基于分数阶微积分的噪声检测和图像去噪

目的 提出一种利用分数阶微分梯度检测图像中的噪声点，并用于改进基于分数阶积分的图像去噪算法性能的算法。方法 该算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，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；然后只对被检测出的噪声点，在8个方向上进行分数阶积分运算完成去噪处理。结果 通过在人工图像中分别添加高斯噪声和椒盐噪声以及在自然图像中分别添加高斯噪声和椒盐噪声的去噪对比实验得出相同结论，即只对图像中检测出的噪声点使用分数阶积分运算进行去噪有更好的去噪性能，获得了更好的视觉效果和更高的峰值信噪比。结论 实验结果表明，基于分数阶微分梯度的噪声检测算法对解决图像去噪和保留图像纹理细节之间的矛盾有所帮助。随着对基于分数阶微分梯度噪声检测方法研究的深入，对图像中噪声检测的准确度会进一步提高，这将提供一种用于改进目前去噪算法性能的研究方向。

Noise detection and image de-noising based on fractional calculus

Objective To preserve the image edge detail and avoid introducing false information during noise removal. This study proposes to detect noise point and improve image de-noising performance using the fractional differential gradient based on fractional calculus. Method The convolution of different-directions factional differential gradient template with noisy images is performed to calculate the fractional differential gradient in different directions. Images of the different directions fractional differential gradient are obtained according to a pre-set threshold value. The pixel is determined as a noise point when its gradient occurs along all selected directions. Only the detected noise points are processed by the variable-order fractional integration operator in eight directions. Result De-noising experiments that involve adding Gaussian noise or impulse noise in artificial and natural images arrive at the same conclusion. The visual effects serve as the subjective criteria, and the peak signal-to-noise ratios serve as the objective evaluation criteria. As the integral order v increases, the image de-noising effect increases, the image texture details become smooth, the image appears blurry, and the peak signal-to-noise ratio decreases. In addition, the de-noising based on the detected noise points and the efficiency of removed noise are enhanced with increasing integral order v. Noise detection based on the fractional differential gradient can help solve the contradiction between image de-noising and detail texture preservation. Conclusion The proposed technique improves image noise detection accuracy. The results of this study may serve as a basis for improving the performance of the current de-noising algorithm.