Abstract
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.
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Censor, Y., Pantelimon, I. & Popa, C. Family constraining of iterative algorithms. Numer Algor 66, 323–338 (2014). https://doi.org/10.1007/s11075-013-9736-5
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DOI: https://doi.org/10.1007/s11075-013-9736-5
Keywords
- Constraining strategy
- Strictly nonexpansive operators
- Fixed points set
- Least squares problems
- Image reconstruction from projections