基于自适应投影算法的分数阶全变分去噪模型*

为了在图像去噪的同时较好地保持图像的弱边缘和纹理细节，提出基于自适应投影算法的分数阶全变分模型.该模型使用Grünwald-Letnikov分数阶微分替代全变分正则项中的一阶导数，通过将图像投影在全变分球体上以解决分数阶全变分的优化问题.并根据图像的局部信息将图像分为纹理区域和非纹理区域，从而自适应计算投影方法中的软阈值.理论分析和实验均表明，文中方法在去除噪声的同时可以消除块效应，并且能有效保持图像的弱边缘和纹理细节.

Fractional Total Variation Denoising Model Based on Adaptive Projection Algorithm

To preserve weak edges and texture details of an image during image denoising, a fractional order total variation denoising model is presented based on adaptive projection algorithm. Firstly, Grünwald-Letnikov fractional order differential is used as a substitute for the first order derivative in the regularization term of total variation model. Secondly, the image is projected to a total variation ball to handle the optimization problem. The image is divided into the texture area and the non-texture area according to the local information of the image, and thus soft threshold values can be calculated adaptively. Both theoretical analysis and experimental results show that the proposed method eliminates the block effect as well as preserves the texture details effectively for removing noise.