Convex set theoretic image recovery via chaotic iterations of approximate projections

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. Methods employing projections onto the individual sets to build a sequence converging to a point in their intersection have proven most useful to obtain set theoretic solutions. They are nonetheless sometimes difficult to implement because of the theoretical or numerical tedium associated with the computation of projections at each iteration. We propose a general parallel iterative method which processes chaotically approximate projections instead of exact ones. Weak and strong convergence results are presented and subgradient projection methods are discussed as a particular case