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

被引:673
作者
Censor, Y
Elfving, T
Kopf, N
Bortfeld, T
机构
[1] Univ Haifa, Dept Math, IL-31905 Haifa, Israel
[2] Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden
[3] Massachusetts Gen Hosp, Dept Radiat Oncol, Boston, MA 02114 USA
[4] Harvard Univ, Sch Med, Boston, MA 02114 USA
关键词
D O I
10.1088/0266-5611/21/6/017
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The multiple-sets 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 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 treatment planning is studied in a separate companion paper and is here only described briefly.
引用
收藏
页码:2071 / 2084
页数:14
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