在图像去噪过程中更多地保持图像的细节信息是很重要的。将基于梯度的总变分图像去噪模型推广到基于分数阶微分的模型，并根据分数阶微分与卷积运算在特殊情形下具有相同的离散格式这一特点，提出了一种易于数值计算的基于卷积积分的图像去噪变分模型，实验结果表明，新模型在提高图像信噪比的同时，可以更好地保持图像的细节信息。

It is important to preserve more detailed information in image denoising. In this paper, we extend the total variation model for image denoising is which based on gradient to a new model based on fractional derivative, and then making use of the characteristic that fractional derivative and convolution integral have the same discrete formula in certain situation,We propose a variational model based on convolution integral which can be computed easily. The numerical results show that our model can not only better improve the PSNR of image,but also preserve more detailed information.