# An Unsupervised Image Denoising Method Using a Nonconvex Low-Rank Model with TV Regularization
## 4 Experimental Results and Analysis
### Medical Image Denoising  
In this section, we selected eight medical images from public datasets for testing, as shown in Figure 8. We show the visual comparison results of three images in Figures 9-11. Among them, Figures 9a, 10a, and 11a are the singular value distribution curves of the denoised image and the original image of each comparison method. We learn that the singular value of the denoised image obtained by the proposed method is closer to the real ground value, which also proves that it has the advantage of suppressing the overpenalized singular value of the classical competition method (RPCA) while maintaining a small singular value. By observing the denoising experiment findings, we discover that in the denoising results of impulse noise (Figure 9), the enlarged images of Figure 9d,h have clear artifacts and little to no noise. In the enlarged image of Figure 9e, the noise is mixed with the structure of the image itself, and the image and noise cannot be distinguished. Although there is not any evident noise in the magnified version of Figure 9f, there is a small blurring of the edge information of the lung tissue and some \"oil painting\" phenomenon. In Figure 9g, there is a great deal of noise, which makes the image unrecognizable. The enlarged image of Figure 9h is very blurred, and there is obvious noise in the image. Conversely, our method (Figure 9i) has the best denoising effect. The image edge structure is highly clear and noise-free, which is nearly identical to the original image. In the experiment of removing Poisson noise, we find that although the denoising effects of these six algorithms are very close, we can still find that Figure 10d,g are obviously darkened, and there are still some impurities in the background of Figure 10f. Figure 10e,h blur the original details of the image, but our method (Figure 10i) does not exhibit these phenomena. Furthermore, when denoising the image containing Gaussian noise, it is obvious from the comparison result diagram in Figure 11 that although the comparison method removes noise to a certain extent, it does not smooth the image when saving the image detail information, leaving the image with insufficient clarity. In conclusion, our approach had a good edge recovery effect, entirely preserved lung parenchyma, and effectively reduced noise. It can be determined that our denoising method was superior to other methods by a subjective visual evaluation. The objective evaluation is shown in Tables 4-6 and Figure 12. It can be seen from Figure 12 that our proposed method also achieved the best effect in medical image denoising. Specifically, when denoising impulse noise, the average PSNR value of NonRPCA was roughly 40% higher than that of the classical RPCA algorithm, and the average PSNR value of our method was about 8% higher than that of NonRPCA. For Poisson noise, the average PSNR of our method was 36% higher than the latest method, AMlogtv, and the average SSIM was 31% higher than TDV, which also showed the effectiveness of our method. Additionally, against the background of Gaussian noise, the average SSIM values of all methods were low, which may be due to the characteristics of Gaussian noise itself, causing the brightness, contrast, and image structure to affect the SSIM value. Moreover, the average SSIM value of our proposed method was still higher than other methods.