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Volume 24 Issue 6
November  2009
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Fang-Fang Dong, Zhen Liu. A New Gradient Fidelity Term for Avoiding Staircasing Effect[J]. Journal of Computer Science and Technology, 2009, 24(6): 1162-1170.
Citation: Fang-Fang Dong, Zhen Liu. A New Gradient Fidelity Term for Avoiding Staircasing Effect[J]. Journal of Computer Science and Technology, 2009, 24(6): 1162-1170.
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A New Gradient Fidelity Term for Avoiding Staircasing Effect

  • 1Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China
    2Department of Mathematics, Zhejiang University of Technology, Hangzhou 310023, China

Funds: This work is supported by the National Natural Science Foundation of China under Grant No. 10801045, Postdoctoral Foundation of Zhejiang Province under Grant Nos. 1098129 and 109001329 from the Zhejiang University of Technology.
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  • Author Bio:

    Fang-Fang Dong received the B.S. degree from the College of Mathematicsand Information Science, Henan Normal University, China, in 2005.Currently, she is a Ph.D. candidate in the Center of MathematicalSciences, Zhejiang University. Her research interests include imageprocessing and partial differential equation.

    Zhen Liu received the M.S. degree from the Department ofMathematics, Henan University in 2002, and the Ph.D. degree from the Institute ofTheoretical Physics, Chinese Academy of Sciences in 2005. Currently,he is a post-doctoral researcher in the Department of Mathematics, Harvard Universityand instructor in the College of Science, Zhejiang University of Technology.His research interests include image processing, structure-preservingnumerical algorithm, and discrete dynamic system.

  • Received Date: September 04, 2008
  • Revised Date: July 15, 2009
  • Published Date: November 04, 2009
    Abstract
  • Image denoising with some second order nonlinear PDEs often leads to a staircasing effect, which may produce undesirable blocky image. In this paper, we present a new gradient fidelity term and couple it with these PDEs to solve the problem. At first, we smooth the normal vector fields (i.e., the gradient fields) of the noisy image by total variation (TV) minimization and make the gradient of desirable image close to the smoothed normals, which is the idea of our gradient fidelity term. Then, we introduce the Euler-Lagrange equation of the gradient fidelity term into nonlinear diffusion PDEs for noise and staircasing removal. To speed up the computation of the vectorial TV minimization, the dual approach proposed by Bresson and Chan is employed. Some numerical experiments demonstrate that our gradient fidelity term can help to avoid the staircasing effect effectively, while preserving sharp discontinuities in images.
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