Image self-similarity property is important to super-resolution reconstruction. However, how to effectively exploit the self-similarity information to reconstruct an underlying high-resolution image is still a challenging problem. The authors propose a novel model for solving the single image upsampling problem with the self-similarity property. First, the authors construct a statistical prior that requires maximising the similarity between the low- and high-resolution image pairs. Then, the authors develop an alternative Gaussian approximation solver based on the Gaussian mixture model to find the optimal high-resolution output. To obtain a better performance, the authors summarise some refined implementation skills to raise the reconstruction quality. For demonstration, a series of objective and subjective measurements are used to evaluate the performance of the model.