Computer Engineering and Applications ›› 2015, Vol. 51 ›› Issue (18): 1-6.

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TV+H1+H0 variational decomposition for taircase reduction

FANG Zhuang1,2, TANG Liming1, CHEN Shiqiang1, XIANG Changcheng1   

  1. 1.School of Science, Hubei University for Nationalities, Enshi, Hubei 445000, China
    2.School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Online:2015-09-15 Published:2015-10-13


方  壮1,2,唐利明1,陈世强1,向长城1   

  1. 1.湖北民族学院 理学院,湖北 恩施 445000
    2.武汉大学 数学与统计学院,武汉 430072

Abstract: A[ TV+H1+H0 ]variational image decomposition model is proposed to reduce the staircase that often appears in Total Variation(TV) based models in image denoising. The model adopts TV to measure the piecewise constant component and[ H1 ]seminorm to measure the piecewise smooth component of image, respectively. And then, the image structure is represented by the sum of TV piece and[ H1 ]piece. Due to the introduction of[ H1 ]piece that is piecewise smooth, the staircase can be reduced in structure component. In addition, the nontrivial property of the proposed model is proven and an alternating iteration algorithm is introduced to solve the model numerically. The proposed model is used to image denoising. The experimental results on both noisy synthetic and real images show that the proposed model, compared with classical ROF model and PVD model, can achieve better performance.

Key words: Total Variation(TV), ROF model, nontrivial property, variational decomposition, image denoising

摘要: 针对基于全变分(Total Variation,TV)极小的变分分解中,结构分量中容易出现阶梯现象而降低图像视觉效果的缺点,提出了一个去除阶梯效应的[TV+H1+H0]变分分解模型。新模型分别采用TV刻画结构分量的分片常值,采用[H1]半范数刻画分片光滑,则图像结构被看成是TV分量与[H1]分量之和。由于新的结构中包含了分片光滑的[H1]分量,所以可以一定程度去除阶梯现象。理论证明了模型的解的非平凡性,并且采用交替迭代算法对模型进行了数值求解。实验中以噪声人造图像和自然图像为实验对象,将分解模型应用到图像去噪,相对于经典的ROF模型和PVD模型,新模型取得了明显的优势。

关键词: 全变分(TV), ROF模型, 非平凡性, 变分分解, 图像去噪