Statistical Multi-Resolution Estimators in Linear Inverse Problems
The choice of the so-called regularization parameter plays a crucial role in linear inverse problems. This parameter is used to contol the trade-off between regularization and fit-to-data. In our talk, we present a novel approach on how to automate this choice in a statistically sound way. The resulting statistical multi-resolution (SMR) estimators are based on extreme-value statistics of weighted projections of the residuals. Apart from theoretic results, we also present an algorithmic framework which allows for fast computation of these estimators. Special emphasis is laid on deconvolution problems, an application from fluorescence microscopy illustrates the performance of our approach.