  In electrical impedance tomography the electrical conductivity inside a
physical body is computed from electro-static boundary measurements. The focus
of this paper is to extend recent result for the 2D problem to 3D. Prior
information about the sparsity and spatial distribution of the conductivity is
used to improve reconstructions for the partial data problem with Cauchy data
measured only on a subset of the boundary. A sparsity prior is enforced using
the $\ell_1$ norm in the penalty term of a Tikhonov functional, and spatial
prior information is incorporated by applying a spatially distributed
regularization parameter. The optimization problem is solved numerically using
a generalized conditional gradient method with soft thresholding. Numerical
examples show the effectiveness of the suggested method even for the partial
data problem with measurements affected by noise.
