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The super-resolution reconstruction (SRR) of images is an ill posed problem. Traditionally, it is treated as a regularized minimization problem. Moreover, one of the major problems concerning SRR is its dependence on an accurate registration. In this paper, we show that a certain amount of registration error may, in fact, be beneficial for the performance of the least mean square SRR (LMS-SRR) adaptive algorithm. In these cases, the regularization term may be avoided, leading to reduction in computational cost that can be important in real-time SRR applications.