## 2 Denoising Technique Comparison  
In this section, we further discuss various existing image-denoising techniques and conduct a comparison study of some techniques based on their noise-reduction rate and high-frequency data loss. Various denoising techniques have been proposed so far. A good noise removal algorithm ought to remove as much noise as possible while safeguarding edges. Gaussian white noise has been dealt with using spatial filters, e.g., the Gaussian filter, the Mean filter, and the Wiener filter [25]. Images can be viewed as a matrix with variant intensity values at each pixel. The spatial filter is a square matrix that performs convolutional production with the image matrix to produce filtered (noise-reduced) images, i.e.,  
\[g(i,j)=k*v(i,j) \tag{1}\]  
where \(v(i,j)\) is the original (noisy) image matrix entry at the coordinate \((i,j)\). \(k\) is the spatial filter (or kernel), and \({}^{*}\) accounts for the convolution. \(g(i,j)\) is the filtered (noisy-reduced) image matrix entry at the coordinate \((i,j)\). All the spatial filters have the benefit of being computationally efficient but the shortcoming of blurring edges [25]. Also, image Gaussian noise reduction can be approached in the wavelet domain. In the conventional Fourier Transform, only frequency information is provided, while temporal information is lost in the transformation process. However, wavelet transformation will keep both the frequency and temporal information of the image [25]. The most widely used wavelet noise-decreasing method is the wavelet threshold method, as it can not only obtain an approximate optimal estimation of the original image but also calculate speedily and adapt widely [25]. The method can be divided into three steps. The first step is to decompose the noise-polluted image by wavelet transformation. Then, wavelets of useful signals will be retained, while most wavelets of noise will be set to zero according to the set threshold. The last step is to synthesize the new noise-reduced image by inverse wavelet transformation of the cleaned wavelets in the previous step [25; 26]. The wavelet transformation method has the benefit of keeping more useful details but is more computationally complex than spatial filters. The threshold affects the performance of the filter. Soft thresholding provides smoother results, while a hard threshold provides better edge preservation [25]. However, whichever threshold is selected, filters that operate in the wavelet domain still filter out (or blur) some important high-frequency useful details in the original image, even though more edges are preserved than with spatial filters. All the aforementioned methods present ways to reduce noise in image processing starting from a noisy image. We can approach this problem with multiple noisy images taken from the same perspective. Assume the same perspective ensures the same environmental conditions (illumination, temperature, etc. ), which affect the image noise level. Given the same conditions, an image noise level taken at a particular time should be very similar to another image taken at a different time. This redundancy can be used for the purpose of improving image precision estimation in the presence of noise. The method that uses this redundancy to reduce noise is called signal averaging (or image averaging in the application of image processing) [27]. Image averaging has the natural advantage of retaining all the image details as well as reducing unwanted noises, given that all the images for the averaging technique are taken from the same perspective. The image-averaging technique is illustrated in Figure 1. Assume a random, unbiased noise signal and that this noise signal is completely uncorrelated with the image signal itself. As noisy images are averaged, the original true image is kept the same, and the magnitude of the noise signal is compressed, thus improving the signal-to-noise ratio.