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Image denoising and deblurring: non-convex regularization, inverse diffusion and shock filter

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Abstract

A large number of applications in image processing and computer vision depend on image quality. In this paper, main concerns are image denoising and deblurring simultaneously in a restoration task by three types of methodologies: non-convex regularization, inverse diffusion and shock filter. We discuss their relations in the context of image deblurring: the inverse diffusion implied by the non-convex regularization, and the superior ability of deblurring edge of the shock filter to that of the inverse diffusion, both in 1D and 2D cases. Finally, we propose a region-based adaptive anisotropic diffusion with shock filter method, which shows advantages of deblurring edges, denoising and smoothing contours in experiments, compared with some related methods. Therein an idea of “divide and rule” is introduced.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, China

    ShuJun Fu

  2. School of Computer Science and Technology, Shandong University, Jinan, 250101, China

    ShuJun Fu & CaiMing Zhang

  3. School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 639798, Singapore

    ShuJun Fu & XueCheng Tai

  4. Department of Mathematics, University of Bergen, Bergen, 5008, Norway

    XueCheng Tai

Authors
  1. ShuJun Fu
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  2. CaiMing Zhang
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  3. XueCheng Tai
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Correspondence to ShuJun Fu.

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Fu, S., Zhang, C. & Tai, X. Image denoising and deblurring: non-convex regularization, inverse diffusion and shock filter. Sci. China Inf. Sci. 54, 1184–1198 (2011). https://doi.org/10.1007/s11432-011-4239-2

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  • DOI: https://doi.org/10.1007/s11432-011-4239-2

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