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A Framework for Image Denoising Using First and Second Order Fractional Overlapping Group Sparsity (HF-OLGS) Regularizer

Title:

A Framework for Image Denoising Using First and Second Order Fractional Overlapping Group Sparsity (HF-OLGS) Regularizer

Kumar, Ahlad ORCID: https://orcid.org/0000-0003-2496-6275, Ahmad, M. Omair ORCID: https://orcid.org/0000-0002-2924-6659 and Swamy, M. N. S. ORCID: https://orcid.org/0000-0002-3989-5476 (2019) A Framework for Image Denoising Using First and Second Order Fractional Overlapping Group Sparsity (HF-OLGS) Regularizer. IEEE Access, 7 . pp. 26200-26217. ISSN 2169-3536

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Official URL: http://dx.doi.org/10.1109/ACCESS.2019.2901691

Abstract

Denoising images subjected to Gaussian and Poisson noise has attracted attention in many areas of image processing. This paper introduces an image denoising framework using higher order fractional overlapping group sparsity prior to sparser image representation constraint. The proposed prior has a capability of avoiding staircase effects in both edges and oscillatory patterns (textures). We adopt the alternating direction method of multipliers for optimizing the proposed objective function by converting it into a constrained optimization problem using variable splitting approach. Finally, we conduct experiments on various degraded images and compare our results with those of several state-of-the-art methods. The numerical results show that the proposed fractional order image denoising framework improves the peak signal to noise ratio of an image by preserving the textures and eliminating the staircases effects. This leads to visually pleasant restored images which exhibit a higher value of Structural SIMilarity score when compared to that of other methods.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Electrical and Computer Engineering
Item Type:Article
Refereed:Yes
Authors:Kumar, Ahlad and Ahmad, M. Omair and Swamy, M. N. S.
Journal or Publication:IEEE Access
Date:2019
Funders:
  • Concordia Open Access Author Fund
  • Horizon Postdoctoral Fellowship, Concordia University
  • Research Chair Program, Concordia University
  • Natural Sciences and Engineering Research Council (NSERC)
  • Regroupement Strategique en Microelectronique du Quebec (ReSMiQ)
Digital Object Identifier (DOI):10.1109/ACCESS.2019.2901691
Keywords:Image denoising, fractional-order, Gaussian and Poisson noise, overlapping group sparsity, alternating direction method of multipliers
ID Code:985230
Deposited By: Krista Alexander
Deposited On:08 Apr 2019 18:15
Last Modified:08 Apr 2019 18:19

References:

1. R. Fergus, B. Singh, A. Hertzmann, S. T. Roweis, W. T. Freeman, "Removing camera shake from a single photograph", ACM Trans. Graph., vol. 25, pp. 787-794, 2006.

2. J.-F. Cai, H. Ji, C. Liu, Z. Shen, "Blind motion deblurring from a single image using sparse approximation", Proc. IEEE Conf. Comput. Vis. Pattern Recognit. (CVPR), pp. 104-111, Jun. 2009.

3. D. Krishnan, R. Fergus, "Fast image deconvolution using hyper-laplacian priors", Proc. Adv. Neural Inf. Process. Syst., pp. 1033-1041, 2009.

4. D. Krishnan, T. Tay, R. Fergus, "Blind deconvolution using a normalized sparsity measure", Proc. IEEE Conf. Comput. Vis. Pattern Recognit. (CVPR), pp. 233-240, Jun. 2011.

5. L. I. Rudin, S. Osher, E. Fatemi, "Nonlinear total variation based noise removal algorithms", Phys. D Nonlinear Phenomena, vol. 60, no. 1, pp. 259-268, 1992.

6. T. Chan, A. Marquina, P. Mulet, "High-order total variation-based image restoration", SIAM J. Sci. Comput., vol. 22, no. 2, pp. 503-516, 2000.

7. M. Lysaker, X.-C. Tai, "Iterative image restoration combining total variation minimization and a second-order functional", Int. J. Comput. Vis., vol. 66, no. 1, pp. 5-18, 2006.

8. K. Papafitsoros, C.-B. Schönlieb, "A combined first and second order variational approach for image reconstruction", J. Math. Imag. Vis., vol. 48, no. 2, pp. 308-338, 2014.

9. M. Lysaker, A. Lundervold, X.-C. Tai, "Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time", IEEE Trans. Image Process., vol. 12, no. 12, pp. 1579-1590, Dec. 2003.

