# An Unsupervised Image Denoising Method Using a Nonconvex Low-Rank Model with TV Regularization
## 4 Experimental Results and Analysis
### Natural Image Denoising  
The eight natural images we selected for testing are shown in Figure 3. We chose three examples to demonstrate the denoising effect of the proposed method and five comparison methods on three types of noise, as shown in Figures 4-6. In Figures 4-6, example ROIs of size 30 \(\times\) 30 pixels are taken (center) and enlarged (bottom right corner) for visualization, and visible image quality upgrades after restoration are presented. Additionally, based on these six methods, we compared the singular values between the original noise-free image and the denoised image, as shown in Figures 4a, 5a and 6a. The results showed that, compared with the five comparison methods, the singular value curve of our method was closer to the original image curve, which indicated that the method obtained the singular value closest to the original clean image. The majority of the images in Figures 4-6 show that, despite the method's various denoising impacts for different noises, our proposed method was still the best when compared to the other five methods. For example, in the denoising results of impulse noise (Figure 4), there are apparent unclear image texture phenomena in Figure 4d. Figure 4e not only retains a lot of noise, but the image structure cannot be identified either. Figure 4f has blurred edges and decreased brightness, while Figure 4g has a certain structural fidelity but a lot of noise residues. Although the noise is removed in Figure 4h, the overall appearance of the image is not clear, and the image structure is not clear. Figure 4: Denoising images of Butterfly by different methods (impulse noise). **(a)** singular value comparison; **(b)** original clean image; **(c)** noisy image (impulse noise); **(d)** RPCA (PSNR = 32.52 dB, SSIM = 0.9635, FSIM = 0.9802); **(e)** AMlogtv (PSNR = 20.87 dB, SSIM = 0.6670, FSIM = 0.9860); **(f)** NonRPCA (PSNR = 33.86 dB, SSIM = 0.9318, FSIM = 0.9592); **(g)** WNNM - RPCA (PSNR = 30.95 dB, SSIM = 0.7651, FSIM = 0.9015); **(h)** TDV (PSNR = 18.41 dB, SSIM = 0.6336, FSIM = 0.7521); **(i)** our method (PSNR = 41.64 dB, SSIM = 0.9863, FSIM = 0.9911). Figure 3: The eight test images: Butterfly, House, Peppers, Lena, Room, Bird, Camera, Starfish. is very blurred, and the image edge cannot be clearly identified. Conversely, Figure 4i not only removes the noise completely but also further enhances the smoothness of the image while preserving the detailed structure of the image. This is due to the positive and effective use of our designed \(\gamma\)-norm and TV norm. In addition, our proposed method preserved the contrast and brightness of the original image well. In the Poisson noise denoising results (Figure 5), we can see that the enlarged parts of Figure 5d-g clearly show that these comparison methods blurred the noise part but did not remove the blurred part, resulting in a less clear image. The detail structure of Figure 5h is very blurred, and the overall clarity of the picture is seriously reduced. Our denoising method (Figure 5i) is more visible to the naked eye than other denoising methods and provides a smoother image. Although the overall denoising results of our method and WNNM-RPCA for Gaussian noise (Figure 6) did not differ significantly, it is nevertheless obvious from the details that our method preserved the clearest image structure and performed the most complete denoising. Figure 5: Denoising images of Starfish by different methods (Poisson noise). **(a)** Singular value comparison; **(b)** original clean image; **(c)** noisy image (Poisson noise); **(d)** RPCA (PSNR = 27.11 dB, SSIM = 0.9119, FSIM = 0.9561); **(e)** AMlogtv (PSNR = 25.65 dB, SSIM = 0.7654, FSIM = 0.9682); **(f)** NonRPCA (PSNR = 28.45 dB, SSIM = 0.9086, FSIM = 0.9541); **(g)** WNNM\(-\)RPCA (PSNR = 28.83 dB, SSIM = 0.9155, FSIM = 0.9582); **(h)** TDV (PSNR = 20.84 dB, SSIM = 0.5388, FSIM = 0.7005); **(i)** our method (PSNR = 29.30 dB, SSIM = 0.9324, FSIM = 0.9690).