A Wavelet Shrinkage Mixed with a Single-level 2D Discrete Wavelet Transform for Image Denoising


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  • Hawkar Qsim Birdawod Department of Business Administration, College of Administration and Financial Sciences, Cihan University-Erbil, Erbil, Iraq https://orcid.org/0000-0002-1256-4618
  • Azhin Mohammed Khudhur Department of Statistics, College of Administration and Economics, Salahaddin University, Erbil, Iraq https://orcid.org/0000-0002-0524-4990
  • Dler Hussein Kadir Department of Statistics, College of Administration and Economics, Salahaddin University, Erbil, Iraq https://orcid.org/0000-0002-1254-721X
  • Dlshad Mahmood Saleh Department of Statistics, College of Administration and Economics, Salahaddin University, Erbil, Iraq | Department of Accounting and Financial, College of Administration and Economics, Lebanese French University, Erbil, Iraq https://orcid.org/0009-0001-3213-9205


The single-level 2D discrete wavelet transform method is a powerful technique for effectively removing Gaussian noise from natural images. Its effectiveness is attributed to its ability to capture a signal's energy at low energy conversion values, allowing for efficient noise reduction while preserving essential image details. The wavelet noise reduction method mitigates the noise present in the waveform coefficients produced by the discrete wavelet transform. In this study, three different wavelet families—Daubechies (db7), Coiflets (coif5), and Fejér-Korovkin (fk4)—were evaluated for their noise removal capabilities using the Bayes shrink method. This approach was applied to a set of images, and the performance was analyzed using the Mean Squared Error (MSE) and Peak Signal-to-Noise Ratio (PSNR) metrics. Our results demonstrated that among the wavelet families tested, the Fejér-Korovkin (fk4) wavelet consistently outperformed the others. The fk4 wavelet family yielded the lowest MSE values, indicating minimal reconstruction error, and the highest PSNR values, reflecting superior noise suppression and better image quality across all tested images. These findings suggest that the fk4 wavelet family, when combined with the Bayes shrink method, provides a robust framework for Gaussian noise reduction in natural images. The comparative analysis highlights the importance of selecting appropriate wavelet families to optimize noise reduction performance, paving the way for further research and potential improvements in image denoising techniques.


Denoising image, Single-level 2D DWT, Wavelet, Bayesshrink threshold, Daubechies (db7), Coiflets (coif5), Fejér-Korovkin (fk4)


X. Jianhui and T. Li, "Image Denoising Method Based on Improved Wavelet Threshold Transform," in 2019 IEEE Sym-posium Series on Computational Intelligence (SSCI), pp. 1064-1067, 2019, doi: 10.1109/SSCI44817.2019.9002923. DOI: https://doi.org/10.1109/SSCI44817.2019.9002923

A. Vyas and J. Paik, "Review of The Application of Wavelet Theory to Image Processing," IEIE Transactions on Smart Pro-cessing and Computing, vol. 5, no. 6, pp. 403-417, 2016, doi: 10.5573/ieiespc.2016.5.6.403. DOI: https://doi.org/10.5573/IEIESPC.2016.5.6.403

R. E. Woods and R. C. Gonzalez, Digital Image Processing, Pearson Education Ltd., 2008.

T. Zhao, Y. Wang, Y. Ren, and Y. Liao, "Approach of Image Denoising Based on Discrete Multi-Wavelet Transform," in 2009 International Workshop on Intelligent Systems and Applications, pp. 1-4, 2009, doi: 10.1109/IWISA.2009.5072757. DOI: https://doi.org/10.1109/IWISA.2009.5072757

A. Khare, M. Khare, Y. Jeong, H. Kim, and M. Jeon, "Despeckling of Medical Ultrasound Images Using Daubechies Complex Wavelet Transform," Signal Processing, vol. 90, no. 2, pp. 428-439, 2010, doi: 10.1016/j.sigpro.2009.07.008. DOI: https://doi.org/10.1016/j.sigpro.2009.07.008

A. Khare, U. Tiwary, W. Pedrycz, and M. Jeon, "Multilevel Adaptive Thresholding and Shrinkage Technique for De-noising Using Daubechies Complex Wavelet Transform," Imaging Sci. J., vol. 58, no. 6, pp. 340-358, 2010, doi: 10.1179/136821910X12750339175826. DOI: https://doi.org/10.1179/136821910X12750339175826

D. L. Donoho and I. M. Johnstone, "Ideal Spatial Adaptation by Wavelet Shrinkage," Biometrika, vol. 81, no. 3, pp. 425-455, 1994, doi: 10.1093/biomet/81.3.425. DOI: https://doi.org/10.1093/biomet/81.3.425

W. T. Kahwachi and H. Q. Birdawod, "A New Hybridization of Bilateral and Wavelet Filters for Noisy De-Noisy Imag-es," Eurasian J. Sci. Eng., vol. 9, no. 1, 2023, doi: 10.23918/EAJSE.V9I1P99. DOI: https://doi.org/10.23918/eajse.v9i1p99