10. G. Gilboa, S. Osher, "Nonlocal operators with applications to image processing", Multiscale Model. Simul., vol. 7, no. 3, pp. 1005-1028, 2008.

11. J. Liu, T.-Z. Huang, Z. Xu, X.-G. Lv, "High-order total variation-based multiplicative noise removal with spatially adapted parameter selection", J. Opt. Soc. Amer. A Opt. Image Sci. Vis., vol. 30, no. 10, pp. 1956-1966, 2013.

12. W. Zhou, Q. Li, "Poisson noise removal scheme based on fourth-order PDE by alternating minimization algorithm", Abstr. Appl. Anal., vol. 2012, Nov. 2012.

13. K. Bredies, K. Kunisch, T. Pock, "Total generalized variation", SIAM J. Imag. Sci., vol. 3, no. 3, pp. 492-526, 2010.

14. X.-D. Wang, X.-C. Feng, W.-W. Wang, W.-J. Zhang, "Iterative reweighted total generalized variation based Poisson noise removal model", Appl. Math. Comput., vol. 223, pp. 264-277, Oct. 2013.

15. Y. Shi, J. Song, X. Hua, "Poissonian image deblurring method by non-local total variation and framelet regularization constraint", Comput. Elect. Eng., vol. 62, pp. 319-329, Aug. 2016.

16. G. Landi, E. L. Piccolomini, "An efficient method for nonnegatively constrained total variation-based denoising of medical images corrupted by Poisson noise", Comput. Med. Imag. Graph., vol. 36, no. 1, pp. 38-46, 2012.

17. S. Bonettini, V. Ruggiero, "On the convergence of primal–dual hybrid gradient algorithms for total variation image restoration", J. Math. Imag. Vis., vol. 44, no. 3, pp. 236-253, 2012.

18. D. Chen, Y. Chen, D. Xue, "Fractional-order total variation image restoration based on primal-dual algorithm", Abstr. Appl. Anal., vol. 2013, Sep. 2013.

19. J. Zhang, Z. Wei, L. Xiao, "Adaptive fractional-order multi-scale method for image denoising", J. Math. Imag. Vis., vol. 43, no. 1, pp. 39-49, 2012.

20. Z. Jun, W. Zhihui, "A class of fractional-order multi-scale variational models and alternating projection algorithm for image denoising", Appl. Math. Model., vol. 35, no. 5, pp. 2516-2528, 2011.

21. Y. Zhang, Y. F. Pu, J. R. Hu, J. L. Zhou, "A class of fractional-order variational image inpainting models", Appl. Math. Inf. Sci., vol. 6, no. 2, pp. 299-306, 2012.

22. Z. Ren, C. He, Q. Zhang, "Fractional order total variation regularization for image super-resolution", Signal Process., vol. 93, no. 9, pp. 2408-2421, 2013.

23. J. Bai, X. C. Feng, "Fractional-order anisotropic diffusion for image denoising", IEEE Trans. Image Process., vol. 16, no. 10, pp. 2492-2502, Oct. 2007.

24. M. Ding, T.-Z. Huang, S. Wang, J.-J. Mei, X.-L. Zhao, "Total variation with overlapping group sparsity for deblurring images under cauchy noise", Appl. Math. Comput., vol. 341, pp. 128-147, Jan. 2019.

25. X.-L. Zhao, F. Wang, M. K. Ng, "A new convex optimization model for multiplicative noise and blur removal", SIAM J. Imag. Sci., vol. 7, no. 1, pp. 456-475, 2014.

26. Z. Gao et al., "Motion tracking of the carotid artery wall from ultrasound image sequences: A nonlinear state-space approach", IEEE Trans. Med. Imag., vol. 37, no. 1, pp. 273-283, Jan. 2018.

27. Z. Gao et al., "Robust estimation of carotid artery wall motion using the elasticity-based state-space approach", Med. Image Anal., vol. 37, pp. 1-21, Apr. 2017.

28. Z. Gao et al., " Robust recovery of myocardial kinematics using dual Hinfty criteria ", Multimedia Tools Appl., vol. 77, no. 17, pp. 23043-23071, 2018.

29. S. Parameswaran, C.-A. Deledalle, L. Denis, T. Q. Nguyen, " Accelerating GMM-based patch priors for image restoration: Three ingredients for a 100times speed-up ", IEEE Trans. Image Process., vol. 28, no. 2, pp. 687-698, Feb. 2018.

