Edge is the key information in the process of image smoothing. Some edges, especially the weak edges, are difficult to maintain, which result in the local area being over-smoothed. For the protection of weak edges, we propose an image smoothing algorithm based on global sparse structure and parameter adaptation. The algorithm decomposes the image into high frequency and low frequency part based on global sparse structure. The low frequency part contains less texture information which is relatively easy to smoothen. The high frequency part is more sensitive to edge information so it is more suitable for the selection of smoothing parameters. To reduce the computational complexity and improve the effect, we propose a bicubic polynomial fitting method to fit all the sample values into a surface. Finally, we use Alternating Direction Method of Multipliers (ADMM) to unify the whole algorithm and obtain the smoothed results by iterative optimization. Compared with traditional methods and deep learning methods, as well as the application tasks of edge extraction, image abstraction, pseudo-boundary removal, and image enhancement, it shows that our algorithm can preserve the local weak edge of the image more effectively, and the visual effect of smoothed results is better.