On the convergence of general projection methods for solving convex feasibility problems with applications to the inverse problem of image recovery

Abstract

For an arbitrary family of closed convex sets with nonempty intersection in a Hilbert space, we consider the classical convex feasibility problem. We study the convergence property of the recently introduced unified projection algorithm B-EMOPP for solving this problem. For this, a new general control strategy is proposed, which we call the ‘quasi-coercive control’. Under mild assumptions, we prove the convergence of B-EMOPP using these new control strategies as well as various other strategies. Several known results are extended and improved. The proposed algorithm is then applied to the inverse problem of image recovery.

Keywords:

• Convex feasibility problem
• image recovery
• projection algorithm
• system of closed convex sets

Acknowledgements

The authors are truly grateful to Jen-Chih Yao for valuable discussions and initiating this collaboration. Moreover, the authors are grateful to the anonymous referees for invaluable suggestions which helped improve the original manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.