基于法向光滑和曲面拟合的高阶去噪模型求解

Higher-Order Denoising Model Solving Based on Normal Smoothing and Surface Fitting

摘要: 高阶变分方程在有效抑制TV模型去噪中的阶梯效应方面表现出色，但其求解过程往往较为复杂。本文针对单位法向量梯度的L₁范数做正则项的高阶变分模型求解问题，提出利用法向光滑和曲面拟合两步将其转化为两个低阶变分模型来求解。对这两个低阶变分模型构造了有效的数值方法，实验结果表明本文提出的方法在峰值信噪比、结构相似性以及计算时间上均优于传统的TV模型。峰值信噪比与结构相似性比TV模型分别高0.3 dB、0.02 dB，在时间上也表现出了较大的差别。

Abstract: Higher-order variational equations are excellent in effectively suppressing the step effect in denoising TV models, but their solution process is often complicated. In this paper, for the problem of solving the higher-order variational model with the L1-parameter of the unit normal vector gradient as a regular term, it is proposed to use two steps of normal smoothing and surface fitting to transform it into two lower-order variational models to solve it. An effective numerical method is constructed for these two low-order variational models, and the experimental results show that the method proposed in this paper outperforms the traditional TV model in terms of peak signal-to-noise ratio, structural similarity, and computation time. The peak signal-to-noise ratio and structural similarity are 0.3 dB and 0.02 dB higher than the TV model, respectively, and also show a large difference in time.