A high-resolution image is reconstructed from a sequence of subpixel shifted, aliased low-resolution frames, by means of stochastic regularized super-resolution (SR) image reconstruction. The Tukey (T), Lorentzian (L), and Huber (H) cost functions are employed for the data-fidelity term. The performance of the particular error norms, in SR image reconstruction, is presented. Actually, their employment in SR reconstruction is preceded by dilating and scaling their influence functions to make them as similar as possible. Thus, the direct comparison of these norms in rejecting outliers takes place. The bilateral total variation (BTV) regularization is incorporated as a priori knowledge about the solution. The outliers effect is significantly reduced, and the high-frequency edge structures of the reconstructed image are preserved. The proposed TTV, LTV, and HTV methods are directly compared with a former SR method that employs the L1-norm in the data-fidelity term for synthesized and real sequences of frames. In the simulated experiments, noiseless frames as well as frames corrupted by salt-and-pepper noise are employed. Experimental results verify the robust statistics theory. Thus, the Tukey method performs best, while the L1-norm technique performs inferiorly to the proposed techniques.