A second order Calderón's method with a correction term and a priori information.

Area of Science:

• Electrical impedance tomography (EIT)
• Inverse problems
• Medical imaging physics

Background:

• Calderón's method provides direct, linearized reconstruction for inverse conductivity problems.
• It yields absolute conductivity and permittivity images without forward modeling.
• Existing methods may have limitations in accuracy or require extensive computational resources.

Purpose of the Study:

• To establish an explicit relationship between Calderón's method and the D-bar method.
• To develop a "higher-order" Calderón's method with improved accuracy.
• To integrate spatial prior information into the reconstruction process.

Main Methods:

• Derivation of an explicit relationship between Calderón's method and the D-bar method.
• Inclusion of a correction term based on this relationship to form a "higher-order" Calderón's method.
• Development of a novel method for incorporating spatial priors.

Main Results:

• Demonstration of the "higher-order" Calderón's method on simulated data.
• Validation of the enhanced method using tank data from the ACE1 EIT system.
• Successful integration and application of spatial priors in conductivity imaging.

Conclusions:

• The enhanced Calderón's method, incorporating D-bar insights, improves conductivity and permittivity reconstruction.
• The inclusion of spatial priors further refines the accuracy of EIT imaging.
• This work advances direct reconstruction methods for practical EIT applications.