Image Denoising Method Based on 3D Block Matching with Harmonic Filtering in Transform Domain
Keywords:
Image denoising, Diffusion model, BM3D, Laplacian-Gaussian algorithmAbstract
Today, I will explain an image denoising method based on 3D block matching with harmonic filtering in the transform domain. This topic is important because digital images are susceptible to noise during acquisition, storage, and transmission. Image denoising is crucial in pre-processing and is a key research area in digital image processing and computer vision. Traditional denoising techniques face limitations such as high computational complexity, so combining multiple methods is more effective. The integration of wave-domain harmonic filtering and 3D block matching (BM3D) introduces a new and efficient denoising algorithm. The Euclidean distance approach is used to group similar 2D image blocks into a 3D array. The inverse transformation reconstructs the image, followed by wavelet decomposition to filter high-frequency noise. To prevent edge blurring, the Laplacian-Gaussian algorithm is applied to refine the diffusion model. Finally, wavelet reconstruction is performed to approximate the original image. Experimental results demonstrate that this approach improves information protection and processing speed, making it highly effective in practice.
References
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Dabov, K., Foi, A., Katkovnik, V., & Egiazarian, K. (2007). Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE transactions on image processing, 16(8), 2080-2095.
Elad, M., Kawar, B., & Vaksman, G. (2023). Image denoising: The deep learning revolution and beyond—a survey paper. SIAM Journal on Imaging Sciences, 16(3), 1594-1654.
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Fan, L., Zhang, F., Fan, H., & Zhang, C. (2019). Brief review of image denoising techniques. Visual Computing for Industry, Biomedicine, and Art, 2(1), 7.
Foi, A., Katkovnik, V., & Egiazarian, K. (2007). Pointwise shape-adaptive DCT for high-quality denoising and deblocking of grayscale and color images. IEEE transactions on image processing, 16(5), 1395-1411.
Hinton, G. E., & Salakhutdinov, R. R. (2006). Reducing the dimensionality of data with neural networks. science, 313(5786), 504-507.
Hwang, H., & Haddad, R. A. (1995). Adaptive median filters: new algorithms and results. IEEE transactions on image processing, 4(4), 499-502.
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Mallat, S. G. (1989). A theory for multiresolution signal decomposition: the wavelet representation. IEEE transactions on pattern analysis and machine intelligence, 11(7), 674-693.
Perona, P., & Malik, J. (1990). Scale-space and edge detection using anisotropic diffusion. IEEE transactions on pattern analysis and machine intelligence, 12(7), 629-639.
Toprak, A., & Güler, İ. (2006). Suppression of impulse noise in medical images with the use of fuzzy adaptive median filter. Journal of Medical systems, 30, 465-471.
Xian-Chun, Z., Mei-Ling, W., Lan-Fang, S., & Lin-Feng, Z. (2015). Diffusion denoising model based on the wavelet and biharmonic equation. Acta Physica Sinica, 64(6).
Xie, J., Xu, L., & Chen, E. (2012). Image denoising and inpainting with deep neural networks. Advances in neural information processing systems, 25.
Yuan, L., & Xu, X. (2015). Adaptive image edge detection algorithm based on canny operator. 2015 4th International Conference on Advanced Information Technology and Sensor Application (AITS),
Cornelis, B., Moonen, M., & Wouters, J. (2014). Reduced-bandwidth multi-channel Wiener filter based binaural noise reduction and localization cue preservation in binaural hearing aids. Signal processing, 99, 1-16.
Dabov, K., Foi, A., Katkovnik, V., & Egiazarian, K. (2007). Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE transactions on image processing, 16(8), 2080-2095.
Elad, M., Kawar, B., & Vaksman, G. (2023). Image denoising: The deep learning revolution and beyond—a survey paper. SIAM Journal on Imaging Sciences, 16(3), 1594-1654.
