Fourth-order partial differential equations for noise removal

@article{You2000FourthorderPD,
  title={Fourth-order partial differential equations for noise removal},
  author={Yu-Li You and Mostafa Kaveh},
  journal={IEEE transactions on image processing : a publication of the IEEE Signal Processing Society},
  year={2000},
  volume={9 10},
  pages={
          1723-30
        }
}
  • Yu-Li YouM. Kaveh
  • Published 1 October 2000
  • Mathematics
  • IEEE transactions on image processing : a publication of the IEEE Signal Processing Society
A class of fourth-order partial differential equations (PDEs) are proposed to optimize the trade-off between noise removal and edge preservation. The time evolution of these PDEs seeks to minimize a cost functional which is an increasing function of the absolute value of the Laplacian of the image intensity function. Since the Laplacian of an image at a pixel is zero if the image is planar in its neighborhood, these PDEs attempt to remove noise and preserve edges by approximating an observed… 

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