The multiple-sets split feasibility problem and its applications for inverse problems
Yair Censor (yairmath.haifa.ac.il)
Abstract: The multiple-sets split feasibility problem requires to find 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 a model for many inverse problems where constraints are imposed on the solutions in the domain of a linear operator as well as in the operator's range. It generalizes the convex feasibility problem as well as the two-sets split 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, generalize earlier work on the split feasibility problem. We offer also a generalization to proximity functions with Bregman distances. Application of the method to the inverse problem of intensity-modulated radiation therapy (IMRT) treatment planning is studied in a separate companion paper and is here only briefly described.
Keywords: Multiple-sets split feasibility; proximity function; Bregman projections; inverse problems; intensity-modulated radiation therapy.
Category 1: Convex and Nonsmooth Optimization (Convex Optimization )
Category 2: Applications -- Science and Engineering
Category 3: Applications -- Science and Engineering (Biomedical Applications )
Citation: Inverse Problems, Vol. 21 (2005), pp. 2071-2084.
Entry Submitted: 11/22/2005
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