## 4 Discussion  
Noise in remote sensing data originates from various sources, including atmospheric interference, sensor noise, and minor deviations of satellites in their orbits. The signal-to-noise ratio (SNR) of the remote sensing data indicates that the average SNR of the original remote sensing data is 0.114. After processing with the multilayer denoising autoencoder, the average SNR increases to 11.8, showing an improvement. This suggests that the multilayer denoising autoencoder can reduce noise in the data to a certain extent. As observed in the subsequent training process of the multilayer denoising autoencoder model, the training loss gradually decreases and eventually stabilizes. Additionally, compared to models trained with the original data, the models trained with data processed by the multilayer denoising autoencoder show an improvement in R\({}^{2}\) values, with an increase of over 0.2 for each model. Moreover, the inversion errors (MSE and MAE) have decreased. These results suggest that the data processed by the multilayer denoising autoencoder still retain the main information of the original data, which aids in extracting effective information for water quality inversion, thereby achieving higher inversion accuracy. This also demonstrates that the spectral features selected in this study contain valid information, laying a foundation for the model to extract and utilize this information for total phosphorus inversion, thereby supporting the rationality of the chosen spectral features. Compared with traditional autoencoders, by requiring the model to restore noisy data during training, the model is forced to learn the robust features of the data, avoiding merely memorizing the details of the training data and instead capturing their underlying structure. Similar to other studies, research by [PERSON] et al. (2018) has shown that using deep learning methods to extract effective information from remote sensing data while reducing noise can significantly improve the inversion accuracy of chlorophyll. The machine learning method based on MSMCF proposed by [PERSON] et al. (2018) in their article demonstrates a certain capacity for noise suppression, enhancing the water quality inversion capability of samples from Shanghai. Feature dimensionality reduction can reduce unnecessary information in features, improving model accuracy and robustness ([PERSON] et al., 2018). Moreover, the complexity of data-driven models  
Figure 10: Inverse map of total phosphorus in Taihu Lake on 24 December 2023.  
increases with the dimensionality of the input data, and over-complexity of the input data may lead to inefficiencies in model operation and overfitting problems. Therefore, it is essential to extract effective features from the data before training the inversion model. Experimental results also show that the bagging model achieves the best inversion effect, with an R\({}^{2}\) of 0.9. This is consistent with the findings of other studies [53]. As an ensemble learning model, bagging integrates multiple base decision tree models, avoiding significant bias generated by single models during prediction and demonstrating stronger robustness and fitting ability. From the correlation analysis, it can be seen that the correlation coefficient between the spectral normalized ratio and total phosphorus is higher than that of the single spectral value, and at the same time, its accuracy of inversion of water quality as a model trained on features is high. These results showed that the spectral normalized ratio can effectively reduce the influence of external factors such as atmospheric composition, sun angle, and sensor angle compared with a single spectral feature and enhance the spectral features by comparing the differences between two or more spectral bands, which makes the model able to capture the differences in spectral features under different total phosphorus concentrations more easily, thus improving the water quality inversion effect.