Computational Aspects of Low Frequency Electrical and Electromagnetic Tomography: a Review Study

This paper studies various mathematical methods for image reconstruction in electrical impedance and magnetic induction tomography. Linear, nonlinear and semilinear methods for the inverse problems are studied. Depending on the application, one of these methods can be selected as the image reconstruction algorithm. Linear methods are suitable for low contrast imaging, and nonlinear methods are used when more accurate imaging results are required. A semilinear method can be used to preserve some properties of the nonlinear inverse solver and at the same time can have some advantages in computational time. Methods design specifically for jump in material distribution as well as dynamical imaging have been reviewed.