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

Hawkar Qsim Birdawod; Azhin Mohammed Khudhur; Dler Hussein Kadir; Dlshad Mahmood Saleh

doi:10.24017/science.2024.2.1

Authors

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

Abstract

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.

Keywords:

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

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