An algorithm for hybrid regularizers based image restoration with Poisson noise

Cong Thang Pham; Thi Thu Thao Tran

Kybernetika (2021)

  • Volume: 57, Issue: 3, page 446-473
  • ISSN: 0023-5954

Abstract

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In this paper, a hybrid regularizers model for Poissonian image restoration is introduced. We study existence and uniqueness of minimizer for this model. To solve the resulting minimization problem, we employ the alternating minimization method with rigorous convergence guarantee. Numerical results demonstrate the efficiency and stability of the proposed method for suppressing Poisson noise.

How to cite

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Pham, Cong Thang, and Tran, Thi Thu Thao. "An algorithm for hybrid regularizers based image restoration with Poisson noise." Kybernetika 57.3 (2021): 446-473. <http://eudml.org/doc/298206>.

@article{Pham2021,
abstract = {In this paper, a hybrid regularizers model for Poissonian image restoration is introduced. We study existence and uniqueness of minimizer for this model. To solve the resulting minimization problem, we employ the alternating minimization method with rigorous convergence guarantee. Numerical results demonstrate the efficiency and stability of the proposed method for suppressing Poisson noise.},
author = {Pham, Cong Thang, Tran, Thi Thu Thao},
journal = {Kybernetika},
keywords = {total variation; image denoising; image deblurring; alternating minimization method},
language = {eng},
number = {3},
pages = {446-473},
publisher = {Institute of Information Theory and Automation AS CR},
title = {An algorithm for hybrid regularizers based image restoration with Poisson noise},
url = {http://eudml.org/doc/298206},
volume = {57},
year = {2021},
}

TY - JOUR
AU - Pham, Cong Thang
AU - Tran, Thi Thu Thao
TI - An algorithm for hybrid regularizers based image restoration with Poisson noise
JO - Kybernetika
PY - 2021
PB - Institute of Information Theory and Automation AS CR
VL - 57
IS - 3
SP - 446
EP - 473
AB - In this paper, a hybrid regularizers model for Poissonian image restoration is introduced. We study existence and uniqueness of minimizer for this model. To solve the resulting minimization problem, we employ the alternating minimization method with rigorous convergence guarantee. Numerical results demonstrate the efficiency and stability of the proposed method for suppressing Poisson noise.
LA - eng
KW - total variation; image denoising; image deblurring; alternating minimization method
UR - http://eudml.org/doc/298206
ER -

References

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  1. Aubert, G., Kornprobst, P., , Applied Mathematical Science 147, Springer-Verlag, New York 2006. DOI
  2. Bardsley, J. M., Goldes, J., , Inverse Probl. Sci. Engrg. 19 (2011), 2, 267-280. DOI
  3. Boyd, S., Parikh, N., al., et, 10.1561/2200000016, Found. Trends Mach. Learn. 3 (2010), 1-122. DOI10.1561/2200000016
  4. Bovik, A. C., Wang, Z., , Morgan and Claypool Publishers, 2006. DOI
  5. Chan, R. H., Chen, K., , Int. J. Comput. Math. 84 (2007), 8, 1183-1198. DOI
  6. Chen, D. Q., Cheng, L. Z., , J. Vis. Commun. Image R. 22 (2011), 7, 643-652. DOI
  7. Chen, Y. M., Wunderli, T., , J. Math. Anal. Appl. 272 (2002), 1, 117-137. DOI
  8. Dupe, F. X., Fadili, M. J., Starck, J L., Deconvolution of confocal microscopy images using proximal iteration and sparse representations., In: I. S. Biomed. Imaging, Paris, France (2008), pp. 736-739. 
  9. Ekeland, I., Temam, R., Convex Analysis and Variational Problems., Classics in Applied Mathematics, SIAM 1999. 
  10. Eckstein, J., Bertsekas, D. P., , Math. Programming 55 (1992), 293-318. DOI
  11. Frosioa, I., Borghese, N. A., , Med. Phys. 36 (2009), 2, 464-479. DOI
  12. He, C., Hu, C., Zhang, W., Shi, B., , IEEE Trans. Image Process. 23 (2014), 12, 4954-4967. DOI
  13. Jiang, L., Huang, J., Lv, X. G., Liu, J., , J. Math. 2013 (2013), 274573. DOI
  14. Jiang, L., Huang, J., Lv, X. G., Liu, J., , Numer. Algorithms 69 (2015), 3, 495-516. DOI
  15. Le, T., Chartrand, R., Asaki, T., , J. Math. Imaging Vis. 27 (2007), 257-263. DOI
  16. Li, F., Shen, C. M., Fan, J. S., Shen, C. L., , J. Vis. Commun. Image Res. 18 (2007), 4, 322-330. DOI
  17. Liu, Q., Yao, Z., Ke, Y., , Nonlinear Anal. Theor. 67 (2007), 6, 1908-1918. DOI
  18. Liu, X., , Comput. Math. Appl. 71 (2016), 8, 1694-1705. DOI
  19. Liu, X., Huang, L., , Math. Methods Appl. Sci. 35, (2012), 5, 520-529. DOI
  20. Liu, X., Huang, L., , J. Electronic Imaging 22 (2013), 3, 033007. DOI
  21. Lv, X. G., Jiang, L., Liu, J., , Appl. Math. Comput. 289 (2016), 20, 132-148. DOI
  22. Ma, M., Zhang, J., al., et, , Math. Probl. Eng. (2020), 3416907. DOI
  23. Micchelli, C. A., Shen, L., Xu, Y., , Inverse Probl. 27 (2011), 4, 045009. DOI
  24. Osher, S., Scherzer, O., , Commun. Math. Sci. 2 (2004), 2, 237-254. DOI
  25. Padcharoen, A., Kumama, P., Martinez-Moreno, J., , J. Comput. Appl. Math.354 (2019), 507-519. DOI
  26. Pham, C. T., Kopylov, A., , Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XL-5/W6 (2015), 101-106. DOI
  27. Pham, C. T., Gamard, G., Kopylov, A., Tran, T. T. T., , Turk. J. Elec. Eng. Comp. Sci. 26 (2018), 2832-2846. DOI
  28. Pham, C. T., Kopylov, A. V., , Comput. Opt. 42 (2018), 838-845. DOI
  29. Pham, C. T., Tran, T. T. T., al., et., , Cybern. Phys. 8 (2019), 73-82. DOI
  30. Pham, C. T., Tran, T. T. T., Gamard, G., , Informatica 31 (2020), 539-560. DOI
  31. Sarder, P., Nehorai, A., , IEEE Signal Process. Magazine 23 (2006), 3, 32-45. DOI
  32. Sawatzky, A., Brune, C., Kasters, T., Wabbeling, F., Burger, M., , Lect. Notes Math. Springer 2090 (2013), 71-142. DOI
  33. Setzer, S., Steidl, G., Teuber, T., , J. Vis. Commun. Image R. 21 (2010), 3, 193-199. DOI
  34. Yan, M., , Lect. Notes Comput. Sci. Springer Berlin Heidelberg 6938 (2011), 33-42. DOI
  35. Zhang, J., Ma, M., Wu, Z., Deng, C., , Math. Probl. Engrg. (2019), 2502731. DOI
  36. Wang, Y., Yang, J., Yin, W., Zhang, Y., , SIAM J. Imaging Sci. 1 (2008), 3, 248-272. DOI
  37. Wen, Y., Chan, R. H., Zeng, T., , Sci. China Math. 59 (2016), 141-160. DOI
  38. Woo, H., Yun, S., , IEEE T. Image Process. 21 (2012), 1701-1714. DOI

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