# A Low-Light Sensor Image Enhancement Algorithm Based on HSI Color Model
## 3 Proposed Method
### Intensity Component Enhancement
The BN algorithm normalizes the output of all the intermediate layers in CNN. So, it deducts the impact on changes of the network data distribution in the training phase of the neural network parameters. Thereby, using BN algorithm speeds up the network convergence and stability [23]. Supposed that \(\{\mu_{1},\cdots,\mu_{n}\}\) is the input data of any intermediate layer of the model, we first obtain their mean and variance respectively as follows. \[E[\mathbf{\mu}]=\frac{1}{m}\sum_{i=1}^{m}\mu_{i} \tag{8}\]  
\[var[\mathbf{\mu}]=\frac{1}{m}\sum_{i=1}^{m}\left(\mu_{i}-E[\mu]\right)^{2} \tag{9}\]  
Then, the data is normalized to data with a mean of 0 and a variance of 1. Figure 6: The model of convolutional module. \[\hat{\mu}_{i}=\frac{\mathbf{\mu}_{i}-E[\mathbf{\mu}]}{\sqrt{var[\mathbf{\mu}]+\mathbf{\varepsilon}}} \tag{10}\]  
where \(\mathbf{\varepsilon}\) is a constant close to 0. Last, the reconstruction parameters \(\mathbf{\alpha}\) and \(\mathbf{\beta}\) are introduced to reconstruct the data after batch normalization and get the final output. The nonlinear mapping part can map the features of the former part from the low-dimensional space to the high-dimensional space. This process is written in following  
\[H_{k-1}(\mathbf{X})=\max(0,\text{BN}(\mathbf{W}_{k-1}*H_{k-2}(\mathbf{X})+\mathbf{b}_{k}))\;k\geq 3 \tag{11}\]  
where \(k\) indicates the depth of the proposed network, equivalently, the \(k-1\) layer is the last layer of the nonlinear mapping part. In order to investigate what the model has learned, we visualize the feature maps in the middle process after training. We randomly select six learned feature maps as shown in Figure 7. Observations prove that the first several layers focus on the high-light regions and the latter layers focus on low-light regions. (4) Reconstruction: In this paper, the low-light image is enhanced based on the reconstruction concept. Reconstruction is to minimize the corresponding intensity component error between the model output and the normal illumination image (namely, ground truth) by training. The original input is considered to contain more details [24]. Therefore, we use concatenation to combine the feature maps of the last ConvBlock and the input image, so that the original information can be preserved for detail restoration. In this part, only one convolution layer is needed, see Equation (11). \[H_{k}(\mathbf{X})=\mathbf{W}_{k}*(H_{k-1}(\mathbf{X}),\mathbf{X})+\mathbf{b}_{k} \tag{12}\]  
In order to automatically learn the network model parameter \(\theta=\{\mathbf{W}_{1}\cdots\mathbf{W}_{k};\mathbf{b}_{1}\cdots\mathbf{b}_{k}\}\), the loss function in Equation (12) can be minimized by back propagation algorithm and stochastic gradient descent method. Assuming a training sample set as \(D=\{(\mathbf{X}_{1},\mathbf{Y}_{1}),\cdots(\mathbf{X}_{i},\mathbf{Y}_{i})\}\). \[H_{1}(\mathbf{X})=max(0,\mathbf{W}_{1}*\mathbf{X}+\mathbf{b}_{1}) \tag{7}\]0  
where \(\mathbf{X}_{i}\) and \(\mathbf{Y}_{i}\) are the samples of the low-light image intensity component in the \(i\)-th input and that of the corresponding ground truth, \(N\) is the number of training samples, and \(\lambda\) as a weight constraint term prevents the over-fitting.