Outlier Removal Power of the L1-Norm Super-Resolution

Super-resolution combines several low resolution images having different sampling into a high resolution image. L1-norm data fit minimization has been proposed to solve this problem in a robust way. The outlier rejection capability of this methods has been shown experimentally for super-resolution. However, existing approaches add a regularization term to perform the minimization while it may not be necessary. In this paper, we recall the link between robustness to outliers and the sparse recovery framework. We use a slightly weaker Null Space Property to characterize this capability. Then, we apply these results to super resolution and show both theoretically and experimentally that we can quantify the robustness to outliers with respect to the number of images.