The multiple-sets split feasibility problem and its applications for inverse problems

The multiple-sets split feasibility problem requires to find a point closesttoafamilyofclosedconvexsetsinonespacesuchthatits image under a linear transformation will be closest to another family of closed convex sets in the image space. It can be a model for many Accepted for publication in the journal Inverse Problems. 1 inverse problems where constraints areimposedonthesolutionsin the domain of a linear operator as well as in the operator’s range. It generalizes the convex feasibility problemaswellasthetwo-setssplit feasibility problem. We propose a projection algorithm that minimizes a proximity function that measures the distance of a point from all sets. The formulation, as well as the algorithm,…

• IS
  Israel Science Foundation
• NI
  National Institutes of Health