一种新的分数阶偏微分方程图像去噪模型

A New Fractional Partial Differential Equation Model for Image Denoising

为克服传统整数阶ROF图像去噪模型在平坦区的阶梯效应,四阶的LLT图像去噪模型虽然能抑制阶梯效应但是去噪后图像视觉效果不好的缺点,提出了一种新的分数阶偏微分方程的图像去噪模型.讨论了新模型中分数阶阶次v与p值对去噪结果的影响,并从主观视觉效果和客观峰值信号比（PSNR）方面对图像的去噪效果进行了评价.实验证明,与二阶的ROF模型,四阶的LLT模型以及分数阶的ROF模型相比,新的去噪模型在最优的分数阶阶次v与一定范围内P值的作用下能够更好的抑制阶梯效应,并且能够在提高图像的峰值信噪比的同时更好的保留图像的边缘和纹理等细节的优点.

To overcome the “staircase effect” brought by the traditional integer order ROF image denoising model in smooth regions and the poor visual effect brought by LLT image denoising model although which can suppress the staircase effect, we proposed a new image denoising model with the fractional partial differential equations in this paper, and discussed the influence of fractional order v and p value in the new model on the denoising results which was then well evaluated by comparison from the aspects of subjective visual effects and PSNR. Experiments show that compared with the two-order ROF model, the four-order LLT model as well as the fractional order ROF model, the new model not only can suppress the staircase effect, but also can improve the image of the peak signal to noise ratio, and can better preserve the image edge and texture details under the action of the optimal fractional order v and appropriate p values.