  Electrical Impedance Tomography gives rise to the severely ill-posed
Calder\'on problem of determining the electrical conductivity distribution in a
bounded domain from knowledge of the associated Dirichlet-to-Neumann map for
the governing equation. The uniqueness and stability questions for the
three-dimensional problem were largely answered in the affirmative in the
1980's using complex geometrical optics solutions, and this led further to a
direct reconstruction method relying on a non-physical scattering transform. In
this paper, the reconstruction problem is taken one step further towards
practical applications by considering data contaminated by noise. Indeed, a
regularization strategy for the three-dimensional Calder\'on problem is
presented based on a suitable and explicit truncation of the scattering
transform. This gives a certified, stable and direct reconstruction method that
is robust to small perturbations of the data. Numerical tests on simulated
noisy data illustrate the feasibility and regularizing effect of the method,
and suggest that the numerical implementation performs better than predicted by
theory.
