隐式开曲面上图像噪声去除的变分模型及其Split Bregman算法

The Variational Model of Image Denoising on an Implicit Open Surface and Its Split Bregman Algorithm

采用符号距离函数的零水平集与另一特征函数取值为1的点的交集表达隐式开曲面,借助于内蕴梯度、内蕴散度等概念,建立了开曲面上图像噪声去除的非线性扩散变分模型。通过引入辅助变量和Bregman迭代参数,设计了所提出模型的Split Bregman算法。最终求解所导出的简单梯度降方程和解析形式的近似广义软阈值公式,实现简单、计算效率高。最后通过多个数值算例对所提出的模型和算法的去噪效果进行了验证。

Based on the concepts of intrinsic gradients, intrinsic divergences and using the intersection set of zero level set of a signed distance function and a characteristic function to express the implicit open surface, a variational model of image denoising on an implicit surface is proposed. Its Split Bregman algorithm is designed by introducing an auxiliary variable and a Bregman iterative parameter, which results in solving a simple gradient descent equation and a generalized soft thresholding formula with high efficiency. Some numerical examples validate the model and its algorithm proposed in this paper.