In constraining iterative processes, the algorithmic operator of the iterative process is pre-multiplied by a constraining operator at each iterative 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.
Bibliographical noteFunding Information:
Acknowledgments We thank Gabor Herman for valuable comments and the anonymous referees for their suggestions which helped to improve the first version of the manuscript. The work of Y.C. was partially supported by grant number 2009012 from the United States-Israel Binational Science Foundation (BSF) and by US Department of Army award number W81XWH-10-1-0170.
- Constraining strategy
- Fixed points set
- Image reconstruction from projections
- Least squares problems
- Strictly nonexpansive operators
ASJC Scopus subject areas
- Applied Mathematics