Diffraction limited images obtained form practical sensing operations need to be processed before they can be used for any decision-making purposes (target detection, tracking, surveillance, etc.). Iterative digital processing algorithms, generally referred to as super-resolution algorithms, that provide not only restoration within the passband of the sensor but also some degree of spectral extrapolation, have been primarily used to process such images. A popular route for the design of these algorithms is to employ a Bayesian framework where an appropriately modeled statistical quantity (likelihood, posterior distribution, etc.) is optimized iteratively. Although powerful algorithms with demonstrable super-resolution capabilities can be synthesized using this approach, the computational demands and the slow convergence of these algorithms can make them rather unattractive to implement in specific situations. Furthermore, the quality of restoration achieved may not be entirely satisfactory in specific cases of imaging where the underlying emission process is not accurately modeled by the assumed probability distribution functions used in the derivation of algorithms. In this paper, we shall describe a set of hybrid algorithms that integrate set theory-based adjustment operations with the iterative steps that perform statistical optimization in order to achieve superior performance features such as faster convergence and reduced restoration errors. Mathematical modeling of constraint sets that facilitate inclusion of specific types of information available will be discussed and the design of projection operators that permit an intelligent utilization of these constraint sets in the iterative processing will be outlined. The restoration and super- resolution performance of these hybrid algorithms will be demonstrated by processing several blurred images acquired from different types of sensing mechanisms and a quantitative evaluation of the benefits in both image and frequency domains will be presented.