分数阶积分的图像去噪算法

为了在去噪的同时更好地保留图像的细节纹理信息,提出一种分数阶积分的图像去噪算法FIDA。论述了FIDA在135°、90°、45°、0°、180°、315°、270°、225°这8个方向上的分数阶积分掩模的构造,及FIDA的数值运算规则。实验以视觉感知和PSNR值两个主、客观标准对FIDA的去噪性能进行度量,表明FIDA去噪算法的有效性:在去噪的同时对图像的边缘纹理细节信息保留较好,尤其是对灰度变化不大的弱边缘和弱纹理细节信息的有效保留。

Fractional Integral Denoising Algorithm

In this paper, we propose an innovation denoising method named fractional integral denoising algorithm (FIDA) in order to remove noise as largely as possible. Our approach is based on the Riemann-Liouville definition of fractional calculus. The structures of FIDA on eight directions are discussed first. In the first aspect,the structures of fractional integral masks for FIDA on eight directions are constructed respectively. The eight directions used in our algorithm are 135 degrees, 90 degress, 45 degrees, 0 degrees, 180 degrees, 315 degrees, 270 degrees and 225 degrees. In addition, we also present the numerical implementation rules of FIDA for digital image. The experimental results show the effectiveness of our method according to the visual perception and peak signal noise ratio (PSNR) subjectively and objectively. Those results also demonstrate that FIDA can effectively remove noise while preserving the image's significant information simultaneously, especially for the edges and texture information with weak variation on gray intensity.