针对L2范数的非局部变分模型在迭代过程中未考虑图像局部梯度信息, 模糊图像细节信息的缺点, 提出了一种基于L1范数的非局部变分模型。首先, 对基于L1范数的非局部变分模型的扩散性能进行了详细的分析。接着, 将该模型应用于退化图像的复原中, 并推导出该模型的Bregman交替迭代求解过程。最后, 通过对比实验, 证明本文提出的L1范数的非局部变分复原模型能更好地重构图像的细节信息, 相对于L2范数的非局部变分模型峰值信噪比提高大于1 dB, 图像复原性能更优。

To overcome the disadvantages that non local total variation based on L2 norm doesn’t consider the nonlocal gradient and can’t effectively recovery image’s texture, a new non local total variation based on L1 norm is proposed. The paper first analyzes the characteristics of the new algorithm, and then employs the new algorithm for image recovery. Bregman iteration scheme is used to optimize the image recovery problems. Finally, the comparing experimental results show that the proposed non local total variation model based on L1 norm reconstructs more image details and gains more 1 dB higher peak signal to noise ratio than non local total variation model based on L2 norm.