Statistical Multiresolution Estimation in Imaging: Fundamental Concepts and Algorithmic Framework

In this paper we introduce a general class of statistical multiresolution estimators and develop an algorithmic framework for computing those. By this we mean estimators that are defined as solutions of convex optimization problems with $\ell_\infty$-type constraints. We employ a combination of an alternating direction augmented Lagrangian technique with Dykstra's algorithm for computing orthogonal projections onto intersections of convex sets. The capability of the proposed method is illustrated by various examples from imaging.