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Image Denoising Using Sparse Representation and Principal Component Analysis

    https://doi.org/10.1142/S0219467822500334Cited by:2 (Source: Crossref)
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    Abstract

    This study proposes an image denoising algorithm based on sparse representation and Principal Component Analysis (PCA). The proposed algorithm includes the following steps. First, the noisy image is divided into overlapped 8×8 blocks. Second, the discrete cosine transform is applied as a dictionary for the sparse representation of the vectors created by the overlapped blocks. To calculate the sparse vector, the orthogonal matching pursuit algorithm is used. Then, the dictionary is updated by means of the PCA algorithm to achieve the sparsest representation of vectors. Since the signal energy, unlike the noise energy, is concentrated on a small dataset by transforming into the PCA domain, the signal and noise can be well distinguished. The proposed algorithm was implemented in a MATLAB environment and its performance was evaluated on some standard grayscale images under different levels of standard deviations of white Gaussian noise by means of peak signal-to-noise ratio, structural similarity indexes, and visual effects. The experimental results demonstrate that the proposed denoising algorithm achieves significant improvement compared to dual-tree complex discrete wavelet transform and K-singular value decomposition image denoising methods. It also obtains competitive results with the block-matching and 3D filtering method, which is the current state-of-the-art for image denoising.

    References

    • 1. M. Diwakar and M. Kumar , “A review on CT image noise and its denoising,” Biomed. Signal Proc. Control 42, 73–88 (2018). Crossref, Web of Science, Google Scholar
    • 2. L. Fan, F. Zhang, H. Fan and C. Zhang , “Brief review of image denoising techniques,” Vis. Comput. Ind. Biomed. Art. 2(1), 7 (2019). Crossref, Google Scholar
    • 3. C. Tian, L. Fei, W. Zheng, Y. Xu, W. Zuo and C. W. Lin , Deep learning on image denoising: An overview, Neural Netw. 131, 251–275 (2020). Crossref, Web of Science, Google Scholar
    • 4. C. Tian, Y. Xu, Z. Li, W. Zuo, L. Fei and H. Liu , Attention-guided CNN for image denoising, Neural Netw. 124, 117–129 (2020). Crossref, Web of Science, Google Scholar
    • 5. D. D. Muresan and T. W. Parks , “Adaptive principal components and image denoising,” in Proc. 2003 Int. Conf. Image Processing, Catalogue No. 03CH37429, Vol. 1, IEEE, 2003, pp. I–101. Crossref, Google Scholar
    • 6. M. Aharon, M. Elad and A. Bruckstein , “K-SVD: An algorithm for designing over complete dictionaries for sparse representation,” IEEE Trans. Signal Process. 54(11), 4311–4322 (2006). Crossref, Web of Science, Google Scholar
    • 7. A. Foi, V. Katkovnik and K. Egiazarian , “Pointwise shape-adaptive DCT for high-quality denoising and deblocking of grayscale and color images,” IEEE Trans. Image Process. 16(5), 1395–1411 (2007). Crossref, Web of Science, Google Scholar
    • 8. K. Dabov et al., “Image denoising with block-matching and 3D filtering, ” in Image Processing: Algorithms and Systems, Neural Networks, and Machine Learning, Vol. 6064 (International Society for Optics and Photonics, 2006), p. 606414. Crossref, Google Scholar
    • 9. A. A. Yahya, J. Tan, B. Su, M. Hu, Y. Wang, K. Liu and A. N. Hadi , “BM3D image denoising algorithm based on an adaptive filtering,” Multimedia Tools Appl. 1(37), (2020). Google Scholar
    • 10. L. Zhang, W. Dong, D. Zhang and G. Shi , “Two-stage image denoising by principal component analysis with local pixel grouping,” Pattern Recognit. 43(4), 1531–1549 (2010). Crossref, Web of Science, Google Scholar
    • 11. S. Routray, A. K. Ray and C. Mishra , “An efficient image denoising method based on principal component analysis with learned patch groups,” Signal, Image Video Process. 13(7), 1405–1412 (2019). Crossref, Web of Science, Google Scholar
    • 12. I. Wickramasingha, M. Sobhy and S. S. Sherif , “Sparsity in bayesian signal estimation, ” in Bayesian Inference, IntechOpen (2017), p. 279. Crossref, Google Scholar
    • 13. R. Medina, X. Alvarez, D. Jadán, J. C. Macancela, R. V. Sánchez and M. Cerrada , “Gearbox fault classification using dictionary sparse based representations of vibration signals,” J. Intell. Fuzzy Syst. 34(6), 3605–3618 (2018). Crossref, Web of Science, Google Scholar
    • 14. L. Zhang, R. Lukac, X. Wu and D. Zhang , “PCA-based spatially adaptive denoising of CFA images for single-sensor digital cameras,” IEEE Trans. Image Process. 18(4), 797–812 (2009). Crossref, Web of Science, Google Scholar
