in this paper, we study projected non-stationary simultaneous it-erative reconstruction techniques (p-sirt). based on algorithmic op-erators, convergence result are adjusted with opial’s theorem. the advantages of p-sirt are demonstrated on examples taken from to-mographic imaging.

The convergence of the projection algorithm for solving the convex feasibility problem for a family of closed convex sets, is in connection with the regularity properties of the family. In the paper [18] are pointed out four cases of such a family depending of the two characteristics: the emptiness and boudedness of the intersection of the family. The case four (the interior of the intersection...

Let X be a Hilbert space and let Cn, n = 1, . . . ,N be convex closed subsets of X . The convex feasibility problem is to find some point x ∈ N ⋂ n=1 Cn, when this intersection is non-empty. In this talk we discuss projection algorithms for finding such a feasibility point. These algorithms have wide ranging applications including: solutions to convex inequalities, minimization of convex nonsmo...

The multiple-set split feasibility problem requires finding a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. It can be amodel for many inverse problemswhere constraints are imposed on the solutions in the domain of a linear operator as well as in the operat...

2 Mathematical Foundations 11 2.1 General Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Geometrical Properties of Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 Strong and Weak Topologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Convex Functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

Abstract The circumcentered-reflection method (CRM) has been applied for solving convex feasibility problems. CRM iterates by computing a circumcenter upon composition of reflections with respect to sets. Since are based on exact projections, their computation might be costly. In this regard, we introduce the circumcentered approximate-reflection (CARM), whose rely outer-approximate projections...