Abstract

Estimating distributed parameters from indirect noisy observations requires a discretization of the unknown quantity to make the forward model computationally feasible. In ill-posed problems, the modeling error due to the discretization may have an adverse impact on the solution if not taken into account properly, in particular, when the  quality of the data is high and the modeling error dominates the noise. To minimize the effect of the modeling error, refinement of the discretization is an option that may increase significantly the computational cost. Computational efficiency may be increased by selectively refining the discretization only where needed, and by using anisotropic discretization. In this talk, the problem is addressed by defining the discretization in terms of a metric that is coupled to the unknown distributed parameter through a Bayesian hypermodel, thus making the discretization part of the inverse problem. Computed examples of this coupled problem include a sparse view tomography problem.