# 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 quality of the computed image is evaluated based on the peak signal-to-noise ratio, which is the logarithm of the mean square error between the original image and the processed image relative to \(\left(2^{n}-1\right)^{2}\). The higher the value of the peak S/N ratio, the lower the distortion of the image and the higher the quality of the image. The Mean Absolute Error (MAE) is defined as follows:  
\[M_{e}=\frac{1}{mn}\sum_{i=0}^{m-1}\sum_{j=0}^{n-1}\lvert I(i,j)-K(i,j)\rvert \tag{13}\]  
The mean absolute error directly reflects the effect of image processing, and the larger the error value, the worse the image is processed by the algorithm. The experimental validation pairs of each index are shown in Figures 10-12. Figure 11: Comparison of peak signal-to-noise ratio of different denoising methods. Figure 12: Comparison of the mean absolute error of different denoising methods. Figure 10: Comparison of mean square error of different denoising methods. It can be seen from Figures 10-12 that through the above different denoising methods for different kinds of defects, nine different sets of evaluation index curves are obtained. Through the curves, it can be learnt that the mean square error of the denoising method proposed in this paper is lower than the other two denoising methods for six different kinds of defects; the peak signal-to-noise ratio is lower than the other two groups for only one kind of defect, and the resistance is higher than the other two denoising methods. Additionally, the mean absolute error is lower than the other two denoising methods for all kinds of defects. The correct average recognition rate in Table 2 is calculated for each algorithm, i.e., Equations (11)-(13), under a multi-noise simulation experimental environment, averaged over 50 simulations and then averaged over six time steps. The correct recognition rate in the table is averaged over space and time and, thus, is the overall average of the correct recognition rate. The computational speed is the computational time of the algorithm itself. used by the algorithm to compute the six time steps in the simulation environment. The noise suppression capability is estimated based on the computational process of the various algorithms, the complexity of which is estimated. The adaptation environment in the table refers to the environment in which the algorithm applies to the target, while the parameter setting requirement refers to the algorithm containing some parameters set according to the actual environment. From Figures 9-11 and Table 2 it can be seen that compared with the existing denoising methods, the denoising method proposed in this paper not only has a higher accuracy, faster denoising speed, and stronger anti-interference ability, but also has a better adaptation to environment. The multi-noise noise reduction method proposed in this paper lays a good foundation for steel surface defect detection; in addition, it shows that the denoising method has good comprehensive performance.