# A Lightweight Reconstruction Model via a Neural Network for a Video Super-Resolution Model
## 2 Materials and Methods
### Network Design  
Three variants of deep neural networks were scrutinized: (1) RNN, (2) DRRN, and (3) DBRRN. These networks accept a video sequence as input and utilize a stack of three-dimensional convolutional layers to extract spatiotemporal data from the video sequence. The RNN incorporates fewer frames as hidden state inputs and processes extensive video sequences cyclically.  
This section offers an in-depth configuration of the complete system pipeline and temporal modeling methodologies. The entire system is bifurcated into two segments: one segment is the time modeling network that takes continuous frames as input and amalgamates them with reference frames. In contrast, the other segment optimizes the network's Loss function by implicitly employing motion information.  
RRN: The Residual Recursive Network (RRN) addresses the issue of gradient vanishing by adopting the residual mapping between layers with identity skip connections. This configuration guarantees a seamless information flow and enables prolonged texture information retention. Consequently, it simplifies the RNN's management of extended sequences while mitigating the risk of gradient disappearance during training. At time step \(t\), the RRN utilizes the ensuing equation to generate the output \(h_{t}\) and to formulate for the next time step \(t+1\):  
\[\widehat{x_{0}}=\sigma(W_{conv2D}\{[I_{t-1},I_{t},o_{t-1},h_{t-1}]\}\]  
\[\widehat{x_{k}}=g(\widehat{x_{k-1}})+\widehat{\mathrm{F}(x_{k-1})},k\epsilon [1,K]\]  
\[h_{t}=\sigma(W_{conv2D}\widehat{\{x_{k}\}})\]  
\[o_{t}=W_{conv2D}\widehat{\{x_{k}\}}\]  
where \(g(\widehat{x_{k-1}})\) symbolizes the identity mapping in the identity residue block, and \(\widehat{\mathrm{F}(x_{k-1})}\) represents the residue mapping in layer \(k\).  
Figure 2: The structure of Depthwise Separable Convolution.  
DRRN: In DRRN, the convolution present in RRN is substituted with depthwise separable convolution. This design modification can curtail the model parameter scope and enhance computational time.  
\[\widehat{x_{0}}=\sigma(W_{\text{Depthwise Separable }conv}\{[I_{t-1},I_{t},o_{t-1},h_{t-1}]\} \tag{2}\] \[\widehat{x_{k}}=g(\widehat{x_{k-1}})+\widehat{\text{F}(x_{k-1}) },ke[1,K]\] \[h_{t}=\sigma(W_{\text{Depthwise Separable }conv}\widehat{\{x_{k}\}})\] \[o_{t}=W_{\text{Depthwise Separable }conv}\widehat{\{x_{k}\}}\]  
DBRRN: Initially, the image is reconfigured by the Pixel Unshuffle layer, which transposes the data from a spatial dimension to a depth dimension. Subsequently, the input data is concatenated and passed into the convolution (Conv) layer, followed by a Rectified Linear Unit (ReLU) [8]. The data then proceeds into a series of stacked Residual Blocks (ResBlock) [12]. Each ResBlock consists of Conv-ReLU-Conv layers, with a skip connection combining the output and input. In one branch, the elements within the ResBlocks of the dual channel are delivered to the Conv-ReLU layer as the output feature. In the other branch, the dual-channel features are processed through a Conv layer and reshaped by the Shuffle layer.