Image restoration and contrast enhancement based on a nonlinear reaction-diffusion mathematical model and divide & conquer technique

In this article, we present a new algorithm for digital image processing noised by mixed Gaussian-impulse noise.  Our mathematical model is based on the divide-conquer technique coupled with a reaction-diffusion system.  We first decompose our image into low and high-frequency components by convolving each with a predefined convolutional filter.  Further, we use a simple scheme of different weights to integrate and collect these processed sub-images into a filtered image.  Finally, we apply our Reaction-Diffusion system to increase the contrast in the image.  A number of experimental results are described to illustrate the performance of our algorithm and show that it is very effective in eliminating mixed Gaussian-impulse noise, increasing the contrast of the image and preserving the edges.

  1. Tomasi C., Manduchi R.  Bilateral filtering for gray and color images.  Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271). 839–846 (1998).
  2. Buades A., Coll B., Morel J.-M.  A non-local algorithm for image denoising.  2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05). 60–65 (2005).
  3. Helstrom C. W.  Image restoration by the method of least squares.  Journal of the Optical Society of America. 57 (3), 297–303 (1967).
  4. Zirhem M., Alaa N.  Texture synthesis by reaction diffusion process.  Annals of the University of Craiova, Mathematics and Computer Science Series. 42, 56–69 (2015).
  5. Alaa N., Zirhem M.  Entropy solution for a fourth-order nonlinear degenerate problem for image decomposition.  J. Adv. Math. Stud. 11, 412–427 (2018).
  6. Alaa N., Zirhem M.  Bio-inspired reaction diffusion system applied to image restoration.  International Journal of Bio-inspired Computation. 12 (2), 128–137 (2018).
  7. Perona P., Malik J.  Scale-space and edge detection using anisotropic diffusion.  IEEE Transactions on Patterns Analysis and Machine Intelligence. 12 (7), 629–639 (1990).
  8. Alvarez L., Lions P. L., Morel J. M.  Image selective smoothing and edge detection by nonlinear diffusion. II.  SIAM Journal of Numerical Analysis. 29 (3), 845–866 (1992).
  9. Catté F., Lions P. L., Morel J. M., Coll T.  Image selective smoothing and edge detection by nonlinear diffusion.  SIAM Journal on Numerical Analysis. 29 (1), 182–193 (1992).
  10. Morfu S.  On some applications of diffusion processes for image processing.  Physics Letters A. 373 (29), 2438–2444 (2009).
  11. Ait Oussous M., Alaa N., Ait Khouya Y.  Anisotropic and nonlinear diffusion applied to image enhancement and edge detection.  International Journal of Computer Applications in Technology. 49 (2), 122–133 (2014).
  12. Mallat S., Hwang W. L.  Singularity detection and processing with wavelets.  IEEE Transactions on Information Theory. 38 (2), 617–643 (1992).
  13. Agaian S., McClendon S. A.  Novel medical image enhancement algorithms.  Proc. SPIE 7532, Image Processing: Algorithms and Systems VIII, 75320W (2010).
  14. Turing A. M.  The chemical basis of morphogenesis.  Phil. Trans. Roy. Soc. Lond. B. 237, 37–72 (1952).
  15. Prigogine I., Nicolis G.  Biological order, structure and instabilities.  Quart. Rev. Biophys. 4, 107–148 (1971).
  16. Gierer A., Meinhardt H.  A theory of biological pattern formation.  Kybernetik. 12, 30–39 (1970).
  17. Ambrosio B., Aziz-Alaoui M. A.  Synchronisation dans un réseau d'équations aux dérivées partielles de type Fitzhugh-Nagumo généralisé, équations aux dérivées partielles et leurs applications.  Actes du colloque Edp-Normandie. 119–131 (2012).
  18. Nomura A., Ichikawa M., Sianipar R. H., Miike H.  Reaction-Diffusion Algorithm for Vision Systems.  Vision Systems: Segmentation and Pattern Recognition. 61–80 (2007).
  19. Charbonnier P., Feraud L., Aubert G., Barlaud M.  Deterministic edge-preserving regularization in computed imaging.  IEEE Transactions on Image processing. 6 (2), 298–311 (1997).
  20. Lopez-Rubio E.  Restoration of images corrupted by gaussian and uniform impulsive noise.  Pattern Recognition. 43 (5), 1835–1846 (2010).
  21. Liu J., Huan Z., Huang H., Zhang H.  An adaptive method for recovering image from mixed noisy data.  International Journal of Computer Vision. 85, 182–191 (2009).
  22. Rodriguez P., Rojas R. A., Wohlberg B.  Mixed gaussian-impulse noise image restoration via total variation.  2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). 1077–1080 (2012).
  23. Liu J., Tai X., Huang H., Huan Z.  A Weighted Dictionary Learning Model for Denoising Images Corrupted by Mixed Noise.  IEEE Transactions on Image Processing. 22 (3),  1108–1120 (2012).
  24. Stout Q. F.  Supporting divide and conquer algorithm in image processing.  J. of Parallel and Distributed Computing. 4 (1), 95–115 (1987).
  25. Bacquey N.  Packing problem: A divide and conquer algorithm on cellular automata.  Automata and JAC. 1–10 (2012).
  26. Zhuang P., Fu X., Huang Y., Ding X.  Image enhancement using divide and conquer strategy.  Journal of Visual Communication and Image Representation. 45, 137–146 (2017).
Mathematical Modeling and Computing, Vol. 8, No. 3, pp. 549–559 (2021)