International Journal of Image, Graphics and Signal Processing (IJIGSP)
IJIGSP Vol. 18, No. 2, 8 Apr. 2026
Cover page and Table of Contents: PDF (size: 1581KB)
Image Denoising in the Contourlet Domain Using RBF Network and Kalman Filter
PDF (1581KB), PP.68-86
Views: 0 Downloads: 0
Author(s)
Index Terms
Image Restoration, Radial Basis Function Neural Networks, Contourlet Transform, Kalman Filters
Abstract
Image denoising remains a fundamental challenge in image processing, particularly when dealing with additive white gaussian noise (AWGN) that degrades visual quality and information content. This paper introduces a novel multi-stage denoising framework that uniquely combines Contourlet transform, radial basis function neural networks (RBFNN), and kalman filtering to effectively preserve important image features while removing noise. The contourlet transform first decomposes images into multi-resolution, directional subbands, providing a sparse representation that better captures geometric structures compared to traditional wavelet approaches. We then employ an RBFNN trained through back-propagation to adaptively threshold the contourlet coefficients based on local image characteristics and noise levels. Finally, kalman filtering is applied as a post-processing step to further suppress residual noise artifacts. Comprehensive experiments conducted on standard benchmark datasets demonstrate that our approach outperforms several state-of-the-art methods, including BM3D and recent deep learning-based techniques, particularly at moderate to high noise levels (σ ≥ 15). Quantitative evaluations show our method achieves superior PSNR improvements of up to 2.4dB and SSIM improvements of 0.12 compared to recent competing approaches, while qualitative results confirm better preservation of edges and textural details. The proposed framework offers an effective balance between computational efficiency and denoising performance, making it suitable for various practical applications.
Cite This Paper
Rachid Benoudi, Youssef Qaraai, Mohamed Ouhda, "Image Denoising in the Contourlet Domain Using RBF Network and Kalman Filter", International Journal of Image, Graphics and Signal Processing(IJIGSP), Vol.18, No.2, pp. 68-86, 2026. DOI:10.5815/ijigsp.2026.02.05
Reference
[1]A. Buades, B. Coll, and J.-M. Morel. A non-local algorithm for image denoising. In 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05), volume 2, pages 60–65, San Diego, CA, USA, 2005. IEEE.
[2]Kostadin Dabov, Alessandro Foi, Vladimir Katkovnik, and Karen Egiazarian. Image denoising by sparse 3-d transform-domain collaborative filtering. IEEE Transactions on Image Processing, 16(8):2080–2095, August 2007.
[3]Kai Zhang, Wangmeng Zuo, Yunjin Chen, Deyu Meng, and Lei Zhang. Beyond a gaussian denoiser: Residual learning of deep CNN for image denoising. IEEE Transactions on Image Processing, 26(7):3142–3155, July 2017.
[4]Ding Liu, Bihan Wen, Yuchen Fan, Chen Change Loy, and Thomas S. Huang. Non-local recurrent network for image restoration, 2018.
[5]Thomas Plo¨tz and Stefan Roth. Neural nearest neighbors networks. In Advances in Neural Information Processing Systems (NeurIPS 2018), volume 31, pages 2341–2351, Montreal, Canada, 2018. Curran Associates, Inc.
[6]M.N. Do and M. Vetterli. The contourlet transform: an efficient directional multiresolution image representation. IEEE Transactions on Image Processing, 14(12):2091–2106, December 2005.
[7]Jooyoung Park and Irwin W. Sandberg. Approximation and radial-basis-function networks. Neural Computation, 5(2):305–316, March 1993.
[8]Rafael C. Gonzalez and Richard E. Woods. Digital Image Processing. Prentice Hall, Upper Saddle River, NJ, USA, 2nd edition, 2002.
[9]Anil K. Jain. Fundamentals of Digital Image Processing. Prentice Hall, Englewood Cliffs, NJ, USA, 1st edition, 1989.
[10]G. Angelopoulos and I. Pitas. Multichannel wiener filters in color image restoration. IEEE Transactions on Circuits and Systems for Video Technology, 4(1):83–87, 1994.
[11]Jaakko Astola and Petri Kuosmanen. Fundamentals of Nonlinear Digital Filtering. CRC Press, Boca Raton, FL, USA, 2020.
[12]Jong-Sen Lee. Digital image enhancement and noise filtering by use of local statistics. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-2(2):165–168, March 1980.
[13]Jong-Sen Lee. Refined filtering of image noise using local statistics. Computer Graphics and Image Processing, 15(4):380–389, April 1981.
[14]Kostadin Dabov, Vladimir Katkovnik, and Karen Egiazarian. Bm3d image denoising with shape-adaptive principal component analysis. In Signal Processing with Adaptive Sparse Structured Representations (SPARS’09), Saint-Malo, France, 2009.
[15]P. Chatterjee and P. Milanfar. Is denoising dead? IEEE Transactions on Image Processing, 19(4):895–911, April 2010.
[16]Anat Levin and Boaz Nadler. Natural image denoising: Optimality and inherent bounds. In 2011 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 2833–2840, Colorado Springs, CO, USA, 2011. IEEE.
[17]Yung-Hsiang Lou, Paolo Favaro, Stefano Soatto, and Mario Bertozzi. Nonlocal similarity image filtering. In Image Analysis and Processing – ICIAP 2009, pages 62–71. Springer, Sorrento, Italy, 2009.
