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A kurtosis-based super-resolution image reconstruction algorithm is proposed in this paper. Firstly, we give the definition of the kurtosis image and analyze its two properties: (i) the kurtosis image is Gaussian noise invariant, and (ii) the absolute value of a kurtosis image becomes smaller as the the image gets smoother. Then we build a constrained absolute local kurtosis maximization function to estimate the high-resolution image by fusing multiple blurred low-resolution images corrupted by intensive white Gaussian noise. The Lagrange multiplier is used to solve the combinatorial optimization problem. Experimental results demonstrate that the proposed method is better than the conventional algorithms in terms of visual inspection and robustness, using both synthetic and real world examples under severe noise background. It has an improvement of 0.5 to 2.0 dB in PSNR over other approaches.