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Deep Feature Gaussian Processes for Single-Scene Aerosol Optical Depth Reconstruction

Shengjie Liu, Lu Zhang

TL;DR

Cloud contamination limits satellite AOD retrieval for high-spatial-resolution, single-scene scenes. We propose Deep Feature Gaussian Processes (DFGP), a hybrid framework that uses CNN-based deep-feature extraction on predictors and Gaussian-process regression on the resulting features to model spatial dependence with scalable variational inference in GPyTorch. Across MODIS and EMIT datasets, DFGP and its variant DFGP_s significantly outperform baseline deep CNNs and random forests in $R^2$ (e.g., $R^2$ up to $0.9211$ on EMIT and $0.7431$ on MODIS) while providing probabilistic uncertainty estimates, albeit with known limitations under the current empirical Bayesian setup. This approach enables accurate, uncertainty-aware single-scene AOD reconstruction for high-resolution remote sensing data, supporting improved urban air quality mapping and cloud-robust aerosol monitoring.

Abstract

Remote sensing data provide a low-cost solution for large-scale monitoring of air pollution via the retrieval of aerosol optical depth (AOD), but is often limited by cloud contamination. Existing methods for AOD reconstruction rely on temporal information. However, for remote sensing data at high spatial resolution, multi-temporal observations are often unavailable. In this letter, we take advantage of deep representation learning from convolutional neural networks and propose Deep Feature Gaussian Processes (DFGP) for single-scene AOD reconstruction. By using deep learning, we transform the variables to a feature space with better explainable power. By using Gaussian processes, we explicitly consider the correlation between observed AOD and missing AOD in spatial and feature domains. Experiments on two AOD datasets with real-world cloud patterns showed that the proposed method outperformed deep CNN and random forest, achieving R$^2$ of 0.7431 on MODIS AOD and R$^2$ of 0.9211 on EMIT AOD, compared to deep CNN's R$^2$ of 0.6507 and R$^2$ of 0.8619. The proposed methods increased R$^2$ by over 0.35 compared to the popular random forest in AOD reconstruction. The data and code used in this study are available at \url{https://skrisliu.com/dfgp}.

Deep Feature Gaussian Processes for Single-Scene Aerosol Optical Depth Reconstruction

TL;DR

Cloud contamination limits satellite AOD retrieval for high-spatial-resolution, single-scene scenes. We propose Deep Feature Gaussian Processes (DFGP), a hybrid framework that uses CNN-based deep-feature extraction on predictors and Gaussian-process regression on the resulting features to model spatial dependence with scalable variational inference in GPyTorch. Across MODIS and EMIT datasets, DFGP and its variant DFGP_s significantly outperform baseline deep CNNs and random forests in (e.g., up to on EMIT and on MODIS) while providing probabilistic uncertainty estimates, albeit with known limitations under the current empirical Bayesian setup. This approach enables accurate, uncertainty-aware single-scene AOD reconstruction for high-resolution remote sensing data, supporting improved urban air quality mapping and cloud-robust aerosol monitoring.

Abstract

Remote sensing data provide a low-cost solution for large-scale monitoring of air pollution via the retrieval of aerosol optical depth (AOD), but is often limited by cloud contamination. Existing methods for AOD reconstruction rely on temporal information. However, for remote sensing data at high spatial resolution, multi-temporal observations are often unavailable. In this letter, we take advantage of deep representation learning from convolutional neural networks and propose Deep Feature Gaussian Processes (DFGP) for single-scene AOD reconstruction. By using deep learning, we transform the variables to a feature space with better explainable power. By using Gaussian processes, we explicitly consider the correlation between observed AOD and missing AOD in spatial and feature domains. Experiments on two AOD datasets with real-world cloud patterns showed that the proposed method outperformed deep CNN and random forest, achieving R of 0.7431 on MODIS AOD and R of 0.9211 on EMIT AOD, compared to deep CNN's R of 0.6507 and R of 0.8619. The proposed methods increased R by over 0.35 compared to the popular random forest in AOD reconstruction. The data and code used in this study are available at \url{https://skrisliu.com/dfgp}.
Paper Structure (12 sections, 11 equations, 4 figures, 3 tables)

This paper contains 12 sections, 11 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Deep Convolutional Neural Networks
  4. Gaussian Processes
  5. Deep Feature Gaussian Processes
  6. Experiments
  7. Data
  8. Experimental Setup
  9. Results
  10. Sensitivity Analysis
  11. Conclusion
  12. Acknowledgements

Figures (4)

  • Figure 1: MODIS AOD, with 1 km spatial resolution.
  • Figure 2: EMIT AOD, with 60 m spatial resolution.
  • Figure 3: Reconstruction results, along with the ground truth.
  • Figure 4: Mean absolute error (MAE) as a function of the number of training samples. (1st row: MODIS-Grid, MODIS-Random; 2nd row: EMIT-Grid, EMIT-Random.)