Sparsity prior for electrical impedance tomography with partial data

Abstract. This paper focuses on applying prior information about inclusions to improve sparsity reconstructions for electrical impedance tomography with measured data on subsets of the boundary. Sparsity is enforced using an `1 norm on the expansion coefficients as the penalty term in a Tikhonov functional, and prior information is incorporated by applying a spatially distributed regularization parameter. The resulting optimization problem allows great flexibility with respect to the choice of measurement boundaries and incorporation of prior knowledge. The problem is solved using a generalized conditional gradient method applying soft thresholding. Numerical examples show the effectiveness of applying prior information to vastly improve reconstructions of inclusions in 2D, even for the partial data problem. 1