The general properties including accuracy and resolution of linear filtering methods for strain estimation

The vast majority of strain imaging systems applies linear filtering to estimate strain from displacement data. Methods such as piecewise-linear least squares regression and staggered strain estimation have come to be widely known and applied, but the properties of these estimators have rarely (or never) been compared quantitatively. Given their tractable properties, careful analysis of linear filters allows us to make numerous observations that are simple, yet valuable. We consider accuracy and resolving power, which raises the question of whether any particular filter offers the best possible accuracy at a given resolution. Our surprising results provide insight at two levels: They highlight general considerations affecting the type of filter that is appropriate for practical applications, and indicate promising avenues for further research.