# A Zero-Reference Low-Light Image-Enhancement Approach Based on Noise Estimation
## 2 Related Works and Methods
### Method
#### 2.2.2 Noise Estimation and Fusion  
We propose a noise-estimation approach based on the color map to derive the noise map for an image, which is subsequently fused with the low-light image to enhance its features. Within the noise-estimation module, the color map of the given input image is calculated and the corresponding noise map is deduced based on this color map. The color map, being an inherent property of the scene that remains unaltered in illumination [9], serves as valuable a priori information for enhancing low-light images. This utilization aims to augment image saturation and mitigate color distortion. Drawing inspiration from Retinex theory [15], the computation of the color map is expressed as Equation (2):  
\[C(x)=\frac{x}{mean_{c}(x)}. \tag{2}\]  
where \(x\) represents the input low-light image, \(C(x)\) represents the color map corresponding to \(x\), and \(mean_{c}(x)\) denotes the average value of each pixel in the RGB channel. Then, the estimation of noise in the input low-light image can be derived from Equation (3):  
\[N(x)=\max\bigl{(}abs(\
abla_{x}C(x)),abs\bigl{(}\
abla_{y}C(x)\bigr{)}\bigr{)}. \tag{3}\]  
where \(\
abla_{x}\) and \(\
abla_{y}\) denote the gradient maps in the x-direction and y-direction of the color map, respectively, and they are used to calculate the maximum value between pixel channel levels \(x\) and \(y\).  
Figure 2: The framework of ZLEN.  
Inspired by [27; 28], we adopted a semantic-aware module to extract features from noisy images. In the semantic-aware module, first, the activation mapping of an image pixel \(M\) is computed. For a given image, let \(f_{k}(x,y)\) denote the activation of cell \(k\) at the spatial grid \((x,y)\); then, the activation mapping of a pixel can be computed by Equation (4):  
\[M(x,y)=\sum_{k}w_{k}f_{k}(x,y). \tag{4}\]  
where \(w_{k}\) denotes the weight corresponding to the pixel in cell \(k\).  
Then, the activation mapping of pixels is used to map the corresponding RGB values of the image to semantically aware feature representations, with the conversion process shown in Equation (5):  
\[F_{s}=m^{\mathrm{T}}X=\sum_{i=1}^{W}\sum_{j=1}^{H}m_{i,j}N_{i,j}. \tag{5}\]  
where \(m_{i,j}\) denotes the weight of the activation map; \(N_{i,j}\) denotes the individual pixel points of \(N(x)\); and \(W\) and \(H\) denote the width and height of the image, respectively.  
Subsequently, a convolutional layer is employed to align the dimensions of the semantic features \(F_{s}\) and image features \(F_{i}\) to the same dimensions, and then the attention map is computed using the transposed attention mechanism according to [26]; as a result, the semantic-aware attention map can be defined by Equation (6):  
\[A=Softmax(L_{k}(F_{i})\times L_{q}(F_{s})/\sqrt{C}). \tag{6}\]  
where \(L_{k}\) and \(L_{q}\) denote the convolutional layers and \(C\) denotes the channel of the feature. Since \(A\) can represent the interrelationship between \(F_{s}\) and \(F_{i}\), the noisy image features obtained through the semantic-aware attention map are given as in Equation (7):  
\[F_{noise}=FN(L(F_{i})\times A+F). \tag{7}\]  
where \(FN\) denotes the feedforward network and \(F_{noise}\) is the feature map extracted from the input noise map.  
Finally, the image features are enhanced by fusing the extracted noise feature map with the input low-light image (Equation (8)) to provide more and more accurate image information for subsequent image illumination enhancement and noise reduction:  
\[F_{fusion}=F_{i}+\beta F_{noise}. \tag{8}\]  
where \(\beta\) denotes the coefficient of the noise feature.