基于CONVEF的四阶各向异性扩散及图像去噪

偏微分方程在图像去噪中有广泛的应用。传统的二阶偏微分方程虽然具有较好的去噪效果,但是处理得到的结果容易产生阶梯效应,这种现象会引起后续图像处理的误判断。You和Kaveh提出了四阶偏微分方程,该模型可以有效的去除阶梯效应,但由于该算法是一个各向同性的滤波算法,因此图像的边缘保护能力有所降低,使去噪结果中边缘和纹理等细节信息丢失。针对以上缺点,提出了基于卷积虚拟电子场(CONVEF)的四阶偏微分方程。新的模型降低了图像在边缘方向的扩散,得到一个有效的各向异性扩散模型,从而在去噪的同时可以更好的保护图像的边缘、纹理等细节特征。

CONVEF-Based Fourth-Order Anisotropic Diffusion for Image Denoising

Partial differential equations(PDEs) have been justified as effective tools for image denoising. The second-order PDEs are effective for image noise removal but they can lead to staircase effects. These staircases can be falsely detected as edges in the successive image processing. The fourth-order PDE introduced by You and Kaveh can alleviate the staircase effect, but it is an isotropic filter and its edge and texture preserving ability is not satisfactory. In light of this, we introduce the convolutional virtual electric field (CONVEF) into the fourth-order PDE for images restoration. Since the CONVEF based fourth-order model possesses anisotropic properties over the image features, it leads to improvement on noise removal and edge and texture preserving over the original model.