A PI^λD^μ-Controlled Calderon’s Method for Triple-Valued Electrical Capacitance Tomography

Electrical capacitance tomography (ECT) utilizes mutual capacitances at the boundary of the region of interest for noninvasive and contactless visualization of the distribution within the field, but the low quality of reconstructed image is a major constraint to its application. A $\text {PI}^{\lambda }\text {D}^{\mu }$ -controlled Calderon’s method is proposed by using the sparsity and low rankness of the triple-valued distributions and online tuning ability of the $\text {PI}^{\lambda }\text {D}^{\mu }$ control scheme. The iterations of the method are realized in a closed control loop. The fractional $\text {PI}^{\lambda }\text {D}^{\mu }$ the controller reduces the difference between the measured capacitance matrix and the estimated capacitance matrix derived from the reconstructed distribution. Calderon’s method is fed by the controller output and generates enhanced edges in the reconstructed image via a Sobel–Feldman operator. Also, the smooth segmentation function is then adopted to fuse the triple values known in advance to improve the image quality. Both numerical simulations and experiments demonstrate that the proposed method yields images of well-defined edges and shapes for triple-valued distributions.