目的 为了在图像平滑过程中达到更好地保留边缘去除细节效果,提出一种以像素强度和梯度的稀疏特性为双重约束的图像平滑算法。方法 该算法首先构造一个像素强度和梯度的0-范数函数,作为平滑模型的约束项;然后采用半二次变量分裂法引入辅助变量,构造最终的较易求解的平滑模型;最后利用交替最小化算法求解该模型,并在傅里叶频域内求解平滑图像的解析解,以加快算法的运行速度。结果 在自然图像上进行的平滑实验并与其他算法对比表明,本文的算法时间仅需3.42 s,比双边滤波算法快7.85 s,能够较好地满足图像平滑保留边缘去除细节的要求以及计算效率的要求。结论 本文以强度和梯度的稀疏特性为约束的图像平滑算法能够较好地去除图像中不重要的细节,保留图像的边缘特征,较好地实现了图像的平滑效果,适用于含有复杂背景噪声的图像平滑去噪及边界增强。

Objective To achieve an improved edge-preserving effect in the image smoothing process, a novel image smoothing algorithm using the sparse feature of pixel intensity and gradient as dual constraints is proposed. Method A pixel intensity and gradient function based on L0 norm is set as a constraint term of the smoothing model. Two auxiliary variables are introduced through half-quadratic splitting strategy to construct the final smoothing models. Finally, the alternating minimization algorithm is applied to solve the model, and a closed-form solution of the smoothed image is obtained in Fourier frequency to accelerate the speed of the algorithm. Result Smoothing experiments on natural images show that the proposed algorithm can better meet the requirements of edge preserving, denoising effects, and real-time applications; the proposed algorithm requires only 3.42 s and is 7.85 s faster than the bilateral filtering algorithm. The experiments demonstrate that the proposed algorithm outperforms other smoothing algorithms. Conclusion The algorithm can remove unimportant details, retain the image edge features in the image, and achieve the effect of image smoothing. Thus, it is applicable to smoothing, denoising, and boundary enhancement of images with a complex background.