Reconstructing conductivity coefficients based on sparsity regularization and measured data in electrical impedance tomography

In this paper, we investigate an inverse problem in electrical impedance tomography. Based on measured data and the sparsity of conductivity coefficients, we use sparse regularization with a suitable fitting functional that replaces the least square functional as often used. Our main results are the differentiability of the new functional, the well-posedness and convergence rates of the regularization method as well as a discussion on Sobolev gradient. Finally, numerical solutions are analyzed and compared for different measured data-sets.