New paper on risk estimators (GSURE et al.)

We had an interesting collaboration with a group at the Institute of Statistics, Ruhr-Universität Bochum about the statistical properties of a certain class of parameter choice rules that became popular in ill-posed inverse problems recently: Methods based on Stein’s unbiased risk estimator (SURE) choose a regularization parameter by minimizing an estimate of a risk function that cannot be minimized directly as it depends on the true, unknown solution. By a mix of theoretical and numerical studies, we could show that the quality of such estimators can severely deteriorate if the ill-posedness of the problem increases, which is unfortunately a natural asymptotic limit in many inverse problems scenarios. The full results can be found in a paper we recently uploaded to arXiv. Big thanks to all the co-authors! [Update: It has been published in Inverse Problems & Imaging .]