RIA: Parallel Projection Methods for Set Theoretic Signal Restoration & Reconstruction

RIA：集合理论信号恢复的并行投影方法

• 批准号: 9308609
• 负责人: Patrick Combettes
• 金额: --
• 依托单位: CUNY City College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9308609&HistoricalAwards=false
• 关键词: RIA; Parallel; Projection; Methods; Set

Combettes The goal of this research is to lay a theoretical and computational foundation for the use of parallel projection methods in set theoretic signal/image restoration and reconstruction. Its main motivation is to overcome the shortcomings of the Method of Successive Projections (MOSP, POCS in the Convex case) that currently prevail in the field: MOSP is not well suited for implementation on parallel processors due to its serial structure; it provides poor solutions if the sets do not intersect (inconsistent formulations); and it converges slowly and there is no general rule for adapting the relaxation coefficients to speed up the iterations. A general Method Of Parallel Projections (MOPP) is being developed in which the current iterate is projected simultaneously onto selected sets and the update is a relaxed convex combination of the projections. Research objectives include, a formal study of the convergence properties of MOPP for convex and nonconvex, as well as for the consistent and inconsistent formulations; development of iteration-dependent, extrapolated overrelaxations to achieve very fast convergence; and investigation of the practical and computational issues pertaining to signal/image recovery applications.

Combettes 这项研究的目标是为在集合论信号/图像恢复和重建中使用平行投影方法奠定理论和计算基础。其主要动机是克服目前该领域流行的连续投影方法（MOSP，凸情况下的 POCS）的缺点：由于 MOSP 的串行结构，不太适合在并行处理器上实现；如果集合不相交（公式不一致），它会提供较差的解决方案；并且它收敛缓慢，并且没有调整松弛系数以加速迭代的通用规则。正在开发一种通用的并行投影方法（MOPP），其中当前迭代同时投影到选定的集合上，并且更新是投影的松弛凸组合。研究目标包括正式研究凸和非凸 MOPP 的收敛特性，以及一致和不一致公式；开发依赖于迭代的外推过度松弛以实现非常快速的收敛；以及与信号/图像恢复应用有关的实际和计算问题的研究。