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本研究的目的是为在集合论信号/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。其主要动机是克服逐次投影法的缺点（MOSP，凸情况下的POCS）：MOSP由于其串行结构，不太适合在并行处理器上实现;如果集合不相交，它提供的解决方案很差（不一致的公式）;并且它收敛缓慢，并且没有用于调整松弛系数以加速迭代的一般规则。一个通用的方法，并行投影（MOPP）正在开发中，目前的投影同时投影到选定的集合和更新是一个宽松的凸组合的投影。研究目标包括，一个正式的研究MOPP的凸和非凸的收敛特性，以及一致和不一致的配方;迭代依赖的发展，外推超松弛，以实现非常快的收敛;和调查有关的信号/图像恢复应用程序的实际和计算问题。