An adaptive second-order partial differential equation based on TV equation and p-Laplacian equation for image denoising

  • Xiaojuan Zhang
  • Wanzhou YeEmail author


This paper introduces an adaptive diffusion partial differential equation (PDE) for noise removal, which combines a total variation (TV) term and a p-Laplacian (1 < p ≤ 2) term. Utilizing the edge indicator, we can adaptively control the diffusion model, which alternates between the TV and the p-Laplacian(1 < p ≤ 2) in accordance with the image feature. The main advantage of the proposed model is able to alleviate the staircase effect in smooth regions and preserve edges while removing the noise. The existence of a weak solution of the proposed model is proved. Experimental results confirm the performance of the proposed method with regard to peak signal-to-noise ratio (PSNR), mean structural similarity (MSSIM) and visual quality.


Image denoising TV p-Laplacian Adaptive equation Weak solution 



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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics College of ScienceShanghai UniversityShanghaiChina
  2. 2.School of Mathematics and Statistics ScienceNorth China University of Water Resources and Electric PowerZhengzhouChina

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