## 3 Method
### TSE-UNet Model  
To reconstruct a dense point cloud from a sparse point cloud, the model needs to have the ability to extract features and high-level semantic understanding from the sparse point cloud, as well as the ability to reconstruct high-level semantics into fine-grained low-level information, to achieve point cloud super-resolution. This process coincides with the design idea of the semantic segmentation model UNet. In addition, because the point cloud is dynamically collected by an autonomous vehicle, the semantic information of a certain frame of point cloud has a strong correlation with the semantic information of the previous frames of point cloud; at the same time, a certain point on the current frame of  
Figure 4: The 2D projections of 3D point clouds. From top to bottom: CARLA32, CARLA128, Ruby32, Ruby128. point cloud has a strong spatial correlation with the surrounding point cloud. Therefore, we propose a method combining the TSE module with UNet, namely TSE-UNet, to achieve the task of point cloud super-resolution. Figure 5 shows the architecture of the TSE-UNet. TSE-UNet incorporates the encoder-decoder structure and skip connections of UNet while introducing temporal feature attention aggregation modules and spatial feature enhancement modules. The encoder is responsible for extracting high-level semantic features from point cloud data. The encoder consists of a pre-processing layer and four stages. The input to the pre-processing layer includes the current frame and the projected images of the previous 15 frames, denoted as \(T=\{T_{i}\mid i\in\{0,1,\ldots,15\}\}\), where the dimension of \(T_{i}\) is \(H\times W\times C\). The pre-processing layer applies the following formula to each input image:  
\[T_{i}^{\prime}=TConv(TConv(T_{i})), \tag{3}\]  
where \(TConv\) represents the transposed convolution operation with a stride of 2 in the height dimension. The dimension of \(T_{i}^{\prime}\) is \(D\times W\times C\), where \(D=4\times H\). The purpose of the pre-processing is to increase the height of the sparse point cloud image to four times its original size, aligning it with the height of the dense point cloud for pixel-level predictions. The structure is consistent across the four stages, comprising adjacent temporal feature aggregation, temporal and spatial feature-enhanced modules, and a down-sampling large-scale dilated convolution. Taking the operations on \(T_{0}\) and \(T_{1}\) in stage 1 as an example, the computation for the adjacent temporal feature aggregation operation is given by the following formula:  
\[F_{01}=Concat(T_{0}^{\prime},T_{1}^{\prime}), \tag{4}\]  
Figure 5: The architecture of TSE-UNet. where _Concat_ denotes the concatenation operation along the depth dimension, resulting in \(F_{01}\) with dimensions \(D\times W\times 2C\). Subsequently, through the temporal and spatial feature-enhanced (TSE) module,  
\[ \begin{split} X_{01}&=Conv(F_{01}),\\ X_{01}&=\sigma(\textit{favg}(X_{01}))\odot X_{01}, \\ X_{01}&=\sigma(PConv(X_{01}))\odot X_{01}, \end{split}  \tag{5}\]  
where _Conv_ represents a 2D convolution with a kernel size of 3 and a stride of 1, utilized to further integrate features between adjacent frames. \(\sigma\) denotes the sigmoid function. _favg_ represents channel-wise average pooling, which calculates the importance of temporal features in the channel dimension and injects it into the original features through element-wise multiplication (\(\odot\)), thereby achieving temporal feature enhancement. _Pconv_ is a point-wise convolution with a kernel size of 1, a stride of 1, and an output dimension of 1, used to assess the importance of spatial dimensions and inject it into the original features through element-wise multiplication, completing spatial feature enhancement. The TSE module maintains the feature dimensions at \(D\times W\times 2C\).