# Sparse Representing Denoising of Hyperspectral Data for Water Color Remote Sensing
## 4 Discussion
### Denoised PRISMA Image  
As previously mentioned, the proposed SR denoising method is the 1-D method. Even the denoising is only dependent on the spectra signals; after the method is iterated over each pixel, the denoising effect will affect the spatial information. We tested it on a 3D PRISMA image cube in this section. The original PRISMA image and the denoised image of bands 442 nm, 555 nm, and 700 nm are shown in Figure 10.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Spectral Index** & **Expression** & **Original \(r\)** & **Denoised \(r\)** \\ \hline Band ratio [54,55] & R710/R680 & 0.719 & 0.721 \\ NDCI [56] & (R710 – R680)/(R710 + R680) & 0.697 & 0.700 \\ Three-band [12] & (1/R680 – 1/R710) \(\times\) R745 & 0.752 & 0.755 \\ Four-band [57] & (1/R680 – 1/R710)/(1/R745 – 1/R720) & 0.695 & 0.698 \\ Enhanced three-band [58] & (1/R680 – 1/R710)/(1/R745 – 1/R710) & 0.743 & 0.748 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Linear correlation coefficients between \(C_{\text{chla}}\) and five spectral indices that calculated from original \(R_{\text{rs}}\) and denoised \(R_{\text{rs}}\).  
For each spectral band, the denoising process kept the general \(R_{\text{rs}}\) spatial distribution of the original image. This further revealed the fidelity of the SR algorithm. In the three bands of the PRISMA image, the \(R(442)\) image showed an obvious salt-and-pepper noise. Together with Figure 8, we can infer that the low SNR level of this band caused this error. In other words, the noise that distributed in the spatial and spectral domains are related. Therefore, the denoised image of band 442 (Figure 10b) successfully erased the random errors. For the other two spectral bands, their images look smooth and clear. This means these two bands are at higher SNR levels. The denoising kept most of the original information and slightly changed the reflectance value (Figure 10f,i). The encouraging image validation result suggests that the 1-D SR denoising method effectively improved the quality of the PRISMA image.  
Finally, we calculated the \(C_{\text{chla}}\) maps from the original PRISMA image and the denoised image, using [PERSON]'s model [55]. From the results (Figure 11), we can see that, in the same way as with the single band images, the spatial distributions of the PRISMA and the denoised image yielded \(C_{\text{chla}}\) maps that are similar. Overall, the denoised \(C_{\text{chla}}\) is highly consistent with the original \(C_{\text{chla}}\), but systematically lower (Figure 11a,b). The difference between the original and denoised images yielded \(C_{\text{chla}}\) that are stronger than  
Figure 10: PRISMA and SR denoised images of band 442 nm (**a**,**b**); 555 nm (**d**,**e**); and 700 nm (**g**,**h**); and the scatter plots of original and denoised images of (**c**) 442 nm; (**f**) 555 nm; and (**i**) 700 nm.  
the ASD results (Table 2). This is reasonable, considering the lower SNR of the PRISMA data will lead to a larger difference after being denoised (Figure 8). Meanwhile, a higher dynamic range after denoising (Figure 11c) reveals that the SR method enhanced the spatial information-capturing ability of the PRISMA image.