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Tikhonov regularization and prior information in electrical impedance tomography
M Vauhkonen1, D Vadász, P A Karjalainen
1Department of Applied Physics, University of Kuopio, Finland.
IEEE Transactions on Medical Imaging
|August 4, 1998
Summary
This study introduces a novel regularization matrix for electrical impedance tomography (EIT). The new method improves impedance distribution reconstruction, even with imperfect prior information.
Area of Science:
- Medical Imaging
- Electrical Engineering
- Computational Mathematics
Background:
- Electrical Impedance Tomography (EIT) reconstructs internal conductivity distributions from boundary measurements.
- Solving the inverse problem in EIT often relies on regularization methods like Tikhonov regularization.
- Existing Tikhonov methods use ad hoc regularization matrices, leading to potentially inappropriate prior assumptions.
Purpose of the Study:
- To develop a regularization matrix construction for EIT that aligns with prior assumptions about impedance distributions.
- To improve the accuracy and robustness of impedance reconstruction in EIT.
Main Methods:
- Proposing a novel approach to construct regularization matrices based on approximating subspaces.
- Utilizing simulations to evaluate the performance of the proposed method against existing schemes.
Main Results:
- The proposed method yields superior impedance reconstructions compared to two other schemes when prior information matches the true object.
- The method demonstrates robustness, providing reasonable estimates even when prior information is incompatible with the true object.
Conclusions:
- The developed regularization matrix construction method enhances EIT reconstruction accuracy.
- This approach offers a more principled way to incorporate prior knowledge into EIT regularization, improving reliability.