Proceedings ArticleDOI
A fast parallel projection algorithm for set theoretic image recovery
Patrick L. Combettes,H. Puh +1 more
- pp 473-476
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TLDR
A new projection algorithm for convex set theoretic image recovery [reconstruction and restoration] is presented that outperforms existing ones, in particular the popular cyclic method of projections onto convex sets [POCS].Abstract:
A new projection algorithm for convex set theoretic image recovery [reconstruction and restoration] is presented. This algorithm comprises all serial and parallel projection methods as particular cases and is straightforwardly implementable on concurrent processors. It proceeds by taking convex combinations of selected projections at each iteration and allows extrapolated relaxations far beyond the range [0,2] used in conventional algorithms. These extrapolated, iteration-dependent relaxations result in very fast convergence. Numerical results are provided which show that the proposed algorithm outperforms existing ones, in particular the popular cyclic method of projections onto convex sets [POCS]. >read more
Citations
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Journal ArticleDOI
Block-iterative algorithms for solving convex feasibility problems in Hilbert and in Banach spaces
Arkady Aleyner,Simeon Reich +1 more
TL;DR: In this paper, convergence theorems for two different block-iterative methods for solving the problem of finding a point in the intersection of the fixed point sets of a finite number of nonexpansive mappings in Hilbert and in finite-dimensional Banach spaces are established.
Construction d'un point fixe commun à une famille de contractions fermes
TL;DR: In this paper, a methode generale for construire un point fixe commun a famille denombrable de contractions fermes sur un espace hilbertien reel and montrons sa convergence is proposed.
Journal ArticleDOI
A Projection-Based Algorithm for Consistent and Inconsistent Constraints
TL;DR: It is shown that the iterates generated by the algorithm converge weakly to a global minimizer of $\hat J$ provided the set of fixed points of the algorithm is nonempty.
Journal ArticleDOI
Summed squared distance error reduction by simultaneous multiprojections and applications
TL;DR: A parallel projection scheme in which projections are performed simultaneously on all constraints at each iteration is presented, and the restriction to weighted L^2 norms leads to a simple and explicit form of this algorithm and allows relaxation and the use of nonconvex sets.
Proceedings ArticleDOI
Projection-based eigenvector decomposition for reduction of blocking artifacts of DCT coded image
Kook Yeon Kwak,Richard A. Haddad +1 more
TL;DR: This work presents a projection on convex sets (POCS)-based method for removing blocking artifacts in reconstructed DCT-encoded images at low-bit rate and achieves an enhanced decoding, both objectively and subjectively.
References
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Iterative methods for the three-dimensional reconstruction of an object from projections
TL;DR: It is shown that in general ART produces erroneous reconstructions, and an alternative iterative method is proposed which will give correct reconstructions under certain conditions.
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Image Restoration by the Method of Convex Projections: Part 1ߞTheory
D. C. Youla,H. Webb +1 more
TL;DR: In this article, a projection operator onto a closed convex set in Hilbert space is proposed for image restoration from partial data which permits any number of nonlinear constraints of a certain type to be subsumed automatically.
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The method of projections for finding the common point of convex sets
TL;DR: Various methods of finding points from the intersection of sets, using projection on to a separate set as an elementary operation are considered, and the strong convergence of the sequences obtained is proved.
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The foundations of set theoretic estimation
TL;DR: The author synthesizes a single, general framework from various approaches to set theoretic estimation, examines its fundamental philosophy, goals, and analytical techniques, and relates it to conventional methods.
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The feasible solution in signal restoration
TL;DR: In this paper, the authors define a feasible solution to the signal restoration problem as the one which satisfies all constraints which can be imposed on the true solution, which are described as closed convex sets.
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