In this talk we will discuss a general concept of statistical multiscale analysis in the context of signal detection and imaging. This provides a large class of fully data driven regularisation methods which can be viewed as a multiscale generalization of the Dantzig selector. We address computational issues as well as the required extreme value theory of the multiscale statistics. Two major example include change point regression and locally adaptive image regularization for deconvolution problems. Our method illustrated with reconstructions of ion channel recordings and protein distributions in nano-biophotonic cell microscopy.
