new constrained optimization problem under the binary level set framework and solve it by the augmented Lagrangian method. Then we propose an efficient gradient-type algorithm based on the additive operator splitting scheme. The proposed algorithm can create new holes during the evolution. Topological changes can be handled automatically and complex geometry can be recovered under a certain amount of noise in the observation data. Numerical examples are presented to show the effectiveness and efficiency of our method.

C. Liu and S. Zhu. (2011). A Semi-Implicit Binary Level Set Method for Source Reconstruction Problems. International Journal of Numerical Analysis and Modeling. 8 (3). 410-426. doi:
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