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In constraining iterative processes, the algorithmic operator of theiterative process is pre-multiplied by a constraining operator at eachiterative step. This enables the constrained algorithm, besides solving theoriginal problem, also to find a solution that incorporates some priorknowledge about the solution. This approach has been useful in imagerestoration and other image processing situations when a single constrainingoperator was used. In the field of image reconstruction from projections apriori information about the original image, such as smoothness or that itbelongs to a certain closed convex set, may be used to improve thereconstruction quality. We study here constraining of iterative processes by afamily of operators rather than by a single operator.

Family Constraining of Iterative Algorithms