# Sparse Representing Denoising of Hyperspectral Data for Water Color Remote Sensing
## 3 Results
### Denoising Performance in the Simulated Dataset  
In this section, we added random errors into the simulated dataset used in the previous section, to yield spectra with different SNRs. By controlling the input error, the simulated SNRs resulted in three levels (30, 50, and 70). Then, we applied the SR and the other three  
Figure 3: Performance of sparse representing method in dictionary dataset.  
algorithms to the noisy spectra and obtained the denoised data. The SNRs of the spectra before and after denoising were calculated and compared.  
We plotted three typical spectra under varied noise levels, together with the SR denoised ones (Figure 5). When the SNR is around 30, the noisy \(R_{\rm rs}\) curves show obvious vibration (Figure 5a). The sharp peaks and valleys caused by random noise at sensitive bands will bring errors into the water-color estimation models. The denoised signals (Figure 5b) look smooth and highly consistent with the original noiseless \(R_{\rm rs}\) curves. When the SNR was set to about 50, the noised spectra (Figure 5c) were obviously smoother than those in Figure 5a. We could only see some slight fluctuations in several bands. The SR denoised curves were nearly indistinguishable with the original signals. When the SNR is about 70, both the noisy and denoised spectra looked the same with the original \(R_{\rm rs}\) curves. This means that the SR method can yield satisfactory results under both high, median, and low noise levels.  
Furthermore, we calculated the SNR of the denoised spectra from the four methods and drew their violin plots. As a comparison, the SNR of the noisy spectra were also calculated (Figure 6). It is interesting that, overall, some of the methods provided even worse results than the noisy signals. In particular, when the SNR is about 70, the SNRs of the denoised spectra are lower than those of the noisy spectra. According to Figure 4, when the SNR was around 70, the noise of the spectra was nearly negligible. Under this situation, all four of the methods destroyed the useful information to different degrees. The SR method kept most of the original signals and its median SNR was 64.30. GS performed better than KRS and Mean; its median SNR was 59.30, which was close to the SR. The SKRS and Mean exhibited a similar performance, their median SNRs were 48.05 and 46.19, respectively. When the input noise level increased, the SNR decreased to about 50 (its median is 52.55) (Figure 6b); the performance of the four methods was similar to that in Figure 6c. What was different is that at this input error level, the SR and GS effectively increased the SNR compared with the noisy signals. Their median SNRs were 56.83 and 53.31, respectively. The KRS and Mean still could not effectively remove the noise and keep useful information synchronously. Their median SNRs were 44.87 and 44.65, respectively. This indicates that they were still over-denoising at this noise level. When we further increased the noise level and the SNR dropped to about 30 (its median is 32.39), the SR-yielded spectra could effectively increase the SNR to a median of 37.49. In the other three algorithms, the Mean outperformed the KRS and GS. Its median SNR was 36.79, which was quite close to the SR. The KRS could also slightly improve the SNR at this input noise level.  
Figure 4: Two representative spectra and their corresponding SR spectra. The SNR indices are 77.41 (**a**) and 67.73 (**b**), respectively.  
Figure 5: Example spectra of three samples under different SNR levels.  
Figure 6: Performance of the four methods at different input SNR levels.