# Infrared Stripe Correction Algorithm Based on Wavelet Analysis and Gradient Equalization
## 5 Experiment and Analysis
### Analog Noise Image Test  
In the simulation image test, two common image quality metric parameters are applied to evaluate the destriping performance, peak signal-to-noise ratio (_PSNR_) and structural similarity index (_SSIM_) of the algorithm [29]. PSNR can measures the pixel error between the output image and the reference image, and a higher _PSNR_ value means a smaller degree of image distortion. The formula is defined as:  
\[PSNR=10\log_{10}\frac{255^{2}}{MSE} \tag{17}\]  
where _MSE_ represents the mean square error between the output image and the reference image. _SSIM_ provides the structural perception evaluation of filtering results within sliding window. The formula is defined as:  
\[SSIM(m,n)=\frac{(2\mu_{m}\mu_{n}+k_{1})(2\sigma_{mn}+k_{2})}{(\mu_{m}^{2}+\mu_ {n}^{2}+k_{1})(\sigma_{m}^{2}+\sigma_{n}^{2}+k_{2})} \tag{18}\]  
where \(m\) and \(n\) represents the image block extracted from the filtered image and the reference image by the sliding window, and \(\sigma_{m}\), \(\sigma_{n}\), \(\mu_{m}\), \(\mu_{n}\), \(\sigma_{mn}\) represents the standard deviation, mean, and cross-correlation of \(m\) and \(n\), respectively. \(k_{1}\) and \(k_{2}\) take constants to avoid the zero-denominator error in division. In experiment, the values of k\({}_{1}\) and k\({}_{2}\) are usually set to 6.5025 and 58.5225 [29]. In actual measurement results, the value of _SSIM_ is usually between 0 and 1. The closer the _SSIM_ value is to 1, the better the structure retention effect after image filtering. Tables 2 and 3 show the values of PSNR and SSIM for several methods respectively, which are obtained through 10 different noise processes. Compared with the three methods, it can be found that the PSNR value and SSIM value of the proposed method are the highest. It shows the superiority of this algorithm. \begin{table}
\begin{tabular}{c c c c c} \hline
**Test Data** & **Source** & **Size** & **Sensor** & **Description** \\ \hline Simulated images & & & & \\ \hline Ceramic & & \(512\times 512\) & — & Widely used gray images, \\ cameraman & & \(512\times 512\) & — & add with different levels of \\ \hline Raw IR images & & & & \\ \hline \hline Suitcase & [PERSON]’s & \(320\times 220\) & Thales Minie-D & Simple scene, Obvious edge information. Slight stripe noise image, small details. \\ \hline leaves & [PERSON]’s & \(640\times 440\) & Thales Minie-D & Simple scene, small details, small details and obvious stripe nonuniformity. \\ \hline people & [PERSON]’s & \(640\times 480\) & Thales Minie-D & Rich scene information, and \\  & dataset & \(640\times 480\) & camera & slight stripe nonuniformity. \\ \hline \end{tabular}
\end{table} 
Table 1: The details of the test data. Figure 9: Three raw infrared images for testing. (**a**) Suitcase from [PERSON]’s dataset [9]; (**b**) Leaves from [PERSON]’s dataset [9]; (**c**) People from [PERSON]’s dataset [9]. All of these images are available at the following link: [[http://demo.ipol.im/demo/glmt_mire/](http://demo.ipol.im/demo/glmt_mire/)]([http://demo.ipol.im/demo/glmt_mire/](http://demo.ipol.im/demo/glmt_mire/)). To illustrate the advantages of the algorithm in this paper, an example is given as shown in Figure 10. It can be clearly seen that the raw image is contaminated by stripe noise with \(\eta\) = 0.17. The results of CNN and TV processing by the algorithm also have obvious stripe noise. By contrast, the results obtained by MHE algorithm are better, but there will be an obvious \"ghost\" problem. Our proposed method achieves the best visual effect on the image, and the stripe noise is basically eliminated. On the whole, our proposed method has achieved remarkable results in stripe correction through objective indexes and observation effects. In the next section, we will use the raw infrared image to evaluate the algorithm.