Abstract: Combining fractional order differential theory with total variation method, a new image denoising model was proposed, which was based on fractional Partial Differential Equation (PDE). Current Total Variation (TV) model was good at denoising and keeping the characteristics of image edge. This new model effectively inherited these advantages; at the same time, it used the fractional differential amplitude-frequency and retained texture details of smooth region effectively. The simulation results show that on one hand, compared with the existing denoising methods, the new model can not only suppress noise better, but also keep the characteristics of image edge better; especially, it is better than the existing integer order partial differential methods since it can retain more texture details. On the other hand, seen from the comparative experiments of PSNR, the model is more effective and practical on image denoising.

Key words: image denoising, fractional differential, Total Variation (TV) model

摘要： 将分数阶微分理论和全变分方法相结合应用于图像去噪，提出了一种基于分数阶偏微分方程的图像去噪新模型。该模型很好地继承了现有的全变分(TV)模型去噪效果与保持图像边缘细节特征的优点，同时利用分数阶微分运算特有的幅频特性优势，较好地保留了图像平滑区域中灰度变化不大的纹理细节。实验结果表明：一方面，与现有去噪方法相比，新模型不仅具有较强的抑制噪声能力，而且能较好地保持图像边缘特征，还能保留更多的图像纹理细节信息，优于常用的整数阶偏微分图像去噪方法；另一方面，从峰值信噪比的对比实验可以看出该模型去噪效果优于其他方法，较好地达到了去噪目的，是一种有效、实用的图像去噪模型。

关键词: 图像去噪, 分数阶微分, 全变分模型