Second-order PDE models have been widely used for suppressing multiplicative noise, but they often introduce blocky artifacts in the early stages of denoising. To resolve this, we propose a fourth-order nonlinear PDE model that integrates diffusion and wave properties. The diffusion process, guided by both the Laplacian and intensity values, reduces noise better than gradient-based methods, while the wave part keeps fine details and textures. The effectiveness of the proposed model is evaluated against two second-order anisotropic diffusion approaches using the Peak Signal-to-Noise Ratio (PSNR) and Mean Structural Similarity Index (MSSIM) for images with available ground truth. For SAR images, where a noise-free reference is unavailable, the Speckle Index (SI) is used to measure noise reduction. Additionally, we extend the proposed model to study color images by applying the denoising process independently to each channel, preserving both structure and color consistency. The same quantitative metrics PSNR and MSSIM are used for performance evaluation, ensuring a fair comparison across grayscale and color images. In all the cases, our computed results produce better results compared to existing models in this genre.

翻译：二阶偏微分方程模型已广泛用于抑制乘性噪声，但其在去噪初期常引入块状伪影。为解决该问题，我们提出一个融合扩散与波动特性的四阶非线性偏微分方程模型。该扩散过程同时受拉普拉斯算子和强度值引导，相较梯度类方法能更有效地降低噪声；波动部分则能保留精细细节与纹理。通过峰值信噪比和平均结构相似性指数对图像（含真值参考）进行评估，将该模型与两种二阶各向异性扩散方法进行性能对比。针对无噪声参考的合成孔径雷达图像，采用散斑指数度量降噪效果。此外，通过在各色彩通道独立执行去噪过程，我们将该模型扩展至彩色图像研究，在保持结构信息的同时维持色彩一致性。采用相同的定量指标PSNR与MSSIM进行性能评估，确保灰度与彩色图像间的公平比较。所有实验结果表明，本文计算结果均优于同类现有模型。