基于分数阶Riemann-Liouville积分的图像去噪

为了在获得更好去噪性能的同时更多地保留图像纹理信息，介绍了分数阶Riemann-Liouville(R-L)积分算子在信号滤波中的作用，将分数阶R-L积分理论引入到数字图像去噪中，并利用阶梯逼近方法来实现数值计算。模型通过设定微小的积分阶次来构建相应的图像去噪掩模，由此实现噪声图像的局部微调，并利用迭代的思想来控制模型的去噪强度，从而获得较好的图像去噪效果。实验结果表明，基于分数阶R-L积分的图像去噪算法较传统的去噪方法不仅可以提高图像的信噪比(SNR)，所提出的算法去噪后图像的信噪比为18.3497dB，较传统去噪方法最低也提升了大约4%，而且可以更好地保留图像的弱边缘和纹理等细节信息。

Image denoising based on Riemann-Liouville fractional integral

To preserve more image texture information while obtaining better denoising performance, the Riemann-Liouville (R-L) fractional integral operator was described in signal processing. The R-L fractional integral theory was introduced into the digital image denoising, and the method of ladder approximation was used to achieve numerical calculation. The model constructed the corresponding mask of image denoising by setting a tiny integral order to achieve local fine-tuning of noise image, and it could control the effect of image denoising by the way of iteration to get better denoising results. The experimental results show that, compared with the traditional image denoising algorithms, the image denoising algorithm based on R-L fractional integral proposed in this paper can enhance the Signal-to-Noise Ratio (SNR) of image, the SNR of denoising image with the algorithm proposed in this paper can reach 18.3497dB, and the lowest growth rate compared to the traditional denoising algorithms increases about 4%. In addition, the proposed algorithm can better retain weak image edge and texture details information of image.