Citation:  XU Xudong, ZHANG Zhihua, M. James C. Crabbe, “Quaternion QuasiChebyshev Nonlocal Means for Color Image Denoising,” Chinese Journal of Electronics, vol. 32, no. 3, pp. 397414, 2023, doi: 10.23919/cje.2022.00.138 
[1] 
J. B. Martens and L. Meesters, “Image dissimilarity,” Signal Processing, vol.70, no.3, pp.155–176, 1998. doi: 10.1016/S01651684(98)001236

[2] 
T. Huang, G. Yang, and G. Tang, “A fast twodimensional median filtering algorithm,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.27, no.1, pp.13–18, 1979. doi: 10.1109/TASSP.1979.1163188

[3] 
Y. Ephraim and D. Malah, “Speech enhancement using a minimummean square error shorttime spectral amplitude estimator,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.32, no.6, pp.1109–1121, 1984. doi: 10.1109/TASSP.1984.1164453

[4] 
J. S. Goldstein, I. S. Reed, and L. L. Scharf, “A multistage representation of the Wiener filter based on orthogonal projections,” IEEE Transactions on Information Theory, vol.44, no.7, pp.2943–2959, 1998. doi: 10.1109/18.737524

[5] 
K. Ito and K. Xiong, “Gaussian filters for nonlinear filtering problems,” IEEE Transactions on Automatic Control, vol.45, no.5, pp.910–927, 2000. doi: 10.1109/9.855552

[6] 
C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in Proceedings of the 6th International Conference on Computer Vision, Bombay, India, pp.839–846, 2002.

[7] 
A. Buades, B. Coil, and J. M. Morel, “A review of image denoising algorithms, with a new one,” Multiscale Modeling & Simulation, vol.4, no.2, pp.490–530, 2005. doi: 10.1137/040616024

[8] 
G. Gilboa and S. Osher, “Nonlocal evolutions for image regularization,” in Proceedings of SPIE 6498, Computational Imaging V, San Jose, United States, pp.64980U, 2007.

[9] 
B. Goossens, H. Luong, J. Aelterman, et al., “A GPUaccelerated realtime NLMeans algorithm for denoising color video sequences,” in Proceedings of the 12th International Conference on Advanced Concepts for Intelligent Vision Systems, Sydney, Australia, pp.46–57, 2010.

[10] 
A. Khmag, S. A. R. Al Haddad, R. A. Ramlee, et al., “Natural image noise removal using nonlocal means and hidden Markov models in transform domain,” The Visual Computer, vol.34, no.12, pp.1661–1675, 2018. doi: 10.1007/s0037101714399

[11] 
M. Diwakar and M. Kumar, “CT image denoising using NLM and correlationbased wavelet packet thresholding,” IET Image Processing, vol.12, no.5, pp.708–715, 2018. doi: 10.1049/ietipr.2017.0639

[12] 
K. N. Plataniotis and A. N. Venetsanopoulos, Color Image Processing and Applications. Springer, Berlin, Heidelberg, 2000.

[13] 
H. Y. Yang, Y. Zhang, P. Wang, et al., “A geometric correction based robust color image watermarking scheme using quaternion exponent moments,” Optik, vol.125, no.16, pp.4456–4469, 2014. doi: 10.1016/j.ijleo.2014.02.028

[14] 
X. Y. Wang, Z. F. Wu, L. Chen, et al., “Pixel classification based color image segmentation using quaternion exponent moments,” Neural Networks, vol.74, pp.1–13, 2016. doi: 10.1016/j.neunet.2015.10.012

[15] 
C. J. Chen, Y. Xu, and X. K. Yang, “User tailored colorization using automatic scribbles and hierarchical features,” Digital Signal Processing, vol.87, pp.155–165, 2019. doi: 10.1016/j.dsp.2019.01.021

[16] 
Ö. N. Subakan and B. C. Vemuri, “A quaternion framework for color image smoothing and segmentation,” International Journal of Computer Vision, vol.91, no.3, pp.233–250, 2011. doi: 10.1007/s1126301003889

