具有纹理保持能力的四阶偏微分方程去噪方法

Texture preserving fourth order PDE-based image denoising

虽然四阶偏微分方程图像去噪方法能得到较好的分段光滑的结果,但这类方法常破坏图像的纹理信息。提出了一种具有保持图像纹理信息能力的四阶偏微分方程去噪模型。利用垂直于梯度方向的图像二阶导数设计了一种新的代价函数。证明了该函数解的存在性与唯一性并给出了其对应的Euler-Lagrange方程。在实验方面,用大量真实的纹理图像验证了新方法。实验结果表明,新方法在去噪的同时图像的边缘与细节得到了较好的保持。

While image noise removal methods based on the fourth order partial differential equations show their advantages in producing piecewise smooth results,they are sensitive to the high frequency components in the images and destroy image texture prominently.This paper proposes a texture preserving fourth order partial differential equations based image denoising model.At first,a cost function relying on second derivatives of image intensity function in the direction orthogonal to the gradient is proposed.Then,it proves the existence and uniqueness of this function, and the proposed fourth order partial differential equations are derived from it using gradient descent flow and Euler-Lagrange function in succession.At last,the method is tested on a broad range of real images and demonstrates good noise suppression without destruction of important edges and textures in the image.