A DIRECT RECONSTRUCTION ALGORITHM FOR THE ANISOTROPIC INVERSE CONDUCTIVITY PROBLEM BASED ON CALDERÓN'S METHOD IN THE...

Area of Science:

• Electrical Engineering
• Applied Mathematics
• Computational Physics

Background:

• Inverse conductivity problems are crucial for various imaging techniques.
• Reconstructing anisotropic conductivity presents unique challenges due to non-uniqueness.
• Existing methods often struggle with complex conductivity distributions.

Purpose of the Study:

• To develop a direct reconstruction algorithm for anisotropic conductivities in 2D.
• To address the non-uniqueness issue in anisotropic inverse conductivity problems.
• To reconstruct the multiplicative scalar field of anisotropic tensors.

Main Methods:

• Adaptation of Calderón's linearization method for anisotropic cases.
• Utilizing quasi-conformal maps in the plane to facilitate the approach.
• Assumption of known entries of unperturbed anisotropic tensors *a priori*.

Main Results:

• A direct reconstruction algorithm for anisotropic conductivity is successfully proposed.
• The method effectively overcomes the non-uniqueness inherent in anisotropic inverse problems.
• Demonstrated efficacy on discontinuous, radially symmetric conductivities with high and low contrast.

Conclusions:

• The proposed direct algorithm offers a viable solution for anisotropic conductivity reconstruction.
• The use of quasi-conformal maps is key to extending Calderón's method to anisotropic scenarios.
• The algorithm shows promise for applications involving complex material properties.