In this study, the issue of reconstructing strain fields from corrupted full-field displacement data is addressed. Two approaches are proposed, a global one based on Finite Element Approximation (FEA) and a local one based on Diffuse Approximation (DA). Both approaches are compared on a case study which is supposed difficult (open-hole tensile test). DA provides more stable results, but is more CPU time consuming. Eventually, it is proposed to monitor locally the filtering effect of both approaches, the prospects being an impending improvement of the reconstruction for both approaches.