Abstract: According to the local characteristics of image, a variable index variational model is proposed based on [Lp] norm. Firstly, a [Lp] norm operator is designed with structure tensor as adaptive adjustment of parameter. It overcomes the traditional operator sensitive to noise. From the perspective of diffusion, the model is anisotropic. In the smooth region of image, diffusion will be executed with equal spread both along the gradient and tangential, while on the edge of the image, diffusion will be executed only along the tangential. The proposed method has good filtering performance, which can preserve edge details effectively during diffusion. The experimental results demonstrate that for medical image, the new algorithm is superior to other kinds of variable index variational model in the aspect of objective performance evaluation and subjective visual effect.

Key words: variable index variational model, [Lp] norm, structure tensor, anisotropy

摘要： 利用图像局部特征，提出了一种基于[Lp]范数的变指数正则变分模型。采用结构张量作为[Lp]范数算子的自适应调整参数，克服了传统算子对噪声敏感的缺陷。从扩散的角度看，该模型是各向异性的，在图像同质区趋于平滑滤波，在图像渐变区趋于沿边缘方向扩散。该方法在扩散的同时更好地保持图像的边缘细节。实验结果表明，该方法对医学图像的复原效果优于其他几种变指数变分模型，各种客观性能指标也更佳。

关键词: 变指数变分模型, [Lp]范数, 结构张量, 各向异性