# A Denoising Method for Multi-Noise on Steel Surface Detection
## 5 Comparison of the Proposed Denoising Method with Other Denoising Methods
### Comparison of Experimental Validation of Each Index after Denoising  
The more common image denoising techniques are spatial image feature denoising and transform domain denoising; the former is mainly in the use of image space for denoising processing [19], while the latter is in the use of image change space for denoising processing [20]. The spatial pixel characteristic denoising method analyzes the relationship between the center pixel and other adjacent pixels within a sliding window of a certain width, thus changing the data of the intermediate image. It can also represent the window size of partial Gaussian and Laplacian filters. Representative filter methods include computational mean filter, operational median filter, Gaussian filter, bilateral filter, etc. The transform domain denoising method separates the useful signal from the noise in the transform domain by means of mathematical transformation, thus filtering out the redundant noise. In denoising using the image transform domain, the most central point is what kind of transformation is performed to convert the image from the spatial domain to  
Figure 9: Comparison of denoising effect. the transform domain. The landmark research methods include Fourier transform, discrete cosine transform, wavelet transform, and multi-dimensional geometric analysis methods. This paper focuses on the above two denoising methods. In terms of image denoising, it needs an evaluation index to measure whether the image quality has improved after denoising an image containing noise, so it introduces an objective evaluation index to compare the image before and after denoising. As a more comprehensive evaluation calculation, three main technical indices of the maximum similarity measurement of images, namely the Mean Square Error (MSE), Peak Signal Noise Ratio (PSNR), and Mean Absolute Error (MAE), are used in the experiments. Low values of MSE and MAE only represent that the processed image is close to the original image. If the original image is blurred and the processed image is a similarly blurred image, then the MSE and MAE can be low, but the usefulness of the processed image would be limited. When training the model, the MSE causes the model to focus more on those data points that differ more from the actual values, thus prompting the model to minimize those differences. The MAE causes the model to focus more on the overall error average across all data points, without zooming in too much or ignoring any part of it. The objective quality evaluation of images generally involves calculating certain statistical characteristics and basic physical parameters of the evaluated image, and the most frequently applied is the similarity test of the image. The similarity of the image is measured by using the deviation of the data between the image processed by the algorithm and the original image to determine how well the algorithm is processed. If the deviation is small, statistically speaking, the similarity of the image is higher because the difference between the algorithm-processed image and the original image is smaller, and thus the quality evaluation index of the algorithm-processed image is higher, and vice versa. This kind of image evaluation is usually applied to the quality evaluation of binary and grayscale maps. Among them, the Mean Square Error (MSE) is defined as follows:  
\[S_{e}=\frac{1}{mn}\sum_{i=0}^{m-1}\sum_{j=0}^{n-1}\|I(i,j)-K(i,j)\|^{2} \tag{11}\]  
\(I(i,j)\) denotes the original image and \(K(i,j)\) denotes the algorithm-processed image. The mean square error, an image quality evaluation index, is equivalent to an intermediate value in image evaluation and provides the initial basis for many subsequent evaluation indexes. The Peak Signal Noise Ratio (PSNR) is defined as follows:  
\[P_{n}=10\times\log_{10}(\frac{MAX_{I}^{2}}{MSE})=20\times\log_{10}(\frac{MAX_{ I}}{MSE}) \tag{12}\]  
\(MAX_{I}\) indicates the value of the largest color value among all pixels in the image.