Mumford–Shah regularization in electrical impedance tomography with complete electrode model

In electrical impedance tomography, we aim to solve the conductivity within a target body through measurements made on surface of target. This inverse problem is severely ill-posed, especially in real applications with only partial boundary data available. Thus regularization has be introduced. Conventionally promoting smooth features used, however, Mumford--Shah regularizer familiar for image segmentation more appropriate targets consisting several distinct objects or materials. It is, numerically challenging. We show theoretically $\Gamma$-convergence that modification Ambrosio--Tortorelli approximation applicable particular complete electrode model measurements. With numerical and experimental studies, confirm this functional works practice produces higher quality results than typical regularizations employed tomography when consists smoothly-varying regions.