Non‐linear fourth‐order telegraph‐diffusion equation for noise removal
Weili Zeng, Xiaobo Lu, Xianghua Tan · IET Image Processing · 2013
Fourth‐order partial differential equations (PDEs) for noise removal are able to provide a good trade‐off between noise removal and edge preservation, and can avoid blocky effects often caused by second‐order PDE. In this study, the authors propose a fourth‐order telegraph‐diffusion equation (TDE) for noise removal. In the authors method, a domain‐based fourth‐order PDE is proposed, which takes advantage of statistic characteristics of isolated speckles in the Laplace domain to segment the image domain into two domains: speckle domain and non‐speckle domain. Then, depending on the domain type, they adopt different conductance coefficients in the proposed fourth‐order PDE. The proposed method inherits the advantage of fourth‐order PDE which is able to avoid the blocky effects widely seen in images processed by second‐order PDE. Furthermore, a TDE processing scheme is derived from previously proposed domain‐based fourth‐order PDE by adding second time derivative, which results in better edge preservation, whereas yielding better improvement in signal‐to‐noise ratio and low noise sensitivity. Experimental results show the effectiveness of the proposed method.