Some Remarks on the Staircasing Phenomenon in Total Variation-Based Image Denoising

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• 作者：Khalid Jalalzai
• 关键词：Total variation ; Image denoising ; Staircasing ; 35J70 ; 65J20 ; 35K65 ; 68U10
• 刊名：Journal of Mathematical Imaging and Vision
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：54
• 期：2
• 页码：256-268
• 全文大小：1,881 KB
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• 作者单位：Khalid Jalalzai (1)
  
  1. CMAP, CNRS, Ecole Polytechnique, 91128 , Palaiseau Cedex, France
  
• 刊物类别：Computer Science
• 刊物主题：Computer Imaging, Vision, Pattern Recognition and Graphics
  Image Processing and Computer Vision
  Artificial Intelligence and Robotics
  Automation and Robotics
  
• 出版者：Springer Netherlands
• ISSN：1573-7683

文摘

This paper deals with the so-called staircasing phenomenon, which frequently arises in total variation-based denoising models in image analysis. We prove in particular that staircasing always occurs at global extrema of the datum and at all extrema of the minimizer. It is also shown that, for radial images, the staircasing always appears at the extrema and at the boundary of the image. We also prove the equivalence between the denoising model and the total variation flow, in the radial case, thus, extending a previous result in dimension one. This equivalence cannot hold in the non-radial case, as it is shown with a counterexample. This connection allows us to understand how the staircase zones and the discontinuities of the denoising problem evolve with the regularization parameter. Keywords Total variation Image denoising Staircasing