[18]Ruomei Yan, Ling Shao, Sascha D. Cvetkovic, and Jan Klijn. Improved nonlocal means based on pre-classification and invariant block matching. Journal of Display Technology, 8(4):212–218, April 2012.
[19]Antonin Chambolle. An algorithm for total variation minimization and applications. Journal of Mathematical Imaging and Vision, 20:163–177, jan 2004.
[20]Michael Elad and Michal Aharon. Image denoising via sparse and redundant representations over learned dictionaries. IEEE Transactions on Image Processing, 15(12):3736–3745, December 2006.
[21]Julien Mairal, Michael Elad, and Guillermo Sapiro. Sparse representation for color image restoration. IEEE Transactions on Image Processing, 17(1):53–69, January 2008.
[22]Weisheng Dong, Lei Zhang, Guangming Shi, and Xin Li. Nonlocally centralized sparse representation for image restoration. IEEE Transactions on Image Processing, 22(4):1620–1630, April 2013.
[23]Linwei Fan, Xuemei Li, Hui Fan, Yanli Feng, and Caiming Zhang. Adaptive texture-preserving denoising method using gradient histogram and nonlocal self-similarity priors. IEEE Transactions on Circuits and Systems for Video Technology, 29(11):3222–3235, November 2019.
[24]Qingyang Xu, Chengjin Zhang, and Li Zhang. Denoising convolutional neural network. In 2015 IEEE International Conference on Information and Automation, pages 00–00. IEEE, August 2015.
[25]Chunwei Tian, Yong Xu, Zuoyong Li, Wangmeng Zuo, Lunke Fei, and Hong Liu. Attention-guided cnn for image denoising. Neural Networks, 124:117–129, April 2020.
[26]Zhuoxiao Li, Faqiang Wang, Li Cui, and Jun Liu. Dual mixture model based cnn for image denoising. IEEE Transactions on Image Processing, 31:3618–3629, 2022.
[27]Reyhaneh Neshatavar, Mohsen Yavartanoo, Sanghyun Son, and Kyoung Mu Lee. Cvf-sid: Cyclic multi-variate function for self-supervised image denoising by disentangling noise from image. In 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), page 17562–17570. IEEE, June 2022.
[28]Jean-Luc Starck, E.J. Candes, and D.L. Donoho. The curvelet transform for image denoising. IEEE Transactions on Image Processing, 11(6):670–684, June 2002.
[29]Tingting Wu, Chaoyan Huang, Shilong Jia, Wei Li, Raymond Chan, Tieyong Zeng, and S. Kevin Zhou. Medical image reconstruction with multi-level deep learning denoiser and tight frame regularization. Applied Mathematics and Computation, 477:128795, September 2024.
[30]Yurong Chen, Hui Zhang, Yaonan Wang, Yimin Yang, and Jonathan Wu. Flex-dld: Deep low-rank decomposition model with flexible priors for hyperspectral image denoising and restoration. IEEE Transactions on Image Processing, 33:1211–1226, 2024.
[31]Zenglin Shi, Pascal Mettes, Subhransu Maji, and Cees G. M. Snoek. On measuring and controlling the spectral bias of the deep image prior. International Journal of Computer Vision, 130(4):885–908, February 2022.
[32]Jianlou Xu, Shaopei You, Yuying Guo, and Yajing Fan. Combining deep image prior and second-order generalized total variance for image denoising. IEEE Access, 11:67912–67921, 2023.
[33]Jingyun Liang, Jiezhang Cao, Guolei Sun, Kai Zhang, Luc Van Gool, and Radu Timofte. Swinir: Image restoration using swin transformer. IEEE International Conference on Computer Vision, 2021.
[34]Syed Waqas Zamir, Aditya Arora, Salman Gupta, Fahad Shahbaz Khan, Jian Sun, Ling Shao, Fatih Porikli, and Ming-Hsuan Yang. Restormer: Efficient transformer for high-resolution image restoration. IEEE Conference on Computer Vision and Pattern Recognition, 2022.
[35]Tingting Wu, Chaoyan Huang, Shilong Jia, Wei Li, Raymond Chan, Tieyong Zeng, and S Kevin Zhou. Medical image reconstruction with multi-level deep learning denoiser and tight frame regularization. Applied Mathematics and Computation, 477:128795, 2024.
[36]Yurong Chen, Hui Zhang, Yaonan Wang, Yimin Yang, and Jonathan Wu. Flex-dld: Deep low-rank decomposition model with flexible priors for hyperspectral image denoising and restoration. IEEE Transactions on Image Processing, 33:1211–1226, 2024.
[37]David Broomhead and David Lowe. Radial basis functions, multi-variable functional interpolation and adaptive networks. Royal Signals And Radar Establishment Malvern (United Kingdom), RSRE-MEMO-4148:321–355, 03 1988.
[38]T. Poggio and F. Girosi. Networks for approximation and learning. Proceedings of the IEEE, 78(9):1481–1497, 1990.
[39]P. Burt and E. Adelson. The laplacian pyramid as a compact image code. IEEE Transactions on Communications, 31(4):532–540, April 1983.
[40]R.H. Bamberger and M.J.T. Smith. A filter bank for the directional decomposition of images: theory and design. IEEE Transactions on Signal Processing, 40(4):882–893, April 1992.
[41]John Immerkær. Fast noise variance estimation. Computer Vision and Image Understanding, 64(2):300–302, September 1996.