Finding best approximation pairs relative to two closed convex sets in Hilbert spaces
Journal of Approximation Theory
A hybrid parallel projection approach to object-based image restoration
Pattern Recognition Letters
EURASIP Journal on Applied Signal Processing
A Deep Monotone Approximation Operator Based on the Best Quadratic Lower Bound of Convex Functions
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
An adaptive projected subgradient approach to learning in diffusion networks
IEEE Transactions on Signal Processing
Adaptive constrained learning in reproducing Kernel Hilbert spaces: the robust beamforming case
IEEE Transactions on Signal Processing
Consistent image decoding from multiple lossy versions
Proceedings of the 2010 ACM workshop on Advanced video streaming techniques for peer-to-peer networks and social networking
Incremental Subgradients for Constrained Convex Optimization: A Unified Framework and New Methods
SIAM Journal on Optimization
Constrained total variation minimization and application in computerized tomography
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Computational Optimization and Applications
An acceleration scheme for cyclic subgradient projections method
Computational Optimization and Applications
An adaptive regularization method for sparse representation
Integrated Computer-Aided Engineering
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Solving a convex set theoretic image recovery problem amounts to finding a point in the intersection of closed and convex sets in a Hilbert space. The projection onto convex sets (POCS) algorithm, in which an initial estimate is sequentially projected onto the individual sets according to a periodic schedule, has been the most prevalent tool to solve such problems. Nonetheless, POCS has several shortcomings: it converges slowly, it is ill suited for implementation on parallel processors, and it requires the computation of exact projections at each iteration. We propose a general parallel projection method (EMOPSP) that overcomes these shortcomings. At each iteration of EMOPSP, a convex combination of subgradient projections onto some of the sets is formed and the update is obtained via relaxation. The relaxation parameter may vary over an iteration-dependent, extrapolated range that extends beyond the interval [0,2] used in conventional projection methods. EMOPSP not only generalizes existing projection-based schemes, but it also converges very efficiently thanks to its extrapolated relaxations. Theoretical convergence results are presented as well as numerical simulations