关键词: 图像去噪, 分数阶微分, 纹理, 峰值信噪比

Abstract: It is important to preserve fine scale features such as texture in the process of image denoising.In this paper，a new space of functions of fractional bounded variation is defined.Based on the new space of functions of fractional bounded variation and the negative Sobolev space，a fractional variational model for image denoising and the project algorithm for solving the model are proposed.The convergence of the algorithm has been proved in this paper also.The numerical results show that the fractional variational model are very effective in improving the peak signal to noise ratio of noisy image and preserving more fine scale features in the process of denoising.

Key words: image denoising, fractional derivative, texture, Peak Signal to Noise Ratio（PSNR）