A Projection-Onto-Convex-Sets Interpretation of Cross-Entropy Based Image Super-Resolution Algorithms

Abstract

Signal recovery problems are generally posed in the form of rigid constraints (constraint sets), flexible constraints (optimization functional) or a combination thereof. Minimum cross-entropy methods1,2 belong to this third category due to an implicit rigid non-negativity constraint. An elegant approach to solving problems of the first category for convex constraint sets is the Projection Onto Convex Sets (POCS)3 technique. POCS has been limited primarily to least-squares projections, although other distance measures have been proposed.4 In this paper, minimum cross-entropy methods are interpreted as parallel cross-entropic POCS algorithms. This interpretation provides a theoretical basis for including rigid constraints in iterative super-resolution algorithms.