30. M. Gong, K. Zhang, T. Liu, D. Tao, C. Glymour, B. Schölkopf, "Domain adaptation with conditional transferable components", Proc. Int. Conf. Mach. Learn., pp. 2839-2848, 2016.

31. M. K. Ng, X. Yuan, W. Zhang, "Coupled variational image decomposition and restoration model for blurred cartoon-plus-texture images with missing pixels", IEEE Trans. Image Process., vol. 22, no. 6, pp. 2233-2246, Jun. 2013.

32. S. Ono, T. Miyata, I. Yamada, "Cartoon-texture image decomposition using blockwise low-rank texture characterization", IEEE Trans. Image Process., vol. 23, no. 3, pp. 1128-1142, Mar. 2014.

33. X. Liu, "A new TGV-Gabor model for cartoon-texture image decomposition", IEEE Signal Process. Lett., vol. 25, no. 8, pp. 1221-1225, Aug. 2018.

34. D.-Q. Chen, L.-Z. Cheng, "Deconvolving Poissonian images by a novel hybrid variational model", J. Vis. Commun. Image Represent., vol. 22, no. 7, pp. 643-652, 2011.

35. R. Chan, A. Lanza, S. Morigi, F. Sgallari, "An adaptive strategy for the restoration of textured images using fractional order regularization", Numer. Math. Theory Methods Appl., vol. 6, no. 1, pp. 276-296, 2013.

36. Y. Pu, "Fractional calculus approach to texture of digital image", Proc. 8th Int. Conf. Signal Process., vol. 2, pp. 1-5, Nov. 2006.

37. P. U. Yi-Fei, "Fractional differential analysis for texture of digital image", J. Algorithms Comput. Technol., vol. 1, no. 3, pp. 357-380, 2007.

38. E. Cuesta, M. Kirane, S. A. Malik, "Image structure preserving denoising using generalized fractional time integrals", Signal Process., vol. 92, no. 2, pp. 553-563, 2012.

39. Y. Wang, Y. Shao, Z. Gui, Q. Zhang, L. Yao, Y. Liu, "A novel fractional-order differentiation model for low-dose CT image processing", IEEE Access, vol. 4, pp. 8487-8499, 2016.

40. J. Liu, T.-Z. Huang, I. W. Selesnick, X.-G. Lv, P.-Y. Chen, "Image restoration using total variation with overlapping group sparsity", Inf. Sci., vol. 295, pp. 232-246, Feb. 2015.

41. S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein, "Distributed optimization and statistical learning via the alternating direction method of multipliers", Found. Trends Mach. Learn., vol. 3, no. 1, pp. 1-122, Jan. 2011.

42. I. W. Selesnick, P.-Y. Chen, "Total variation denoising with overlapping group sparsity", Proc. IEEE Int. Conf. Acoust. Speech Signal Process. (ICASSP), pp. 5696-5700, May 2013.

43. G. Peyré, J. Fadili, "Group sparsity with overlapping partition functions", Proc. 19th Eur. Signal Process. Conf., pp. 303-307, Aug. 2011.

44. M. Figueiredo, J. Bioucas-Dias, "An alternating direction algorithm for (overlapping) group regularization", Signal Process. Adapt. Sparse Struct. Represent., 2011.

45. J. Zhang, Z. Wei, L. Xiao, "A fast adaptive reweighted residual-feedback iterative algorithm for fractional-order total variation regularized multiplicative noise removal of partly-textured images", Signal Process., vol. 98, pp. 381-395, May 2014.
46. M. R. Hestenes, "Multiplier and gradient methods", J. Optim. Theory Appl., vol. 4, no. 5, pp. 303-320, 1969.

47. D. R. Hunter, K. Lange, "A tutorial on MM algorithms", Amer. Statist., vol. 58, no. 1, pp. 30-37, 2004.

48. M. A. T. Figueiredo, J. M. Bioucas-Dias, R. D. Nowak, "Majorization–minimization algorithms for wavelet-based image restoration", IEEE Trans. Image Process., vol. 16, no. 12, pp. 2980-2991, Dec. 2007.

49. M. R. Hestenes, E. Stiefel, Methods of Conjugate Gradients for Solving Linear Systems, Washington, DC, USA:NBS, vol. 49, no. 1, 1952.

