# Efficient Gamma-Based Zero-Reference Deep Curve Estimation for Low-Light Image Enhancement
## 3 Methodology
### Global Channel Attention (GCA)  
In this section, we introduce a novel channel attention mechanism specifically designed for channel reconstruction. Our approach represents an advancement based on the SE [35] attention mechanism, which enhances feature representation through a two-step process. Initially, the squeeze operation compresses spatial information of each channel into a single descriptor via global average pooling:  
\[z_{c}=\mathbf{F}_{sq}(\mathbf{u}_{c})=\frac{1}{H\times W}\sum_{i=1}^{H}\sum_{j=1 }^{W}\mathbf{u}_{c}(i,j) \tag{7}\]  
where \(z_{c}\) is the channel descriptor, \(\mathbf{u}_{c}\) represents the \(c\)-th channel of feature map, \(H\) and \(W\) denote the height and width of the feature map, and \(\mathbf{F}_{sq}\) is the squeeze function. Subsequently, the excitation operation captures nonlinear interdependencies between channels through a two-layer fully connected network:  
\[\mathbf{s}=\mathbf{F}_{ex}(\mathbf{z},\mathbf{W})=\sigma(g(\mathbf{z}, \mathbf{W}))=\sigma(\mathbf{W}_{2}\delta(\mathbf{W}_{1}\mathbf{z})), \tag{8}\]  
where \(\mathbf{s}\) represents the channel attention weights, \(\mathbf{F}_{ex}\) is the excitation function, \(\delta\) represents the ReLU activation function, \(\mathbf{W}_{1}\in\mathbb{R}^{\hat{\gamma}\times\mathbb{C}}\) and \(\mathbf{W}_{2}\in\mathbb{R}^{\mathbb{C}\times\hat{\gamma}}\) denote dimensionality-reduction and dimensionality-increasing parameter matrices, respectively, and \(\sigma\) is the sigmoid activation function. The final reconstruction occurs through channel-wise multiplication:  
\[\bar{\mathbf{x}}_{c}=\mathbf{F}_{scale}(\mathbf{u}_{c},s_{c})=s_{c}\cdot \mathbf{u}_{c}, \tag{9}\]  
where \(\bar{\mathbf{x}}_{c}\) is the recalibrated feature, \(s_{c}\) is the attention weight for channel \(c\), and \(\mathbf{F}_{scale}\) denotes the channel-wise scaling function. Building upon our analysis of SE module, we propose an exceptionally lightweight channel attention mechanism. For a feature map \(\mathbf{x}\in\mathbb{R}^{\mathbb{C}\times H\times W}\), we initially apply global average pooling to acquire channel descriptors:  
\[z_{c}=\frac{1}{H\times W}\sum_{i=1}^{H}\sum_{j=1}^{W}\mathbf{x}_{c}(i,j), \tag{10}\]  
where \(z_{c}\) is the global descriptor for channel \(c\), \(\mathbf{x}_{c}\) represents the \(c\)-th channel of input feature map, and \(H\) and \(W\) are the spatial dimensions. Next, we remove the other tedious steps in Equation (8) and directly apply the softmax activation function to these channel descriptors:  
\[a_{c}=\frac{e^{z_{c}}}{\sum_{k=1}^{\mathbb{C}}e^{z_{k}}}, \tag{11}\]  
where \(a_{c}\) is the attention weight for channel \(c\), and the formula represents the softmax activation function that normalizes the exponential values across all channels. Finally, we reconstruct the original features using the generated channel weights:  
\[\bar{\mathbf{x}}_{c}=\mathbf{x}_{c}\times a_{c}, \tag{12}\]  
where \(\bar{\mathbf{x}}_{c}\) is the recalibrated output for channel \(c\), \(\mathbf{x}_{c}\) is the original feature, and \(a_{c}\) is the computed attention weight. Therefore, our approach only retains the channel weight assignment mechanism in SE attention mechanism, removing modules such as dimensionality-reduction and dimensionality-increasing layers. The proposed attention module can be inserted after any convolutional layer to perform channel reconstruction. Despite its simplicity, our experimental results demonstrate that this channel attention mechanism maintains performance while substantially reducing computational complexity, offering a novel approach for lightweight network architecture design.