关键词: 分数阶Riemann-Liouville积分, 柯西公式, 迭代, 去噪掩模, 图像去噪, 阶梯逼近

Abstract: 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.

Key words: Riemann-Liouville (R-L) fractional integral, Cauchy formula, iteration, denoising mask, image denoising, ladder approximation