# An Unsupervised Image Denoising Method Using a Nonconvex Low-Rank Model with TV Regularization
## 4 Experimental Results and Analysis  
In this section, we compare our proposed RPCA method based on a nonconvex low-rank approximation and TV regularization with five state-of-the-art methods qualitatively and quantitatively, including the robust principal component analysis (RPCA) [45],nonconvex log total variation model (AMlogtv) [46], nonconvex rank RPCA (NonRPCA) [42], weighted nuclear norm minimization-robust principal component analysis (WNNM\(-\)RPCA) [47], and total directional variation (TDV) [48]. We explore the denoising effect of our method on three common noises (salt-and-pepper noise (impulse noise), Poisson noise, and Gaussian noise). Additionally, we also perform facial image denoising experiments in Section 4.3 to demonstrate that our method is capable of preserving important image features while removing noise. An objective evaluation can avoid the uncertainty of subjective vision. Therefore, we use the peak signal-to-noise ratio (PSNR) [49], Structure similarity index measure (SSIM) [50], and feature similarity index measure (FSIM) [51] to evaluate the image quality objectively. The PSNR refers to the ratio of the maximum possible power of the maximum achievable signal strength to the destructive noise power that impacts its representation accuracy. It is often used to evaluate the quality of a denoised image compared to the original image. The SSIM is an index to measure the similarity of two images, and its value is usually affected by the brightness, contrast, and structure of the image. The FSIM is a quality assessment method based on the degree of feature similarity between the ground truth and the denoised image created using the human visual system. High values of the three metrics are desirable.  
In order to verify the denoising effect of our method in different scenarios, in terms of dataset selection, we used standard, authoritative, and widely used natural image, clinical medical image, and facial image datasets for denoising experiments. The experiment used eight standard grayscale images of 256 \(\times\) 256 randomly chosen from the digital image processing dataset, namely Butterfly, House, Peppers, Lena, Living Room, Bird, Camera, and Starfish. The medical image denoising experiment was conducted by randomly selecting eight 512 \(\times\) 512 lung CT images from the LungCT-Diagnosis dataset ([[https://wiki.cancerimagingarchive.net](https://wiki.cancerimagingarchive.net)]([https://wiki.cancerimagingarchive.net](https://wiki.cancerimagingarchive.net)), accessed on 26 May 2023). The data in LungCT-Diagnosis are from the Moffitt Cancer Center. The dataset has a total of 61 patients, each patient has a different number of 512 \(\times\) 512 lung tumor images, and these images are diagnostic-enhanced CT scan images. In addition, the images in the Extended Yale B dataset were used in the facial image denoising experiment. The dataset has a total of 38 subjects; each subject has 64 images with a size of 192 \(\times\) 168, all taken under different lighting. Due to different lighting conditions, the images of each object have different degrees of serious damage.  
All the experiments in this paper were implemented in MATLAB 2018a. The host processor was an Intel(R) Core (TM) i5-9400F CPU 2.90 GHz, and the operating system was 64-bit. Furthermore, the method proposed in this paper was based on a matrix of \(m\times n\), with the following parameter settings: \(\mu=1\times 10^{-3}\), \(\gamma=0.01\), \(\tau=1\times 10^{-5}\), and \(\lambda=1/\sqrt{\max(m,n)}\).