Regularized Shock Filters and Complex Diffusion

  • Guy Gilboa
  • Nir A. Sochen
  • Yehoshua Y. Zeevi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2350)


We address the issue of regularizing Osher and Rudin’s shock filter, used for image deblurring, in order to allow processes that are more robust against noise. Previous solutions to the problem suggested adding some sort of diffusion term to the shock equation. We analyze and prove some properties of coupled shock and diffusion processes. Finally we propose an original solution of adding a complex diffusion term to the shock equation. This new term is used to smooth out noise and indicate inflection points simultaneously. The imaginary value, which is an approximated smoothed second derivative scaled by time, is used to control the process. This results in a robust deblurring process that performs well also on noisy signals.


Shock filters deblurring denoising image enhancement complex diffusion image features 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Guy Gilboa
    • 1
  • Nir A. Sochen
    • 2
  • Yehoshua Y. Zeevi
    • 1
  1. 1.Department of Electrical EngineeringTechnion - Israel Institute of TechnologyTechnion City, HaifaIsrael
  2. 2.Department of Applied MathematicsUniversity of Tel-AvivTel-AvivIsrael

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