用噪声检测算法改进理想低通滤波器

针对图像去噪算法存在滤除噪声与保留图像边缘细节之间的矛盾，提出了一种使用基于分数阶微分梯度的随机噪声检测算法来提高理想低通滤波器的去噪性能的方法。首先，使用不同方向的分数阶微分梯度模板与含噪声图像进行卷积，计算出图像在不同方向上的分数阶微分梯度；然后，依据预先设定的阈值获得不同方向的分数阶微分梯度检测图，将在所有选定方向上梯度都发生跳变的像素点判定为噪声点；最后，只对图像中被检测出的噪声点用理想低通滤波器进行滤波，可使图像在去除噪声和保留图像细节两方面同时获得较优的效果。实验结果表明，所提算法不仅可以获得更好的视觉效果，而且去噪后图像的峰值性噪比(PSNR)表明去噪后的图像更接近原始图像，使用理想低通滤波器获得的最大PSNR为29.0893dB，所提算法获得的最PSNR为34.7027dB。将分数阶微积分用于图像去噪，为提高图像去噪性能提供了一个新的研究方向。

Improving ideal low-pass filter with noise detection algorithm

For the contradiction between filtering noise and preserving image detail in image denoising algorithms, a random noise detection algorithm based on fractional differential gradient, was proposed to improve denoising performance of the ideal low-pass filter in this paper. Firstly, the fractional differential gradient templates of different directions were used to convolve with noisy images, and calculate fractional differential gradients in different directions. Then according to a pre-set threshold value, the fractional differential gradient detection figures in different directions could be obtained. If the pixel gradients occurred hopping in all selected directions, and this pixel was determined to be a noise pixel. Finally, only the detected noise pixels were processed by ideal low-pass filter. The denoised image could get a better effect of removing the noise and preserving image detail at the same time. The experimental results show that the proposed algorithm can get a better visual effect, the Peak Signal-to-Noise Ratio (PSNR) of denoised image indicates the denoised image is more closer to the original image: The maximum PSNR by using the ideal low-pass filter is 29.0893dB, meanwhile the maximum PSNR obtained by the proposed algorithm is 34.7027dB. It is an exploration of fractional calculus for image denoising, and provides a new research direction to improve performance of image denoising.