Abstract
Image denoising methods generally remove not only noise but also fine-scale textures and thus degrade the subjective image quality. In this paper, we propose a method of recovering the texture component that is lost under a state-of-the-art denoising method called weighted nuclear norm minimization (WNNM). We recover the image texture with a linear minimum mean squared error estimator (LMMSE filter), which requires statistical information about the texture and noise. This requirement is the key problem preventing the application of the LMMSE filter for texture recovery because such information is not easily obtained. We propose a new method of estimating the necessary statistical information using Stein’s lemma and several assumptions and show that our estimated information is more accurate than the simple estimation in terms of the Fréchet distance. Experimental results show that our proposed method can improve the objective quality of denoised images. Moreover, we show that our proposed method can also improve the subjective quality when an additional parameter is chosen for the texture to be added.
Highlights
Image denoising methods generally remove noise and fine-scale textures and degrade the subjective image quality
Weighted nuclear norm minimization for image denoising (WNNM) [16] is an optimization-based method based on an nonlocal self-similarity (NLSS)-based objective function
We introduce several nontrivial assumptions to estimate the covariance matrices regarding the texture and noise that are used in the LMMSE filter based on Stein’s lemma
Summary
Image denoising methods that can estimate a noiseless, clean natural image (original image) from a noisy observation are actively being studied [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]. The covariance matrices that are used in the suboptimal Wiener filter are calculated from sample observation patches, which are chosen using a nonfixed search window As another method of managing the distant relationships characterizing texture, a denoising method using the total generalized variation (TGV) and low-rank matrix approximation via nuclear norm minimization has been proposed [21]. Because we define the texture as the difference between the original and denoised images, we can utilize the information obtained in the denoising process to estimate the texture covariance matrices more . We introduce several nontrivial assumptions to estimate the covariance matrices regarding the texture and noise that are used in the LMMSE filter based on Stein’s lemma. In this paper, we show new experimental results obtained on two image datasets (contains 110 images in total) to confirm our method’s effectiveness
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