Aiming at the unsatisfactory restoration of the detail information such as boundary artifacts for the conventional blind image inversion algorithm does not consider the characteristics of the spatial target image itself, a joint sparse prior constraint blind inversion algorithm based on sparse representation is proposed. Firstly, according to the sparse feature of space object image gradient, the L₀ norm of image gradient is used to extract the salient edge information of image which is beneficial to blur kernel estimation. Secondly, the L_p norm and L₀ norm are used to constrain the gradient distribution and space domain of image, so as to ensure the significant contrast between the pixels of the inverted image and the inclusion of edges and textures in the image. Finally, Laplacian distribution priori is used to constrain the blur kernels in order to ensure the sparseness of the blur kernels. An alternative iteration strategy is adopted to optimize the proposed model, and then the estimated values of the blur core and the space target image are obtained. The experimental results show that, compared with several representative blind inversion algorithms, the proposed method can estimate more accurate blur kernels, and has better restoring ability to image edge and texture details, and achieves better inversion results under both subjective and objective evaluation.