## 3 Experiments and Comparison
### Quantitative Analysis of the Nonuniformity Correction Effect of the Algorithms  
In order to better analyze the image correction effect, this paper uses PSNR, roughness, and the energy of vertical gradient for quantitative analysis. In this quantitative analysis, the infrared image in Figures 5 and 6 with added simulated horizontal stripes and 100 randomly selected frames from the FLIRADAS dataset are employed. All images are 8-bit images. The definition of PSNR is described as follows:  
\[\text{PSNR}=10\text{log}_{10}\frac{255^{2}}{\text{MSE}} \tag{16}\]  
where MSE is the mean square error between the original image and the input image. The higher the value of PSNR means the image is closer to the original image, and the better the correction effect. The PSNR results are shown in Table 3.  
Figure 8: Nonuniformity correction effect of [PERSON] [16], [PERSON] [17], [PERSON] [18], and our proposed algorithm. In order to better show the nonuniformity correction effect of each algorithm, this figure selects local magnified images of building, bus, and stairs to compare the effect of each algorithm. The parts in the red circle in the images are the parts where the non-uniform correction results of the contrast algorithm are not good. Figure 9: Real infrared focal plane linear array non-uniform correction of [PERSON] [16], [PERSON] [17], [PERSON] [18], and our proposed algorithm. The resolution of the presented image is 1024 \(\times\) 4096 due to the high resolution of the scanned image, as shown in this figure, in order to more accurately compare the denoising effect. It could be seen that our proposed algorithm has the best nonuniformity correction effect with the highest PSNR value. Due to the TV regularization of the wavelet transform DC component, the technique of [PERSON] [18] yields the lowest PSNR of the image. This means that the DC component of the whole frame is changed. The algorithm of [PERSON] [16] has a lower image PSNR in the image \"hand\", which may come from the fact that this image has more high-frequency details; after the three-stage wavelet transform high-frequency component processing, the image obtains more distortion. The roughness is another indicator to measure the image correction effect, and its definition is as follows:  
\[p=\frac{||h*g||+||h^{T}*I||}{||I||} \tag{17}\]  
where \(||\cdot||\) denotes the L-1 norm, \(*\) means the convolution operation, \(h=[-1,1]\), and \(I\) denotes the input image. The smoother the image means the lower the roughness of the image. However, this does not imply a superior picture correction effect. The process of smoothing the image may lose the image's high-frequency information. Therefore, this experiment considers that the closer the roughness of the image is to the original image, the better the effect is. The results of roughness are shown in Table 4.  
According to the data in Table 4, the roughness of the corrected image generated by our proposed technique is the closest to that of the original image. The image roughness of Wang [18] is the lowest, and the image is the smoothest, which is consistent with the correction effects of different algorithms in Figure 8. Since the nonuniformity noise of the infrared column scan image is in the horizontal direction, the image is not as smooth as the original image in the vertical direction; the energy of vertical gradient is another indicator of the nonuniformity correction effect, and its definition is as follows:  
\[E=\sum_{i=1}^{H-1}\sum_{j=1}^{W}\frac{[I(i,j)-I(i+1,j)]^{2}}{(H-1)\times W} \tag{18}\]  
where \(I(i,j)\) is the input image, \(H\) is the height of the image, and \(W\) is the width of the image. The results of the energy of vertical gradient are shown in Table 5.