[17] 
B. J. Chen, H. Z. Shu, H. Zhang, et al., “Quaternion Zernike moments and their invariants for color image analysis and object recognition,” Signal Processing, vol.92, no.2, pp.308–318, 2012. doi: 10.1016/j.sigpro.2011.07.018

[18] 
A. Buades, B. Coil, and J. M. Morel, “Nonlocal means denoising,” Image Processing on Line, vol.1, pp.208–212, 2011. doi: 10.5201/ipol.2011.bcm_nlm

[19] 
A. Buades, B. Coll, and J. M. Morel, “Image processing on line: nonlocal means denoising,” Available at: http://www.ipol.im/pub/algo/bcm non local means denoising/, 2022.

[20] 
Q. Li, J. F. Teng, Q. M. Zhao, et al., “Wavelet domain wiener filter and its application in signal denoising,” in Proceedings of the 3rd International Conference on Wavelet Analysis and Its Applications (WAA), Chongqing, China, pp.839–846, 2003.

[21] 
F. Z. Zhang, “Quaternions and matrices of quaternions,” Linear Algebra and Its Applications, vol.251, pp.21–57, 1997. doi: 10.1016/00243795(95)005439

[22] 
B. J. Chen, Q. S. Liu, X. M. Sun, et al., “Removing Gaussian noise for colour images by quaternion representation and optimisation of weights in nonlocal means filter,” IET Image Processing, vol.8, no.10, pp.591–600, 2014. doi: 10.1049/ietipr.2013.0521

[23] 
G. H. Wang, L. Yang, X. Wei, et al., “An improved nonlocal means filter for color image denoising,” Optik, vol.173, pp.157–173, 2018. doi: 10.1016/j.ijleo.2018.08.013

[24] 
Z. G. Jia, Q. Y. Jin, M. K. Ng, et al., “Nonlocal robust quaternion matrix completion for largescale color image and video inpainting,” IEEE Transactions on Image Processing, vol.31, pp.3868–3883, 2022. doi: 10.1109/TIP.2022.3176133

[25] 
X. Y. Li, Y. C. Zhou, and J. Zhang, “Quaternion nonlocal total variation for color image denoising,” in Proceedings of 2019 IEEE International Conference on Systems, Man and Cybernetics, Bari, Italy, pp.1602–1607, 2019.

[26] 
R. Franzen, “Kodak lossless true color image suite,” Available at: http://r0k.us/graphics/kodak, 1999.

[27] 
S. Roth and M. J. Black, “Fields of experts: A framework for learning image priors,” in Proceedings of 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Diego, CA, USA, pp.860–867, 2005.

[28] 
L. Zhang, X. L. Wu, A. Buades, et al., “Color demosaicking by local directional interpolation and nonlocal adaptive thresholding,” Journal of Electronic Imaging, vol.20, no.2, article no.023016, 2011. doi: 10.1117/1.3600632

[29] 
Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Processing Letters, vol.9, no.3, pp.81–84, 2002. doi: 10.1109/97.995823

[30] 
B. Magnier, “Edge detection evaluation: A new normalized figure of merit,” in Proceedings of 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brighton, UK, pp.2407–2411, 2019.

[31] 
A. Khmag, “Additive Gaussian noise removal based on generative adversarial network model and semisoft thresholding approach,” Multimedia Tools and Applications, vol.82, no.5, pp.7757–7777, 2023. doi: 10.1007/s11042022135696

[32] 
Y. Peng, “Quantitative method based on cotangent similarity degree in threevalued Łukasiewicz logic,” Chinese Journal of Electronics, vol.30, no.1, pp.134–144, 2021. doi: 10.1049/cje.2020.11.011

[33] 
Y. F. Li, Q. J. Zhao, W. B. Zhang, et al., “A simultaneous cartoontexture image segmentation and image decomposition method,” Chinese Journal of Electronics, vol.29, no.5, pp.906–915, 2020. doi: 10.1049/cje.2020.08.006

[34] 
M. Li and C. Xu, “Variational image restoration and decomposition in shearlet smoothness spaces,” Chinese Journal of Electronics, vol.26, no.5, pp.1017–1021, 2017. doi: 10.1049/cje.2017.08.021
