# Estimating the Spectral Response of Eight-Band MSFA One-Shot Cameras Using Deep Learning
## 4 Experiments and Results
### Quantitative Results  
Table 2 presents three models suitable for estimating the spectral response of 8-band MSFA one-shot cameras: VDSR, DRCN, and LapSRN, using several performance metrics.  
The loss function indicates the error between the predicted and actual images. The values obtained are 0.0061, 0.0047, and 0.0057 for the VDSR, DRCN, and LapSRN models. The DRCN model has the lowest loss, with 0.0047.  
PSNR measures the quality of the reconstructed image, with higher values indicating better quality. DRCN achieves the highest PSNR at 25.5059, compared to VDSR at 23.6255 and LapSRN at 23.9505. SSIM evaluates the structural similarity between the original and reconstructed images. Values close to 1 indicate better similarity. DRCN also outperforms other models with an SSIM of 0.8355, while LapSRN has the lowest SSIM at 0.8047.  
SAM measures the angle between spectral vectors, with lower values indicating better performance. DRCN has the lowest SAM value, 0.13215, indicating better spectral fidelity than VDSR, 0.17293, and LapSRN, 0.17764.  
The RMSE quantifies the average magnitude of errors between the predicted and actual values. A lower RMSE value indicates better model accuracy. DRCN has the lowest RMSE, at 0.05849, while VDSR has the highest, at 0.06916.  
MAE, which measures the average absolute errors in predictions, is a critical factor in evaluating the algorithms. DRCN's best performance, with an MAE of 0.0415, highlights its accuracy, while VDSR's highest MAE, at 0.0525, indicates its lower accuracy.  
We can list hypotheses for which DRCN performs better:  
DRCN (deeply recursive convolutional network) uses deeply recursive architectures that better capture complex and delicate details in images and could justify why DRCN outperforms other models in terms of PSNR, SSIM, and SAM, where accuracy and fidelity to detail are paramount.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Setting** & **Values** \\ \hline Optimizer & Adam \\ Learning rate & \(10^{-3}\) \\ Loss function & Mean Squared error \\ Epochs & 100 \\ Batch size & 8 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of algorithm configuration.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Models** & **Loss** & **PSNR** & **SSIM** & **SAM** & **RMSE** & **MAE** \\ \hline VDSR & 0.0061 & 23.6255 & 0.8135 & 0.17293 & 0.06916 & 0.0525 \\ DRCN & 0.0047 & 25.5059 & 0.8355 & 0.13215 & 0.05849 & 0.0415 \\ LapSRN & 0.0057 & 23.9505 & 0.8047 & 0.17764 & 0.06534 & 0.04861 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of metric values for each model.  
In addition, its recursive mechanism would allow predictions to be refined at each iteration, thus capturing more nuances in image reconstruction. This capability could justify its better balance between noise reduction and texture preservation and its superior performance in terms of loss, RMSE, and MAE compared to VDSR and LapSRN models.  
Figures 12-14 present the learning curves for the loss, PSNR, and SSIM metrics:  
Figure 12 illustrates the learning and validation curves of the VDSR-based model, focusing on three key metrics: PSNR, SSIM, and the loss function (loss). These curves allow one to follow the evolution of the model's performance at each iteration during training.  
Figure 13 illustrates the learning and validation curves of the DRCN-based model, focusing on three key metrics: PSNR, SSIM, and the loss