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Numerical Algorithms for Discrete Models of Image Denoising

  • Author / Creator
    Zhao, Hanqing
  • In this thesis, we develop some new models and efficient algorithms for image denoising. The total variation model of Rudin, Osher, and Fatemi(ROF) for image denoising is considered to be one of the most successful deterministic denoising models. It exploits the non-smooth total variation (TV) semi-norm to preserve discontinuities and to keep the edges of smooth regions sharp. Despite its simple form, the TV semi-norm results in a strongly nonlinear Euler-Lagrange equation and poses computational challenge in solving the model efficiently. Moreover, this model produces so-called staircase effect. In this thesis, we propose several new algorithms and models to solve these problems. We study the discretized ROF model and propose a new algorithm which does not involve partial differential equations. Convergence of the algorithm is analyzed. Numerical results show that this algorithm is efficient and stable. We then introduce a denoising model which utilizes high-order difference to approximate piece-wise smooth functions. This model eliminates undesirable staircases, and improves both visual quality and signal-to-noise ratio. Our algorithm is generalized to solve the high-order models. A relaxation technique is proposed for the iteration scheme, aiming to accelerate our solution process. Finally, we propose a method combining total variation and wavelet packets to improve performance on texture-rich images. The ROF model is utilized to eliminate noise, and a wavelet packet transform is used to enhance textures. The numerical results show that the combinational method exploits the advantages of both total variation and wavelet packets.

  • Subjects / Keywords
  • Graduation date
    2010-11
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R31X3M
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Doctoral
  • Department
    • Department of Mathematical and Statistical Sciences
  • Supervisor / co-supervisor and their department(s)
    • Jia, Rong-Qing (Mathematics)
  • Examining committee members and their departments
    • Han, Bin (Mathematics)
    • Chui, Charles (Mathematics, University of Missouri - St. Louis)
    • Mandal, Mrinal (Electrical and Computer Engineering)
    • Li, Michael (Mathematics)
    • Jia, Rong-Qing (Mathematics)