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

点击翻译按钮获取中文摘要

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.