一种基于PDE与结构-纹理分解的图像去噪方法

An Image Denoising Method Based on PDE and Structure-texture Decomposition

结合二阶偏微分方程的ROF图像去噪模型与四阶偏微分方程的LLT去噪模型,提出了一种结构-纹理分解的图像去噪模型。该模型先将噪声图像分解成结构、纹理和噪声三部分,然后利用ROF模型来控制图像的结构部分,利用LLT模型来控制图像的纹理部分,再将两部分耦合则得图像去噪的泛函极小问题。利用变分法获得与泛函极小问题等价的Euler-Lagrange方程后,然后采用梯度下降法求解所得等价方程,从而实现图像去噪。实验仿真结果表明本文提出的模型不仅能有效地去除噪声,而且在去噪的同时尽可能地保持图像的纹理特征。

Based on the noise removal behavior of the second - order ROF model and the fourth - order LLT model, a new denoising model of image structure - texture decomposition is proposed. First, the model decomposes a noise image into three parts：structure, texture and noise. Then the ROF model is used to control structures of the image and the LLT model to control textures of the image. Furthermore, a coupled functional minimization model was introduced to removal noises. Obtaining the equivalent Euler - Lagrange equations of the functional minimizalion by the variational method, we use the gradient decent algorithm to solve the equivalent equations in order to noises. Resuhs of the experiments showed that the proposed model can not only remove noises effectively, hut also keep textures of image as possible .