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

详细信息

发表期刊/会议

Inverse Problems

发表日期

2005-11-21

发表年份

2005

摘要

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, 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. 1