带边缘补偿的分数阶积分图像去噪算法

针对分数阶积分的图像去噪算法容易丢失图像细节特征的问题，提出了一种带边缘补偿的分数阶积分图像去噪算法。介绍了分数阶积分算子具有尖锐的低通性能，将分数阶Cauchy公式引入到数字图像去噪中，并利用斜坡法来近似计算分数阶积分的数值解。在迭代去噪的过程中，该算法在图像信噪比（SNR）上升阶段，设定较高微小积分阶次来构建去噪掩模；在图像信噪比开始下降阶段，设定较低微小积分阶次来构建去噪掩模，并采用边缘补偿机制来部分恢复图像的细节信息。由仿真实验可知，提出的图像去噪算法由于在迭代去噪的过程中采用了不同的分数阶积分阶次和边缘补偿机制，与已有的降噪算法相比，可以在去除噪声的同时适当恢复原始图像的细节信息，由此获得更高的信噪比和更佳的视觉效果。

Image denoising algorithm using fractional-order integral with edge compensation

To solve the problem of losing edge and texture information in the existing image denoising algorithms based on fractional-order integral, an image denoising algorithm using fractional-order integral with edge compensation was presented. The fractional-order integral operator has the performance of sharp low-pass. The Cauchy integral formula was introduced into digital image denoising, and the image numerical calculation of fractional-order integral was achieved by the method of slope approximation. In the process of iterative denoising, the algorithm built denoising mask by setting higher tiny fractional-order integral order at the rising stage of image Signal-to-Noise Ratio (SNR); and the algorithm built denoising mask by setting lower small fractional-order integral order at the declining stage of image SNR. Additionally, it could partially restore the image edge and texture information by the mechanism of edge compensation. The image denoising algorithm using fractional-order integral proposed in this paper makes use of different strategies of the fractional-order integral order and edge compensation mechanism in the process of iterative denoising. The experimental results show that compared with traditional denoising algorithm, the denoising algorithm proposed in this paper can remove the noise to obtain higher SNR and better visual effect while appropriately restoring the edge and texture information of image.