## 2 Dark Current Noise Correction Method Based on Dark Pixels
### Dark Current Noise Correction Model
#### 2.4.3 Acquisition and Pre-Processing of Feature Data  
The acquisition and pre-processing of feature data was achieved as follows. The detection system was powered on and the detector was oriented to collect feature data from the blackbody at the same temperature. As dark pixels' processing and other temporal noise in the system are non-uniform, when processing the feature data the mean value of multiple valid dark pixels' responses was taken to eliminate the non-uniformity of the dark current response; the mean value of multiple frames of dark pixels' responses was taken to reduce the effect of other temporal noise. The feature data of dark pixels are calculated as:  
\[g_{\text{dark\_average}}(t)=\frac{\sum_{k=0}^{N_{\text{frame}}}\sum_{j=0}^{m 1}\sum_{i=0}^{m1}g_{\text{dark}}(i,j,k)}{N_{\text{frame}}\cdot m_{1}\cdot n_ {1}} \tag{4}\]  
where \(g_{\text{dark}}(i,j,k)\) is the response value of the dark pixel; \((i,j,k)\) refer to the serial numbers of rows, columns, and frames, respectively; \(m_{1}\), \(n_{1}\), and \(N_{\text{frame}}\) are the number of rows, columns, and frames in the dark pixel area, respectively; and \(t\) is the number of the feature data in time order. \(N_{\text{frame}}\) needs to be selected according to the detector imaging pixel output frequency and frame frequency. When the number of feature data is small, the \(N_{\text{frame}}\) should be low (1 to 10). When the number of feature data is large, \(N_{frame}\) should be chosen according to the frequency of the pixel response fluctuations. Choosing an appropriate \(N_{\text{frame}}\) allows for the acquisition of sufficient features and reduces the amount of data processing. The mean frame (\(N_{\text{frame}}\)) response of each single imaging pixel is obtained by calculating:  
\[g_{\text{pe\_average}}(i,j,t)=\frac{\sum_{k=0}^{N_{\text{frame}}}g_{\text{ pixel}}(i,j,k)}{N_{\text{frame}}} \tag{5}\]  
where \(g_{\text{pixel}}(i,j,k)\) is the response value of the imaging pixel. The magnitudes of \(g_{\text{dark\_average}}(t)\) and \(g_{\text{pe\_average}}(i,j,t)\) are randomly distributed in time, and the relationship between these two types of characteristic data is nonlinear. When the value interval of the feature data is wide, the least-squares method and segmented best-slope-averaging method have large fitting errors [36; 37]. The RNN has a strong nonlinear fitting ability and is suitable for solving the regression problem of non-linear functions [38]. As shown in Figure 6, to construct the mapping relationship from \(g_{\text{dark\_average}}(t)\) to \(g_{\text{pe\_average}}(i,j,t)\), the RNN was selected to build the model so that the feature data at each moment occupied the weight in the model and the number of input layers was reduced. The calculation process from the input layer to the output layer is shown in Equation (6). \[g_{\text{pe\_average}}(i,j)^{\langle t\rangle}=Ug_{\text{dark\_average}}(t)^{ \langle t\rangle}+Wa^{(t-1)}+b \tag{6}\]where \(U\) represents the weight matrix from the input layer to the hidden layer; \(W\) represents the weight matrix from the hidden layer to the hidden layer; \(a^{(t-1)}\) represents the output vector of the hidden layer at moment \(t-1\); and \(b\) represents the deviation matrix from the input layer to the hidden layer [39]. In this model, \(U\) represents the weight of the feature data of a certain group t of dark pixels arriving at the intermediate hidden layer. \(V\) represents the weight of the feature data of the central hidden layer arriving at a certain imaging pixel of the same group t. \(W\) represents the weight from the feature data hiding layer of the previous group to the feature data hiding layer of the next group t. As the ordinal number t of the group increases, the closer the \(W\) of the intergroup weights comes to the final result. After training, a model of the regional dark pixels' mean response, \(g_{\text{RNN\_dark}}(k)\), with the dark level correction value \(g_{\text{RNN\_img}}(i,j,k)\) of the imaging pixel, was obtained.