The Multiple-Sets Split Feasibility Problem and Its Applications for Inverse Problems
主 题: The Multiple-Sets Split Feasibility Problem and Its Applications for Inverse Problems
报告人: Prof. Yair Censor (University of Haifa)
时 间: 2006-07-17 下午 2:00 - 4:00
地 点: 理科一号楼 1114
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.