An adaptive Tikhonov regularization parameter choice method for electrical resistance tomography

• A spatially adaptive regularization parameter method is proposed for the inverse problem of ERT.
• The method adaptively updates the regularization parameters during the iteration process.
• The method provides spatially varying parameter for each pixel of the reconstructed image. Large regularization parameters for the smooth background region.
• Small regularization parameters for the object region.

Electrical resistance tomography (ERT) reconstructs the conductivity distribution from the boundary changes of electrical measurements. The inverse problem of ERT is seriously ill-posed where regularization methods are needed to treat this ill-posedness. A proper choice of regularization parameter which controls the degree of smoothing is very important for these regularization methods. Although have been a variety of methods, such as L-curve method, to choose a reasonable parameter for the problem, these methods usually result in a scalar parameter which cannot distinctly express the spatial characteristic of the conductivity distribution. So a spatially adaptive regularization parameter choice method is proposed for regularizing the inverse problem of ERT based on Tikhonov regularization. Since large regularization parameters can stabilize and smoothen the solution, while small regularization parameters can approximate and sharpen the solution, the proposed method adaptively updates the regularization parameters during the iteration process and provides spatially varying parameter for each pixel of the reconstructed image. When the iteration is stopped, large regularization parameters for the smooth background region and small regularization parameters for the object region can be obtained. The method is discussed using simulated data for some typical conductivity distributions, and further applied to the analysis of real measurement data acquiring from the practical system. The results demonstrate that flexible regularization parameter vectors can be achieved for different distributions and the strength of regularization is adaptively provided for different regions in a specific distribution. The adaptive method achieves an efficient and reliable regularization solution and has outstanding performance in noise immunity especially in smooth background regions.