# Estimating the Spectral Response of Eight-Band MSFA One-Shot Cameras Using Deep Learning
## 3 Materials and Methods
### Deep-Learning Algorithms
#### 3.2.3 Laplacian Pyramid Super-Resolution Network (LapSRN)  
The Laplacian pyramid super-resolution network (LapSRN) is a neural-network architecture designed for image super-resolution. It was introduced to improve image quality and resolution using a hierarchical approach inspired by the Laplacian pyramid.  
LapSRN uses a Laplacian pyramid to represent images at different resolution scales. The Laplacian pyramid decomposes an image into a series of frequency subbands, allowing the network to process image details at various resolution levels stepwise [22; 23].  
Figure 9: Modified DRCN architecture.  
* The LapSRN architecture includes several levels, each corresponding to a different resolution scale.
* Each pyramid level contains a convolutional block that extracts image features at that specific scale. This block consists of several convolutional layers followed by ReLU activation. The equation resulting from this model is the following: \[F=K_{1}*I\] (8)
* **F**: The initial output of the first transformation applied to the input image.
* \(K_{1}\): A filter or convolution kernel applied to the input image.
* \(I\): The input image could be a multispectral or low-resolution image.  
This equation represents an initial transformation in which a convolution kernel \(K_{1}\) is applied to the input image \(I\) to obtain the first representation \(F\). This is used to extract low-level features, such as edges or textures.  
\[L_{j}=K_{pyramid}*R_{10} \tag{9}\]
* \(L_{j}\): An intermediate exit (perhaps at the pyramid level) at step j.
* \(K_{pyramid}\): A kernel or filter linked to a pyramid-type structure, often used for multi-scale super-resolutions.
* \(R_{10}\): The final output of the recursive step (probably after 10 iterations).  
This equation suggests that the final recursion \(R_{10}\) is combined with a specific kernel \(K_{pyramid}\), indicating a multi-scale mechanism. This allows information from different levels of detail to be aggregated, thereby enhancing the model's ability to produce images with fine features at different resolutions.  
\[O=K_{final}*L_{2} \tag{10}\]  
* O: The final output of the model.
* \(K_{final}\): A final kernel applied to the previous output for the final transformation.
* \(L_{2}\): The output of the second stage in the pyramid or another network module.  
This last equation combines the kernel \(K_{final}\) with the intermediate output \(L_{2}\) to produce the result O. This final step can be seen as a refinement, where all the information obtained previously is integrated to generate the final version of the image with improved resolution or other desired properties.  
Algorithm 3 presents the pseudocode of the LapSRN algorithm.  
```
Input: I, \(K_{1}\), \(K_{r1}\), \(K_{r2}\), \(K_{pyramid}\), \(K_{final}\) Output: O Step 1: Apply the first convolution to extract features from the input image \(F=K_{1}*I\) Step 2: Initialize the first residual block \(R_{0}=F\) Step 3: Apply the residual blocks For i = 1 to 10 \(R_{i}=K_{r2}*ReLU(K_{r1}*R_{i-1})+R_{i-1}\) Step 4: Create Laplace pyramid levels For j = 1 to 2 \(R_{10}=K_{pyramid}*R_{10}\) Step 5: Final output \(O=K_{final}*R_{10}\)
```  
**Algorithm 3**LapSRN