with the participation of

The ambition of the proposed workshop is to bring together researchers working on all aspects of regularization relevant to statistical data analysis. Given the background of the organizers, the proposed participants are predominantly statisticians, but we seek to maintain a golden ratio of representatives from other fields from image processing, approximation theory and pure mathematics. We believe that the risks of this diversity of viewpoints will be rewarded by valuable cross-fertilization of ideas.

In theoretical statistics, regularization is usually interpreted either in Bayesian terms, or as some form of Stein-like shrinkage. Other disciplines, notably image processing, offer more pragmatic, but not less interesting perspectives, and often furnish a more aggressive attacks on computational aspects. At the risk of some statistical chauvinism, recent developments in the statistical literature offer promising new approaches to the fine-tuning of regularization techniques, particularly in the selection of regularization parameters. In applied statistics, regularization - often identified as ``penalty-based methods'', ``soft thresholding'' - is associated primarily with nonparametric regression and density estimation, often referred to rather imprecisely as ``smoothing''. One of the primary objectives of the proposed workshop would be to encourage a further diversification of smoothing objectives. In applications, regularization offers a unifying perspective on many diverse ill-posed inverse problems, a wide range of problems concerned with recovering information from indirect and usually noisy measurements, arising in geophysics, stereology, tomography, climatology and econometrics.

The word "workshop" has been deliberately chosen to distinguish the organization of the meeting from the more serial and more formal setting of a "conference". Drawing on the best aspects of the Oberwolfach tradition, we hope to be able to contribute to the vital new traditions of the Banff International Research Station.