Most of the norms used in the field of digital image (and volume) correlation to register
two images (or volumes) lead to ill-posed problems. One of the frequent solutions is to
enforce a restricted kinematics requiring a compromise between the richness of the
solution (i.e., the spatial resolution) and the measurement uncertainty. An alternative
route is to use a displacement norm that permits to alleviate this compromise by the means
of a mechanical regularization used when the gray levels do not give enough information.
It is then possible to compute a displacement vector for each pixel or
voxel, inducing lower residuals (in terms of experimental data) while
decreasing the noise sensitivity. The resolution performance of these different approaches
is discussed, and compared for the analysis of a tensile test on a cast iron specimen
based on a pair of tomographic images. As representative reconstructed volumes lead to a
large number of degrees of freedom, a dedicated GPU computational strategy has been
developed and implemented.