Adaptively Regularized Bases-Expansion Subspace Optimization Methods for Electrical Impedance Tomography

Objective:
In this work, to deal with the difficulties in choosing regularization weighting parameters and low spatial resolution problems in difference electrical impedance tomography (EIT), we propose two adaptively regularized bases-expansion subspace optimization methods (AR-BE-SOMs).
Methods:
Firstly, an adaptive
$L^{1}$
-norm based total variation (TV) regularization is introduced under the framework of BE-SOM. Secondly, besides the additive regularization method, an adaptive weighted
$L^{2}$
-norm multiplicative regularization is further proposed. The regularized objective functions are optimized by conjugate gradient method, where the unknowns in both methods are updated alternatively between induced contrast current (ICC) and conductivity domain.
Conclusion:
Both numerical and experimental tests are conducted to validate the proposed methods, where AR-BE-SOMs show better edge-preserving, anti-noise performance, lower relative errors, and higher structure similarity indexes than BE-SOM.
Significance:
Unlike the common regularization techniques in EIT, the proposed regularization factors can be obtained adaptively during the optimization process. More importantly, AR-BE-SOMs perform well in reconstructions of some challenging geometry with sharp corners such as the “heart and lung” phantoms, deformation phantoms, triangles and even rectangles. It is expected that the proposed AR-BE-SOMs will find their applications for high-quality lung health monitoring and other clinical applications.