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Perturbation-resilient block-iterative projection methods with application to image reconstruction from projections. (English) Zbl 1191.94013

Summary: A block-iterative projection algorithm for solving the consistent convex feasibility problem in a finite-dimensional Euclidean space that is resilient to bounded and summable perturbations (in the sense that convergence to a feasible point is retained even if such perturbations are introduced in each iterative step of the algorithm) is proposed. This resilience can be used to steer the iterative process towards a feasible point that is superior in the sense of some functional on the points in the Euclidean space having a small value. The potential usefulness of this is illustrated in image reconstruction from projections, using both total variation and negative entropy as the functional.

MSC:

94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
15-04 Software, source code, etc. for problems pertaining to linear algebra
65F30 Other matrix algorithms (MSC2010)

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