Numerical Algorithms manuscript No. (will be inserted by the editor) Family Constraining of Iterative Algorithms

Abstract In constraining iterative processes, the algorithmic operator of the iterative process is pre-multiplied by a constraining operator at each itera-tive step. This enables the constrained algorithm, besides solving the original problem, also to find a solution that incorporates some prior knowledge about the solution. This approach has been useful in image restoration and other image processing situations when a single constraining operator was used. In the field of image reconstruction from projections a priori information about the original image, such as smoothness or that it belongs to a certain closed convex set, may be used to improve the reconstruction quality. We study here constraining of iterative processes by a family of operators rather than by a single operator. Keywords constraining strategy · strictly nonexpansive operators · fixed points set · least squares problems · image reconstruction from projection