Fourth-order partial differential equations for noise removal

By Yu-Li You, M. Kaveh. IEEE Transactions on Image Processing, 2000

881 citations recorded by the source corpus.

Subfields: Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/53ac4c91c7fd3e21a9e12e254825d28adb79ad0e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Graphics and Computer-Aided Design

1. Murali Rao
2. Julia Neumann
3. Jian Bai
4. Gabriele Steidl
5. Chunlin Wu
6. Xuecheng Tai
7. Yin Zhang
8. Xiangchu Feng

In Computer Vision and Pattern Recognition

1. Wotao Yin
2. Yin Zhang
3. Chunlin Wu
4. Xuecheng Tai
5. Junfeng Yang
6. Gabriele Steidl
7. Yunmei Chen
8. Murali Rao

Citations in the corpus

• Augmented Lagrangian Method, Dual Methods, and Split Bregman Iteration for ROF, Vectorial TV, and High Order Models (2010, methodology): “The model immediately attracted much attention and has been extended to high order models [13, 46, 27, 29, 24, 35] and vectorial models for color image restoration [34, 2, 4, 14]; see [15] for an overview.”
• Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional (2005, background): “To overcome this spurious effect, higher-order PDEs have been of special interest over the last few years (Lysaker et al., 2003; Chan et al., 2000; You and Kaveh, 2000; Lysaker et al., 2004; Osher et al., 2003; Bertozzi and Greer, 2004; Greer and Bertozzi, 2003a, 2003b, 2004; Scherzer, 1998;…”
• Splines in Higher Order TV Regularization (2006, background): “some artefacts in form of white points which were also mentioned in [34].”
• Infimal convolution regularizations with discrete ℓ1-type functionals (2011, neutral): “For various other variational and PDE approaches involving higher order derivatives, see [11, 15, 22, 24, 30, 41, 43].”
• Fractional-Order Anisotropic Diffusion for Image Denoising (2007, methodology): “Digital Object Identifier 10.1109/TIP.2007.904971 absolute value of the Laplacian of the image intensity function [15].”
• Variable Exponent, Linear Growth Functionals in Image Restoration (2006, methodology): “We also refer the reader to the work in [15, 16, 26, 35] for an alternate variational approach for reducing staircasing by minimizing second order functionals.”
• A New Alternating Minimization Algorithm for Total Variation Image Reconstruction (2008, background): “Higher-order derivatives of u are used in [27, 44], for example, to reduce staircasing effects.”
• Image Denoising Using the Higher Order Singular Value Decomposition (2013, neutral): “Some PDEs are obtained from the Euler Lagrange equations corresponding to functionals that are based on a piecewise constant [28] or piecewise linear [40] model for natural images.”