It is a great challenge to maintain details while suppressing and eliminating noise of the image. Considering the nonconvexity property of the diffusion function and the hypersensitivity of the Laplace operator to noise in the Y-K model, a fourth-order PDE image denoising model (Con_G&L model) is proposed in this paper. This model is constructed by a new convexity-preserving diffusion function which guarantees the corresponding energy functional has a globally unique minimum solution. At the same time, the Gaussian filter is combined with the Laplace operator in this model, and as a result, the noisy image is smoothed before the diffusion process, which improves the ability of capturing the details and edges of the noisy image greatly. Furthermore, by analyzing the statistical properties of the undecimated discrete wavelet transform (UDWT) coefficients of noisy image, we observe that the noise information is mainly distributed in the high-frequency sub-bands, and based on this, the proposed Con_G&L model is applied in the high-frequency sub-bands of the UDWT to get the denoising method. The proposed method removes the image noise effectively with the image texture and other details of the image being maintained. Meanwhile, the generation of false edges and the staircase effect can be suppressed. A large number of simulation experiments verify the effectiveness of the proposed method.

中文翻译：

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基于保凸扩散函数的PDE模型的UDWT图像去噪方法

在抑制和消除图像噪点的同时保持细节是一个巨大的挑战。考虑到YK模型中扩散函数的非凸性和拉普拉斯算子对噪声的超敏感性，提出了一种四阶PDE图像去噪模型（Con_G＆L模型）。该模型由新的保凸性扩散函数构造而成，该函数确保相应的能量函数具有全局唯一的最小解。同时，在该模型中将高斯滤波器与拉普拉斯算子组合在一起，结果，在扩散过程之前对噪声图像进行了平滑处理，这极大地提高了捕获噪声图像的细节和边缘的能力。此外，通过分析噪声图像的未抽取离散小波变换（UDWT）系数的统计特性，我们观察到噪声信息主要分布在高频子带中，并在此基础上将提出的Con_G＆L模型应用于噪声UDWT的高频子带获得去噪方法。所提出的方法在保持图像的图像纹理和其他细节的情况下有效地去除了图像噪声。同时，可以抑制伪边缘的产生和阶梯效应。大量的仿真实验验证了该方法的有效性。将L模型应用于UDWT的高频子带，得到去噪方法。所提出的方法在保持图像的图像纹理和其他细节的情况下有效地去除了图像噪声。同时，可以抑制伪边缘的产生和阶梯效应。大量的仿真实验验证了该方法的有效性。将L模型应用于UDWT的高频子带，得到去噪方法。所提出的方法在保持图像的图像纹理和其他细节的情况下有效地去除了图像噪声。同时，可以抑制伪边缘的产生和阶梯效应。大量的仿真实验验证了该方法的有效性。