Smoothing images,especially with rich texture,is an important problem in computer vision.Obtaining an ideal result is difficult due to complexity,irregularity,and anisotropicity of the texture.Besides,some properties are shared by the texture and the structure in an image.It is a hard compromise to retain structure and simultaneously remove texture.To create an ideal algorithm for image smoothing,we face three problems.For images with rich textures,the smoothing effect should be enhanced.We should overcome inconsistency of smoothing results in different parts of the image.It is necessary to create a method to evaluate the smoothing effect.We apply texture pre-removal based on global sparse decomposition with a variable smoothing parameter to solve the first two problems.A parametric surface constructed by an improved Bessel method is used to determine the smoothing parameter.Three evaluation measures:edge integrity rate,texture removal rate,and gradient value distribution are proposed to cope with the third problem.We use the alternating direction method of multipliers to complete the whole algorithm and obtain the results.Experiments show that our algorithm is better than existing algorithms both visually and quan-titatively.We also demonstrate our method\'s ability in other applications such as clip-art compression artifact removal and content-aware image manipulation.