In order to obtain a super-resolution prior model with higher confidence and balance the reconstructed results between noise and details, this paper establishes a Gauss-Lorenz hybrid prior model based on the mixed sparse representation framework. This prior model's advantages and specific application schemes are studied. Firstly, according to the type of prior information, the advantages and problems of some traditional algorithms are introduced. Next, the statistical characteristics of different components of the image are modeled separately. Then, based on the analysis of the mixed sparse framework, the Gauss-Gibbs prior and the Lorenz prior, the super-resolution algorithm based on the Gauss-Lorenz hybrid prior under the group sparse framework is illustrated. Finally, the implementation and the final iteration scheme are introduced. The aim of noise suppression while maintaining details in the reconstruction process has been completed, which can be used for in more complex environments with super-resolution resconstruction.