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Abstract Although the traditional TV (Total Variation) model owns excellent image denoising ability, there are staircase effect problems for TV model. In this article, two detection operators for staircase effect problem are proposed. The staircase effect problem can be solved effectively by introducing two operators into traditional TV model. On the basis, it proposes an adaptive total variation model for image denoising. When dealing with image edge, it can still use the traditional TV model. Its purpose is to maintain the advantages in edge protection for TV model. When it is in the smooth area of image, linear diffusion is used to avoid the staircase effect. Keywords Image denoising variation




Staircase effect




Detection operator




Total

1 Introduction In the field of image processing, image denoising technology has been the focus of the study. In recent years, the image denoising methods based on partial differential equation had made great breakthrough. In 1990, Perona and Malik proposed the image denoising method based on anisotropic diffusion, called PM model [1]. The model used Laplace operator instead of the traditional nonlinear operator. Though it had achieved good denoising effect, there were serious step effect problems. In order to remedy the defects of the PM model, You and Kaveh proposed a four order partial differential equation, named Y-K model. But the Y-K model had brought the new “dot effect” problems [2]. And the partial differential equation of higher order increases the computational complexity greatly. In 1992, Rudin, Osher and Fatemi proposed the image denoising methods of total variation, called TV model [3]. G. Xiaoling (&)
Y. Jie
Z. Xiao School of Information Science and Engineering, Hebei North University, Zhangjiakou 075000, Hebei, China e-mail: [email protected] © Springer Science+Business Media Singapore 2016 J.C. Hung et al. (eds.), Frontier Computing, Lecture Notes in Electrical Engineering 375, DOI 10.1007/978-981-10-0539-8_16

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The TV model was a functional minimization problem substantially. It can control the image to diffusion in the gradient direction orthogonal. The TV model made a qualitative leap comparised with the PM model and the Y-K model. Although the TV model showed strong advantage in the image denoising, it also appeared serious staircase effect problems in the smooth area.

2 Traditional TV Model Traditional TV(Total Variation) model was proposed by Rudin, Osher and Fatemi. It was also known as the ROF model. And it was a image denoising model based on partial differential equation [4]. The equation is as follows: Z  ETV ¼ X

 1 2 jruj þ kðu  u0 Þ dxdy 2

ð1Þ

This equation can be further expanded into the form of the following:  2 uxx uy  2ux uy uxy þ uyy ðux Þ2 @u 1 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  kðu  u0 Þ  2  2ffi @t ð ux Þ 2 þ uy ðux Þ2 þ uy

ð2Þ

uxx u2y 2ux uy uxy þ uyy u2x u2x þ u2y

is the second order derivative along the tangent direction of the .qffiffiffiffiffiffiffiffiffiffiffiffiffiffi u2x þ u2y is the diffusion coefficient. I