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Mathematical Problems in Engineering
Volume 2018 (2018), Article ID 1542509, 19 pages
Research Article

Image Denoising Using Singular Value Difference in the Wavelet Domain

Min Wang,1,2 Wei Yan,1,2 and Shudao Zhou1,2

1College of Meteorology and Oceanography, National University of Defense Technology, Nanjing 211101, China
2Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science & Technology, Nanjing 210044, China

Correspondence should be addressed to Min Wang; moc.361@1080uy

Received 15 July 2017; Revised 27 October 2017; Accepted 14 November 2017; Published 17 January 2018

Academic Editor: Raffaele Solimene

Copyright © 2018 Min Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Singular value (SV) difference is the difference in the singular values between a noisy image and the original image; it varies regularly with noise intensity. This paper proposes an image denoising method using the singular value difference in the wavelet domain. First, the SV difference model is generated for different noise variances in the three directions of the wavelet transform and the noise variance of a new image is used to make the calculation by the diagonal part. Next, the single-level discrete 2-D wavelet transform is used to decompose each noisy image into its low-frequency and high-frequency parts. Then, singular value decomposition (SVD) is used to obtain the SVs of the three high-frequency parts. Finally, the three denoised high-frequency parts are reconstructed by SVD from the SV difference, and the final denoised image is obtained using the inverse wavelet transform. Experiments show the effectiveness of this method compared with relevant existing methods.