Abstract
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.
Highlights
Wavelet transform [1,2,3,4,5,6] and singular value decomposition (SVD) [7] have been widely used as transform domain methods [8] in image denoising
We introduce two parameters related to the size of the image and the intensity of the added noise to adjust the Singular value (SV) difference function: gn (x)
According to the shape of SV difference curves vary regularly with the size of the image of Figures 2(a)–2(c); the longitudinal shrinkage coefficients p(m) in the three directions can be calculated by the fitting function of maximum values with 3-degree polynomial divided by the fitting function of standard size (200): pH
Summary
Wavelet transform [1,2,3,4,5,6] and singular value decomposition (SVD) [7] have been widely used as transform domain methods [8] in image denoising. In [9], a denoising algorithm based on adaptive SVD in the wavelet domain is proposed. An adaptive representation method is proposed [10] using the K-means and singular value decomposition (K-SVD), which uses a greedy algorithm to learn an overcomplete dictionary for image representation and denoising. In [18], a denoising method based on spatially adaptive iterative singular value thresholding (SAIST) is proposed. An image denoising method is proposed using the SV difference in the wavelet domain.
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