## 1 Introduction
abruptly after that. At the same time, the red curve decreases in a relatively stable manner and its RMSE reaches 6.28 after 50 frames, decreasing consistently around 30% over the IRLMS's and at least 50% over the NN-NUC's. Obviously, due to its fast convergence speed and stability with hardly any rebound, the PCA-NUC method presents a superior performance compared to the other two methods. As is well-known, SVD is a computational expensive operation. Moreover, many practical factors, such as memory hierarchy and operating system planning, must be considered in real systems. In this paper, our primary focus lies in evaluating the operational speed of various methods. The following tests have been carried out on a PC with an Intel(R) Core(TM) i5 processor and a 16 Gbyte RAM as well as on the Visual Studio 2019 platform. As shown in Table 1, a rough average of the CPU time consumed per frame of the three algorithms is displayed. Due to the higher operational needs of PCA-NUC, such as registration and SVD, it is more time-consuming compared to the other two algorithms. In the following subsection, PCA-NUC is applied to a set of 14-bit real infrared data, which was acquired using an \(320\times 256\) HgCdTe FPA camera operating in the 8-14 \(\upmu\)m range. When testing the NUC performance with real infrared data, the roughness index (\(\rho\)), which measures the high-pass content of an image, can be adopted as a reference for comparison to obtain the calibration data needed to perform a radiometrically accurate correction. The definition of \(\rho\) can be written as follows:  
\[\rho=\frac{mean(|L*Y|)}{mean(Y)} \tag{13}\]  
where \(L\) represents a Laplacian filter; \(*\) is the discrete convolution operator. \(Y\) is the image, and \(mean(Y)\) represents the mean value of \(Y\). The roughness evolution of the three tested algorithms and the result of the mean roughness over the video sequence are presented in Figure 3 and Table 2, respectively. \begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Average CPU Time(s)** \\ \hline NN-NUC & 0.006 \\ IRLMS & 0.087 \\ PCA-NUC & 0.146 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Average CPU time consumed per frame for the three algorithms. Figure 3: Roughness versus frames using different NUC methods. As shown in Figure 3, all three methods display a distinct capability of correcting nonuniformity. During whole the sequence, PCA-NUC exhibits the lowest roughness among all three methods. The curves of the other two algorithms drop dramatically in the first 50 frames and fluctuate around the mean value in the remaining frames. The PCA-NUC method presents an excellent performance when compared with the other two methods. Figure 4 shows frame 30 of the real infrared video sequence. The true scene irradiance is displayed in Figure 4a. The outputs obtained using the NN-NUC, IRLMS, and PCA-NUC methods are shown in Figure 4b-d, respectively. As shown in Figure 4b,c, the clear residual fixed-pattern noise is noticeable. Since the motion of the scene is not sufficient, it is a tough task to correct low spatial frequency nonuniformity effectively. The red arrow shows the residual patches of fixed-pattern noise. The results demonstrate that, within only 30 frames, the FPN was almost eliminated with the proposed PCA-NUC method. As shown in Figure 5, another sample image (the 140 th) of the real infrared data is displayed, in which all three NUC methods eliminate the nonuniformity presented in the raw image. The camera moved in the vertical direction from the bottom-up, then suddenly moved to the right. In the outputs, especially in Figure 5b, ghosting artifacts are noticeable (indicated with the red arrow). Also, the residual low spatial nonuniformity is visible in Figure 5b. There exists some residual nonuniformity that can be perceived in the output of the IRLMS method. However, in the PCA-NUC's output, neither ghost artifacts nor residual inhomogeneity can be detected by the naked eye.