### 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

### 去除阶梯效应的[TV+H1+H0]变分分解模型

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.