Comparing different types of approximators for choosing the parameters in the regularization of ill-posed problems

Regularized approximations to the solutions of ill-posed problems typically vary from over-smoothed, inaccurate reconstructions to under-smoothed and unstable solutions as the regularization parameter varies about its optimal value. It thus makes sense to compare two (or more) regularized approximations, and seek the parametervalues where the distance between the approximations is a minimum. This paper advances the theory and practice of this methodology. The method appears to workvery well and be very stable, particularly in the presence of extreme error levels.