Given that the existing image denoising methods damage the texture details of an image, a new method based on fractional integration is proposed. First, the fractional-order integral formula is deduced by generalizing the Cauchy integral, and then the approximate value of the fractional-order integral operator is estimated by a numerical method. Finally, a fractional-order integral mask operator of any order is constructed in eight pixel directions of the image. Simulation results show that the proposed image denoising method can protect the edge texture information of the image while removing the noise. Moreover, this method can obtain higher image feature values and better image vision after denoising than the existing denoising methods, because a texture protection mechanism is adopted during the iterative processing.

鉴于现有的图像去噪方法会破坏图像的纹理细节，因此提出了一种基于分数积分的新方法。首先，通过推广柯西积分来推导分数阶积分公式，然后通过数值方法估算分数阶积分算子的近似值。最后，在图像的八个像素方向上构造任意阶数的分数阶积分掩码运算符。仿真结果表明，所提出的图像去噪方法能够在去除噪声的同时保护图像的边缘纹理信息。而且，由于在迭代处理过程中采用了纹理保护机制，因此该方法在去噪后可以获得比现有去噪方法更高的图像特征值和更好的图像视觉效果。