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 .]
The papers that the last few posts announced are all accepted and now go through the different stages of a publication. The most recent versions are linked on my google scholar page. Again a big thanks to all the co-authors and reviewers!
We just submitted our paper “Accelerated High-Resolution Photoacoustic Tomography via Compressed Sensing” to Physics in Medizin and Biology. It contains a lot of the work I did at the UCL so far. It is already arXiv. Big thanks to all the co-authors!
“Using reciprocity for relating the simulation of transcranial current stimulation to the EEG forward problem” just went into press for NeuroImage! The uncorrected proof can be found here and on bioRxiv. Big thanks to the first author Sven Wagner!
I finally submitted a paper about the extension to the single component Gibbs sampler that allows to sample a lot more types of posteriors in Bayesian inversion. It is titled “Fast Gibbs sampling for high-dimensional Bayesian inversion” and after lying around for quite a bit as a draft, I now finalized it and submitted it to Inverse Problems. The pre-print can be found on arXiv.