    • 15. R. C. Gonzalez, R. E. Woods and B. R. Masters , Digital Image Processing, 3rd edn. (Pearson International Edition, 2008). Google Scholar
    • 16. S. G. Chang, B. Yu and M. Vetterli , “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Process. 9(9), 1522–1531 (2000). Crossref, Web of Science, Google Scholar
    • 17. Z. Hou , “Adaptive singular value decomposition in wavelet domain for image denoising,” Pattern Recognit. 36(8), 1747–1763 (2003). Crossref, Web of Science, Google Scholar
    • 18. A. Pizurica and W. Philips , “Estimating the probability of the presence of a signal of interest in multiresolution single-and multiband image denoising,” IEEE Trans. Image Process. 15(3), 654–665 (2006). Crossref, Web of Science, Google Scholar
    • 19. A. Pizurica, W. Philips, I. Lemahieu and M. Acheroy , “A joint inter-and intrascale statistical model for Bayesian wavelet based image denoising,” IEEE Trans. Image Process. 11(5), 545–557 (2002). Crossref, Web of Science, Google Scholar
    • 20. J. Portilla, V. Strela, M. J. Wainwright and E. P. Simoncelli , “Image denoising using scale mixtures of Gaussians in the wavelet domain,” IEEE Trans. Image Process. 12(11), 1338–1351 (2003). Crossref, Web of Science, Google Scholar
    • 21. S. Routray, A. K. Ray and C. Mishra , “Image denoising by preserving geometric components based on weighted bilateral filter and curvelet transform,” Optik 159, 333–343 (2018). Crossref, Web of Science, Google Scholar
    • 22. G. Chen and B. Kégl , “Image denoising with complex ridgelets,” Pattern Recognit. 40(2), 578–585 (2007). Crossref, Web of Science, Google Scholar
    • 23. M. Elad and M. Aharon , “Image denoising via sparse and redundant representations over learned dictionaries,” IEEE Trans. Image Process. 15(12), 3736–3745 (2006). Crossref, Web of Science, Google Scholar
    • 24. D. Barash , “Fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation,” IEEE Trans. Pattern Anal. Mach. Intell. 24(6), 844–847 (2002). Crossref, Web of Science, Google Scholar
    • 25. A. Buades, B. Coll and J.-M. Morel , “A review of image denoising algorithms, with a new one,” Multiscale Model. Simul. 4(2), 490–530 (2005). Crossref, Web of Science, Google Scholar
    • 26. C. Kervrann and J. Boulanger , “Optimal spatial adaptation for patch-based image denoising,” IEEE Trans. Image Process. 15(10), 2866–2878 (2006). Crossref, Web of Science, Google Scholar
    • 27. K. Dabov, A. Foi, V. Katkovnik and K. Egiazarian , “Image denoising by sparse 3D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16(8), 2080–2095 (2007). Crossref, Web of Science, Google Scholar
    • 28. S. Routray, A. K. Ray, C. Mishra and G. Palai , “Efficient hybrid image denoising scheme based on SVM classification,” Optik 157, 503–511 (2018). Crossref, Web of Science, Google Scholar
    • 29. M. H. Alkinani and M. R. El-Sakka , “Patch-based models and algorithms for image denoising: A comparative review between patch-based images denoising methods for additive noise reduction,” EURASIP J. Image Video Process. 2017, 1–27 (2017). Crossref, Web of Science, Google Scholar
    • 30. D. Gupta and M. Ahmad , “Brain MR image denoising based on wavelet transform,” Int. J. Adv. Technol. Eng. Explor. 5(38), 11–16 (2018). Crossref, Google Scholar
    • 31. V. Fedak and A. Nakonechnyy , “Adaptive wavelet thresholding for image denoising using sure minimization and clustering of wavelet coefficients,” Tech. Trans. Electr. Eng. 31, 197–210 (2015). Google Scholar
    • 32. I. W. Selesnick, R. G. Baraniuk and N. G. Kingsbury , “The dual-tree complex wavelet transform,” IEEE Signal Process. Mag. 22(6), 123–151 (2005). Crossref, Web of Science, Google Scholar
    • 33. A. K. Verma, B. S. Saini and T. Kaur , Image denoising using Alexander fractional hybrid filter, Int. J. Image Graph. 18(1) (2018). Link, Web of Science, Google Scholar
    • 34. O. Prakash and A. Khare , Medical image denoising based on soft thresholding using biorthogonal multiscalewavelet transform, Int. J. Image Graph. 14(1), (2014). Google Scholar
    • 35. J. Yuan and J. Wang , Perona-Malik model with a new diffusion coefficient for image denoising, Int. J. Image Graph. 16(2), (2016). Link, Google Scholar
    • 36. Y. C. Pati, R. Rezaiifar and P. S. Krishnaprasad , “Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition,” in Proc. 27th Asilomar Conf. Signals, Systems and Computers, IEEE, 1993, pp. 40–44. Crossref, Google Scholar
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