Image Denoising Combining the P-M Model and the LLT Model


In this paper, we present a noise removal technique by combining the P-M model with the LLT model. The combined technique takes full use of the advantage of both filters which is able to preserve edges and simultaneously overcomes the staircase effect. We use a weighting function in our model, and compare this model with the P-M model as well as other fourth-order functional both in theory and numerical experiment.

Share and Cite:

Yang, Q. (2015) Image Denoising Combining the P-M Model and the LLT Model. Journal of Computer and Communications, 3, 22-30. doi: 10.4236/jcc.2015.310003.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Catt, F., Lions, P., Morel, J. and Coll, T. (1992) Image Selective Smoothing and Edge Detection by Nonlinear Diffusion. SIAM Journal on Numerical Analysis, 29, 182-193.
[2] Duran, J., Buades, A., Coll, B., et al. (2014) A Nonlocal Variational Model for Pansharpening Image Fusion. SIAM Journal on Imaging Sciences, 7, 761-796.
[3] Jin, Y., Jost, J. and Wang, G. (2004) A New Nonlocal Model for Image Denoising. Journal of Mathematical Imaging and Vision, 48, 93-105.
[4] Lysaker, M., Lundervold, A. and Tai, X.C. (2003) Noise Removal Using Fourth-Order Partial Differential Equation with Applications to Medical Magnetic Resonance Images in Space and Time. IEEE Transactions on Image Processing, 12, 1579-1590.
[5] Lieu, L.H. and Vese, L.A. (2008) Image Restoration and Decomposition via Bounded Total Variation and Negative Hilbert-Sobolev Spaces. Applied Mathematics & Optimization, 58, 167-193.
[6] Rudin, L., Osher, S. and Fatemi, E. (1992) Nonlinear Total Variation Based Noise Removal Algorithms. Physica D, 60, 259-268.
[7] Surya Prasath, V.B. and Vorotnikov, D. (2004) On a System of Adaptive Coupled PDEs for Image Restoration. Journal of Mathematical Imaging and Vision, 48, 35-52.
[8] Alvarez, L., Lions, P. and Morel, J. (1992) Image Selective Smoothing and Edge Detection by Nonlinear Diffusion. II. SIAM Journal on Numerical Analysis, 29, 845-866.
[9] Jin, Y., Jost, J. and Wang, G. (2012) A Nonlocal Version of the Osher-Sol-Vese Model. Journal of Mathematical Imaging and Vision, 44, 99-113.
[10] Perona, P. and Malik, J. (1990) Scale-Space and Edge Detection Using Anisotropic Diffusion. IEEE Transaction on Pattern Analysis and Machine Intelligence, 12, 629-639.
[11] Kim, S. and Lim, H. (2009) Fourth-Order Partial Differential Equation for Effective Image Denoisng. 7th Mississippi State-UAB Conference on Differential Equation and Computational Simulation. Electronic Journal of Differential Equations, 17, 107-121.
[12] Liu, X.W., Huang, L.H. and Guo, Z.Y. (2011) Adaptive Fourth-Order Partial Differential Equation Filter for Image Denoising. Applied Mathematics Letters, 24, 1282-1288.
[13] Wang, L.Q., Xiao, L., Huang, L.L. and Wei, Z.H. (2011) Nonlocal Total Variation Based Speckle Noise Removal Method for Ultrasound Image. 2011 4th International Congress on Image and Signal Processing (CISP), 2, 709-713.
[14] You, Y.L. and Kaveh, M. (2000) Fourth-Order Partial Differential Equation for Noise Removal. IEEE Transaction on Image Processing, 9, 1723-1731.
[15] Zhou, G.X., Zhang, Q.S. and Tan, X.H. (2011) Image Enhancement and Denoising by Forward and Backward Fourth Order Partial Differential Equations. In: Lin, S. and Huang, X., Eds., Advances in Computer Science, Environment, Ecoinformatics, and Education, Springer-Verlag, Berlin, 514-519.
[16] Gilboa, G. and Osher, S. (2007) Nonlocal Linear Image Regularization and Supervised Segmentation. Multiscale Modeling & Simulation, 6, 595-630.
[17] Liu, T.H. and Xiang, Z.Y. (2013) Imaging Restoration Combing the Second-Order and Fourth-Order PDEs. Mathematical Problems in Engineering, 2013, Article ID: 743891.
[18] Wang, H.B., Wang, Y.Q. and Ren, W.Q. (2012) Image Denoising Using Anisotropic Second and Fourth Order Diffusions Based on Gradient Vector Convolution. ComSIS, 9, 1493-1511.
[19] Li, X.P. and Chen, T.W. (1994) Nonlinear Diffusion with Multiple Edginess Thresholds. Pattern Recognition, 27, 1029-1037.
[20] Lou, Y.F., Zhang, X.Q., Osher, S. and Bertozzi, A. (2010) Image Recovery via Nonlocal Operators. Journal of Scientific Computing, 42, 185-197.

Copyright © 2022 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.