Elmoataz, A., Desquesnes, X., & Lézoray, O. (2012). Non-local morphological PDEs and $ p $-Laplacian equation on graphs with applications in image processing and machine learning. IEEE Journal of Selected Topics in Signal Processing, 6(7), 764-779.
Buades, A., Coll, B., & Morel, J.-M. (2005). A non-local algorithm for image denoising. 2005 IEEE computer society conference on computer vision and pattern recognition (CVPR'05),
Cornelis, B., Moonen, M., & Wouters, J. (2014). Reduced-bandwidth multi-channel Wiener filter based binaural noise reduction and localization cue preservation in binaural hearing aids. Signal processing, 99, 1-16.
Dabov, K., Foi, A., Katkovnik, V., & Egiazarian, K. (2007). Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE transactions on image processing, 16(8), 2080-2095.
Elad, M., Kawar, B., & Vaksman, G. (2023). Image denoising: The deep learning revolution and beyond—a survey paper. SIAM Journal on Imaging Sciences, 16(3), 1594-1654.
Elmoataz, A., Desquesnes, X., & Lézoray, O. (2012). Non-local morphological PDEs and $ p $-Laplacian equation on graphs with applications in image processing and machine learning. IEEE Journal of Selected Topics in Signal Processing, 6(7), 764-779.
Fan, L., Zhang, F., Fan, H., & Zhang, C. (2019). Brief review of image denoising techniques. Visual Computing for Industry, Biomedicine, and Art, 2(1), 7.
Foi, A., Katkovnik, V., & Egiazarian, K. (2007). Pointwise shape-adaptive DCT for high-quality denoising and deblocking of grayscale and color images. IEEE transactions on image processing, 16(5), 1395-1411.
Hinton, G. E., & Salakhutdinov, R. R. (2006). Reducing the dimensionality of data with neural networks. science, 313(5786), 504-507.
Hwang, H., & Haddad, R. A. (1995). Adaptive median filters: new algorithms and results. IEEE transactions on image processing, 4(4), 499-502.
Krizhevsky, A., Sutskever, I., & Hinton, G. E. (2012). Imagenet classification with deep convolutional neural networks. Advances in neural information processing systems, 25.
LeCun, Y. (1989). Generalization and network design strategies. Connections in Perspective.
LI, W.-g., & ZHAO, X.-m. (2013). Multi-wavelet image denoising based on artifical bee colony algorithm. Journal of Chongqing University of Posts and Telecommunication (Natural Science Edition), 25(4), 532-537.
Mallat, S. G. (1989). A theory for multiresolution signal decomposition: the wavelet representation. IEEE transactions on pattern analysis and machine intelligence, 11(7), 674-693.
Perona, P., & Malik, J. (1990). Scale-space and edge detection using anisotropic diffusion. IEEE transactions on pattern analysis and machine intelligence, 12(7), 629-639.
Toprak, A., & Güler, İ. (2006). Suppression of impulse noise in medical images with the use of fuzzy adaptive median filter. Journal of Medical systems, 30, 465-471.
Xian-Chun, Z., Mei-Ling, W., Lan-Fang, S., & Lin-Feng, Z. (2015). Diffusion denoising model based on the wavelet and biharmonic equation. Acta Physica Sinica, 64(6).
Xie, J., Xu, L., & Chen, E. (2012). Image denoising and inpainting with deep neural networks. Advances in neural information processing systems, 25.
Yuan, L., & Xu, X. (2015). Adaptive image edge detection algorithm based on canny operator. 2015 4th International Conference on Advanced Information Technology and Sensor Application (AITS),
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Published
2025-04-15
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Articles
How to Cite
[1]
“Image Denoising Method Based on 3D Block Matching with Harmonic Filtering in Transform Domain”, Int. J. Inform. Inf. Sys. and Comp. Eng., vol. 7, no. 1, pp. 59–69, Apr. 2025, Accessed: Apr. 19, 2025. [Online]. Available: https://ojs.unikom.ac.id/index.php/injiiscom/article/view/15615
