deFOREST: Fusing Optical and Radar satellite data for Enhanced Sensing of Tree-loss

TL;DR

This work introduces deFOREST, a deforestation-detection pipeline that fuses optical (Sentinel-2) and SAR (Sentinel-1) data through a discrete Karhunen–Loève expansion–driven anomaly framework and a Hidden Markov Model. By projecting optical data onto a residual eigenspace and applying a nonparametric concentration bound, the method yields anomaly features that improve land-cover classification and change detection when integrated with SAR signals. Across a 92.19 km × 91.80 km Amazon region, the hybrid optical-SAR approach achieves the highest accuracy and is notably more robust to sparse optical data than optical-only methods or recent baselines like FNRT. The work demonstrates that KL-based anomaly representations, combined with probabilistic fusion, offer a practical and scalable solution for cloud-prone tropical forests and can enhance near-real-time monitoring and carbon-emission assessments.

Abstract

In this paper we develop a deforestation detection pipeline that incorporates optical and Synthetic Aperture Radar (SAR) data. A crucial component of the pipeline is the construction of anomaly maps of the optical data, which is done using the residual space of a discrete Karhunen-Loève (KL) expansion. Anomalies are quantified using a concentration bound on the distribution of the residual components for the nominal state of the forest. This bound does not require prior knowledge on the distribution of the data. This is in contrast to statistical parametric methods that assume knowledge of the data distribution, an impractical assumption that is especially infeasible for high dimensional data such as ours. Once the optical anomaly maps are computed they are combined with SAR data, and the state of the forest is classified by using a Hidden Markov Model (HMM). We test our approach with Sentinel-1 (SAR) and Sentinel-2 (Optical) data on a $92.19\,km \times 91.80\,km$ region in the Amazon forest. The results show that both the hybrid optical-radar and optical only methods achieve high accuracy that is superior to the recent state-of-the-art hybrid method. Moreover, the hybrid method is significantly more robust in the case of sparse optical data that are common in highly cloudy regions.

Figures (24)

• Figure 1: Monitoring land cover fusion pipeline for remote sensing data. This may include optical and radar data.
• Figure 2: Illustrative example of the separation capabilities of the KL expansion by applying the transformation to the nominal and anomalous data. (a) The blue balls represent the nominal behavior such as the starting state of the land cover and orange balls the signal anomaly (changes in the land cover state). These observations points are mixed with each other, which makes it hard to build a decision surface. (b) After forming the residual $\boldsymbol{\eta} := (\mathbf{u} - {\mathbb E} \left[ \mathbf{v} \right] ) - \mathbf{P}^m(\mathbf{u} - {\mathbb E} \left[ \mathbf{v} \right] )$, the blue balls correspond to coefficients $r_k$ that are subject to the null hypothesis $H_0$ (nominal class). Thus from equation \ref{['residual']} the coefficients are centered around the origin with high probability. Conversely, under the alternative hypothesis $H_A$ (signal anomaly) the coefficients $\tilde{r}_k$ (orange balls) are likely not to concentrate around zero. This makes it easier to build a separation surface for the two classes.
• Figure 3: Environmental change from Sentinel 2 satellite data acquired in the Brazilian Amazon. The data show a logging event and subsequent recovery of the forest. The is applied with the goal of detecting the timing and location of the change. The feature information will be used to track the state of the forest. As an example we track the land cover change in the small red box.
• Figure 4: Anomaly sequence in a pixel-level time series of satellite data depicting environmental change illustrated in the red pixel of Figure\ref{['PR:Fig2']}. The projection operator $\mathbf{P}^{m}$ is applied spatially to each frame, with the anomaly quantified and plotted against time. A robust LOESS is performed on the sequence (blue line). Logging of forest is detected on day 3484, with anomaly level increasing. After logging, forest is allowed to recover, with recovery mostly determined on day 3704. On day 3909 (red marker) a localized anomaly is in caused by cloud screening (image for day 3909 in Figure\ref{['PR:Fig2']}).
• Figure 5: Deforestation state of the forest is tracked with optical observations. This is achieved by applying a Hidden Markov Model to the $i^{th}$ pixel with the observation sequence $\zeta(t_k)=\boldsymbol{\eta}(i,t_k)$. The state of the land cover for the $i^{th}$ pixel is {forest, cloud or shadow, deforestation}. A Hidden Markov Model and Viterbi algorithm are used to classify the state of the forest $\gamma(t_k)$ at time $t_k$. The red pixels classify trees that have been cleared. The white pixels corresponds to clouds or dark shadow. The black points corresponds to a well known cloud masking algorithm, which could not detect the light clouds and dark shadows. These are particularly difficult to detect.

Theorems & Definitions (14)

• Theorem 2.1
• Remark 1
• Theorem 2.2
• Remark 2
• Remark 3
• Remark 4
• Remark 5
• Theorem S.I.1
• proof
• Theorem S.I.2