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 methods^1,2 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.

© 1995 Optical Society of America