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 quantitatively. We also demonstrate our method’s ability in other applications such as clip-art compression artifact removal and content-aware image manipulation.

平滑图像，尤其是具有丰富纹理的图像，是计算机视觉中的重要问题。由于纹理的复杂性，不规则性和各向异性，难以获得理想的结果。此外，图像中的纹理和结构还共享一些属性。保留结构并同时去除纹理是一项艰难的折衷。为了创建理想的图像平滑算法，我们面临三个问题。对于纹理丰富的图像，应增强平滑效果。我们应该克服图像不同部分的平滑结果不一致。有必要创建一种评估平滑效果的方法。我们使用基于全局稀疏分解并带有可变平滑参数的纹理预去除来解决前两个问题。通过改进的贝塞尔方法构造的参数化曲面用于确定平滑参数。为解决第三个问题，提出了三种评估措施：边缘完整性率，纹理去除率和梯度值分布。我们使用乘法器的交替方向方法来完成整个算法并获得结果。实验表明，无论从视觉上还是从数量上来说，我们的算法都优于现有算法。我们还展示了我们的方法在其他应用程序中的能力，例如剪贴画压缩伪像去除和内容感知图像处理。我们使用乘法器的交替方向方法来完成整个算法并获得结果。实验表明，无论从视觉上还是从数量上来说，我们的算法都优于现有算法。我们还展示了我们的方法在其他应用程序中的能力，例如剪贴画压缩伪像去除和内容感知图像处理。我们使用乘法器的交替方向方法来完成整个算法并获得结果。实验表明，无论从视觉上还是从数量上来说，我们的算法都优于现有算法。我们还展示了我们的方法在其他应用程序中的能力，例如剪贴画压缩伪像去除和内容感知图像处理。