提出四阶灰度指示扩散模型，有效去除斑点噪声并保留纹理细节。
New Fourth-Order Grayscale Indicator-Based Telegraph Diffusion Model for Image Despeckling
- 融合扩散与波动特性，用梯度和强度双重引导降噪。
- 在真实图像上PSNR和MSSIM均优于传统二阶模型。
- 适用于灰度与彩色合成图像，适合遥感影像去斑点处理。
二阶偏微分方程（PDE）模型常用于抑制乘性噪声，但早期去噪易产生块状伪影。为此，本文提出一种结合扩散与波动特性的四阶非线性PDE模型。扩散过程由拉普拉斯算子和像素强度共同引导，比基于梯度的方法更有效地降噪；波动部分则有助于保持细小结构与纹理。在有真实参考图像的场景中，采用峰值信噪比（PSNR）与平均结构相似性指数（MSSIM）评估性能；对于无真值的SAR图像，则使用斑点指数（SI）衡量去噪效果。此外，将该模型扩展至彩色图像时，独立对每个通道进行去噪，以保持结构与色彩一致性。所有测试中，本方法在定量指标上均优于同类模型。
原文摘要 · Abstract (English)
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.
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