Convergence and Perturbation Resilience of Dynamic String-Averaging Projection Methods

We consider the convex feasibility problem (CFP) in Hilbert space and concentrate on the study of string-averaging projection (SAP) methods for the CFP, analyzing their convergence and their perturbation resilience. In the past, SAP methods were formulated with a single predetermined set of strings and a single predetermined set of weights. Here we extend the scope of the family of SAP methods to allow iteration-index-dependent variable strings and weights and term such methods dynamic string-averaging projection (DSAP) methods. The bounded perturbation resilience of DSAP methods is relevant and important for their possible use in the framework of the recently developed superiorization heuristic methodology for constrained minimization problems.Comment: Computational Optimization and Applications, accepted for publicatio

Symmetry of disciform scars in bilateral age-related macular degeneration.

The size of the final macular scar in subretinal neovascularisation (SRNV) is one of the most important determinants of final visual function in patients with subfoveal disease. We studied patients with bilateral macular scars from age-related subretinal neovascular membranes retrospectively in order to determine whether or not fellow eyes behave similarly. We found a significant correlation between eyes in terms of final scar size (r = 0.50, p less than 0.01). We found that 50% of fellow eyes with large macular scars (greater than 3 x 10(6) microns2) had similar sized lesions, while only 16% of fellow eyes with small macular scars (less than 0.5 x 10(6) microns2) had large scars (p less than 0.01). We discuss the significance of these findings in relation to the pathogenesis of subretinal neovascular membranes, and their implications for treatment