The paper considers the problem of multi-frame super-resolution under applicative noise which generates distributed regions of outlying observations in low resolution images. The analysis of existing solutions is performed. They include algorithms based on spin-glass models and Markov random fields used to remove applicative noise. The authors suggest their own approach, which involves using a recurrent algorithm of quasi-linear optimal filtering of a sequence of low resolution images together with superpixel segmentation performed in order to determine the regions damaged by applicative noise. The considered algorithms are compared as applied to a set of test images. The results of the experiment demonstrate that the suggested approach allows for more accurate recovery of HR images than the existing analogues.