基于感知的使用SDE的乘性噪声去除
Perception-based multiplicative noise removal using SDEs
AI总结：
本研究针对SAR等图像中的乘性噪声问题，提出基于SDE扩散模型的去噪方法，通过对数域几何布朗运动建模与Fokker-Planck方程推导逆过程，实验表明其感知指标优于现有方法，传统指标性能具竞争力。
摘要：
乘性噪声，也称为散斑噪声或胡椒噪声，通常会影响合成孔径雷达（SAR）、激光或光学透镜生成的图像。与通常由热过程或外部因素产生的加性噪声不同，乘性噪声是系统固有的，源于漫反射的波动。这些波动会导致同一信号的多个幅度各异的副本被叠加在一起。因此，散斑抑制（即去除乘性噪声）需要采用与加性噪声去除不同的技术。\n 在本文中，我们提出了一种使用基于随机微分方程（Stochastic Differential Equations，SDE）的扩散模型的新方法来解决乘性噪声问题。我们证明了乘性噪声可以在对数域中被有效地建模为几何布朗运动过程。利用福克-普朗克（Fokker-Planck）方程，我们推导出了用于图像去噪的相应逆过程。为了验证我们的方法，我们在两个不同的数据集上进行了大量实验，将我们的方法与经典信号处理技术以及当代基于CNN的去噪模型进行了比较。我们的结果表明，所提出的方法在FID和LPIPS等基于感知的指标上显著优于现有方法，同时在PSNR和SSIM等传统指标上保持了具有竞争力的性能。
英文摘要：
Multiplicative noise, also known as speckle or pepper noise, commonly affects images produced by synthetic aperture radar (SAR), lasers, or optical lenses. Unlike additive noise, which typically arises from thermal processes or external factors, multiplicative noise is inherent to the system, originating from the fluctuation in diffuse reflections. These fluctuations result in multiple copies of the same signal with varying magnitudes being combined. Consequently, despeckling, or removing multiplicative noise, necessitates different techniques compared to those used for additive noise removal. In this paper, we propose a novel approach using Stochastic Differential Equations based diffusion models to address multiplicative noise. We demonstrate that multiplicative noise can be effectively modeled as a Geometric Brownian Motion process in the logarithmic domain. Utilizing the Fokker-Planck equation, we derive the corresponding reverse process for image denoising. To validate our method, we conduct extensive experiments on two different datasets, comparing our approach to both classical signal processing techniques and contemporary CNN-based noise removal models. Our results indicate that the proposed method significantly outperforms existing methods on perception-based metrics such as FID and LPIPS, while maintaining competitive performance on traditional metrics like PSNR and SSIM.
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