50. H. R. Sheikh, Z. Wang, L. Cormack, A. C. Bovik, LIVE Image Quality Assessment Database Release 2, 2016, [online] Available: http://live.ece.utexas.edu/research/quality.

51. Z. Wang, A. C. Bovik, H. R. Sheikh, E. P. Simoncelli, "Image quality assessment: From error visibility to structural similarity", IEEE Trans. Image Process., vol. 13, no. 4, pp. 600-612, Apr. 2004.

52. X. K. Yang, W. S. Ling, Z. K. Lu, E. P. Ong, S. S. Yao, "Just noticeable distortion model and its applications in video coding", Signal Process. Image Commun., vol. 20, no. 7, pp. 662-680, Aug. 2005.

53. X. H. Zhang, W. S. Lin, P. Xue, "Improved estimation for just-noticeable visual distortion", Signal Process., vol. 85, no. 4, pp. 795-808, 2005.

54. X. Zhang, W. Lin, P. Xue, "Just-noticeable difference estimation with pixels in images", J. Vis. Commun. Image Represent., vol. 19, no. 1, pp. 30-41, Jan. 2008.

55. Z. Wei, K. N. Ngan, "Spatio-temporal just noticeable distortion profile for grey scale image/video in DCT domain", IEEE Trans. Circuits Syst. Video Technol., vol. 19, no. 3, pp. 337-346, Mar. 2009.

56. A. Liu, W. Lin, M. Paul, C. Deng, F. Zhang, "Just noticeable difference for images with decomposition model for separating edge and textured regions", IEEE Trans. Circuits Syst. Video Technol., vol. 20, no. 11, pp. 1648-1652, Nov. 2010.

57. D. Chen, Y. Chen, D. Xue, "Fractional-order total variation image denoising based on proximity algorithm", Appl. Math. Comput., vol. 257, pp. 537-545, Apr. 2015.

58. C. Sutour, C.-A. Deledalle, J.-F. Aujol, "Adaptive regularization of the NL-means: Application to image and video denoising", IEEE Trans. Image Process., vol. 23, no. 8, pp. 3506-3521, Aug. 2014.

59. V. Estellers, S. Soatto, X. Bresson, "Adaptive regularization with the structure tensor", IEEE Trans. Image Process., vol. 24, no. 6, pp. 1777-1790, Jun. 2015.

60. M. Janev, S. Pilipović, T. Atanacković, R. Obradović, N. Ralević, "Fully fractional anisotropic diffusion for image denoising", Math. Comput. Model., vol. 54, no. 1, pp. 729-741, 2011.

61. S. Tao, W. Dong, Z. Xu, Z. Tang, "Fast total variation deconvolution for blurred image contaminated by Poisson noise", J. Vis. Commun. Image Represent., vol. 38, pp. 582-594, Jul. 2016.

62. X.-G. Lv, L. Jiang, J. Liu, "Deblurring Poisson noisy images by total variation with overlapping group sparsity", Appl. Math. Comput., vol. 289, pp. 132-148, Oct. 2016.

63. H. Fang, L. Yan, H. Liu, Y. Chang, "Blind Poissonian images deconvolution with framelet regularization", Opt. Lett., vol. 38, no. 4, pp. 389-391, 2013.

64. L. Yan, H. Fang, S. Zhong, "Blind image deconvolution with spatially adaptive total variation regularization", Opt. Lett., vol. 37, no. 14, pp. 2778-2780, 2012.

65. X. Gong, B. Lai, Z. Xiang, " A L 0 sparse analysis prior for blind Poissonian image deconvolution ", Opt. Express, vol. 22, no. 4, pp. 3860-3865, 2014.

66. J. G. Nagy, K. Palmer, L. Perrone, "Iterative methods for image deblurring: A MATLAB object-oriented approach", Numer. Algorithms, vol. 36, no. 1, pp. 73-93, 2004.

67. K. Zhang, W. Zuo, Y. Chen, D. Meng, L. Zhang, "Beyond a Gaussian Denoiser: Residual learning of deep CNN for image denoising", IEEE Trans. Image Process., vol. 26, no. 7, pp. 3142-3155, Jul. 2017.

68. K. Zhang, W. Zuo, L. Zhang, "FFDNet: Toward a fast and flexible solution for CNN-based image denoising", IEEE Trans. Image Process., vol. 27, no. 9, pp. 4608-4622, Sep. 2018.
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