Modern digital cameras are quickly reaching the fundamental physical limit of their native resolution. Super-resolution (SR) aims at overcoming this limit. SR combines several images of the same scene into a high resolution image by using differences in sampling caused by camera motion. The main difficulty encountered when designing SR algorithms is that the general SR problem is ill-posed. Assumptions on the regularity of the image are then needed to perform SR. Thanks to advances in regularization priors for natural images, producing visually plausible images becomes possible. However, regularization may cause a loss of details. Therefore, we argue that regularization should be used as sparingly as possible, especially when the restored image is needed for further precise processing. This paper provides principles guiding the local choice of regularization parameters for SR. With this aim, we give an invertibility condition for affine SR interpolation. When this condition holds, we study the conditioning of the interpolation and affine motion estimation problems. We show that these problems are more likely to be well posed for a large number of images. When conditioning is bad, we propose a local total variation regularization for interpolation and show its application to multi-image demosaicking.