scaled by $r$, the radius of the smallest circle enclosing the physical domain, effectively scaling the problem to be contained in the unit disc. The spatial grid was represented by a uniform $64\operatorname{\times}64$ $z$-grid on $[-1.05,1.05]^2$ with stepsize $h_z=0.0677$.

For a point of comparison, we include reconstructions of the [[ACE1 data]{}]{}, computed by the Gauss-Newton reconstruction algorithm. The inverse problem was solved by minimizing the objective functional $$\label{eq:objective_functional}
r({\zeta}) = \parallel ( {\phi}_m - {\phi}_{c} )\parallel_{2}^2 + \alpha^2 \parallel {F(\zeta}-{\zeta}\;^*) \parallel_{2}^2,$$ where $\phi_m$ is the vector of measurements, $\phi_c$ is the computed forward problem, $\zeta$ is the impeditivity distribution of the domain, $\alpha$ is the regularization parameter, $F$ is a Gaussian high-pass filter and ${\zeta}\;^*$ is a constant estimate of the impeditivity that also is used as the initial guess. The weight of the regularization was adjusted by visual examination, and in the reconstructions presented was $\alpha = 0.005$. To reduce computational effort and time consumption, the number of elements in the finite element mesh is reduced by applying the approximation error theory \[[@Kaipio2004a]\], where a Bayesian modeling error approach is used to treat approximation and modeling errors.

In this implementation, the forward problem was solved at each iteration with 