L. Wang, H. Xu, and Y. Liu, "A Novel Dynamic Load Identification Approach for Multi-Source Uncertain Structures Based on The Set-Theoretical Wavelet Transform and Layered Noise Reduction," Structures, vol. 51, 2023, doi: 10.1016/j.istruc.2023.03.037. DOI: https://doi.org/10.1016/j.istruc.2023.03.037

C. González-Rodríguez, M. A. Alonso-Arévalo, and E. García-Canseco, "Robust Denoising of Phonocardiogram Signals Using Time-Frequency Analysis and U-Nets," IEEE Access, vol. 11, pp. 52466-52479, 2023, doi: 10.1109/ACCESS.2023.3280453. DOI: https://doi.org/10.1109/ACCESS.2023.3280453

S. L. Shabana Sulthana and M. Sucharitha, "Two-Phase Speckle Noise Removal in US Images: Speckle Reducing Im-proved Anisotropic Diffusion and Optimal Bayes Threshold," Int. J. Image Graph., 2550071, 2024, doi: 10.1142/S0219467825500718. DOI: https://doi.org/10.1142/S0219467825500718

Y. Jin, X. Zhang, M. Liu, L. Wang, and J. Li, "A Novel Deep Wavelet Convolutional Neural Network for Actual ECG Signal Denoising," Biomed. Signal Process. Control, vol. 87, 105480, 2024, doi: 10.1016/j.bspc.2023.105480. DOI: https://doi.org/10.1016/j.bspc.2023.105480

S. Abut, H. Okut, and K. J. Kallail, "Paradigm Shift from Artificial Neural Networks (Anns) to Deep Convolutional Neu-ral Networks (Dcnns) in The Field of Medical Image Processing," Expert Systems with Applications, 122983, 2023, doi: 10.1016/j.eswa.2023.122983. DOI: https://doi.org/10.1016/j.eswa.2023.122983

T. H. Ali, S. H. Mahmood, and A. S. Wahdi, “Using A Proposed Hybrid Method of Neural and Wavelet Networks to Estimate the Time Series Model," Tikrit J. Admin. Econ. Sci., vol. 18, no. 57, 3, pp. 432-448, 2022, doi: 10.25130/tjaes. DOI: https://doi.org/10.25130/tjaes.

T. H. Ali and D. M. Saleh, "Comparison Between Wavelet Bayesian and Bayesian Estimators to Remedy Contamination in Linear Regression Model," PalArch's Journal Archaeology of Egypt/Egyptology, vol. 18, no. 10, pp. 3388-3409, 2021.

M. Chowdhury, M. Hoque, and A. Khatun, "Image Compression Using Discrete Wavelet Transform," IJCSI International Journal of Computer Science Issues, vol. 9, pp. 327-330, 2012.

I. Daubechies, "Orthonormal Bases of Compactly Supported Wavelets," Communications on Pure and Applied Mathematics, vol. 41, no. 7, pp. 909-996, 1988, doi: 10.1002/cpa.3160410705. DOI: https://doi.org/10.1002/cpa.3160410705

T. H. Ali and D. M. Saleh, "Proposed Hybrid Method for Wavelet Shrinkage with Robust Multiple Linear Regression Model: With Simulation Study," Qalaai Zanist Journal, vol. 7, no. 1, pp. 920-937, 2022, doi: 10.25212/lfu.qzj.7.1.36. DOI: https://doi.org/10.25212/lfu.qzj.7.1.36

M. Nielsen, "On the Construction and Frequency Localization of Finite Orthogonal Quadrature Filters," J. Approx. Theo-ry, vol. 108, no. 1, pp. 36-52, 2001, doi: 10.1006/jath.2000.3514. DOI: https://doi.org/10.1006/jath.2000.3514

B. Anjali and S. Jagroop, "Coiflet Wavelet Transform Image Compression Based on JPEG Images," International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering, vol. 5, no. 7, pp. 6358-6363, 2016, doi :10.15662/IJAREEIE.2016.0507088.

A. Dixit and P. Sharma, "A Comparative Study of Wavelet Thresholding for Image Denoising," IJ Image, Graphics and Signal Processing, vol. 12, pp. 39-46, 2014, doi: 10.5815/ijigsp.2014.12.06. DOI: https://doi.org/10.5815/ijigsp.2014.12.06

S. K. Mohideen, S. A. Perumal, and M. M. Sathik, "Image De-Noising Using Discrete Wavelet Transform," International Journal of Computer Science and Network Security, vol. 8, no. 1, pp. 213-216, 2008.

S. D. Ruikar and D. D. Doye, "Wavelet Based Image Denoising Technique," International Journal of Advanced Computer Science and Applications, vol. 2, no. 3, 2011, doi: 10.14569/IJACSA.2011.020309. DOI: https://doi.org/10.14569/IJACSA.2011.020309


How to Cite

H. Q. Birdawod, A. M. Khudhur, D. H. Kadir, and D. M. Saleh, “A Wavelet Shrinkage Mixed with a Single-level 2D Discrete Wavelet Transform for Image Denoising”, KJAR, vol. 9, no. 2, pp. 1–12, Jul. 2024, doi: 10.24017/science.2024.2.1.

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