Image recovery by convex combinations of projections

Limit Theorems of Operators by Convex Combinations of Nonexpansive Retractions in Banach Spaces

“…In 1991, Crombez [4] proved the following: Let T=: 0 I+ r i=1 : i T i with T i =I+* i (P i &I) for all i, 0<* i <2, : i >0, i=0, 1, 2, ..., r, r i=0 : i =1, where each P i is the metric projection of H onto C i and C 0 = r i=1 C i is nonempty. Then starting from an arbitrary element x of H, the sequence [T n x] converges weakly to an element of C 0 .…”

Asymptotic behavior of averaged and firmly nonexpansive mappings in geodesic spaces

“…For this case we give here a quadratic rate of asymptotic regularity for the sequence generated by the alternating projection method. Additionally, we focus on a parallel projection scheme (see [14] for more references on parallel projection methods) defined in terms of weighted averages of nonexpansive retractions which extends a method studied in Hilbert spaces by Crombez [15] and later generalized by Takahashi and Tamura [55] in the setting of uniformly convex Banach spaces. We show that this method finds a natural counterpart in the geodesic setting and give a rate of asymptotic regularity for U CW -hyperbolic spaces.…”

Extrapolation algorithm for affine-convex feasibility problems

“…This is precisely the parallel block-iterative algorithm discussed in [23] which, in turn, covers the projection methods of [1,2,3,9,22,26,32,33,34,40,47,49], the firmly nonexpansive operator methods of [10,19,43,53], the subgradient projection methods of [3,15,21,31,50,54,55], the proximal point algorithms of [4,44,52], and the equilibrium programming algorithm of [25].…”