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-Lo\`{e}ve (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.

翻译：本文开发了一种融合光学与合成孔径雷达（SAR）数据的森林砍伐检测流程。该流程的关键环节在于构建光学数据的异常图，这是通过离散Karhunen-Loève（KL）展开的残差空间实现的。异常量化的依据是对森林正常状态下残差分量分布所设定的集中界。该界限无需预先获知数据的分布特性，这与统计参数方法形成鲜明对比——后者通常假设已知数据分布，这种假设在实际中往往难以成立，尤其对于如本文所涉及的高维数据而言。完成光学异常图计算后，将其与SAR数据融合，并利用隐马尔可夫模型（HMM）对森林状态进行分类。我们使用Sentinel-1（SAR）和Sentinel-2（光学）数据，在亚马逊雨林一片$92.19\,km \times 91.80\,km$区域内对该方法进行了验证。结果表明：融合光学-雷达方法与纯光学方法均实现了优于当前先进混合方法的高精度检测。此外，在云雾密集区域常见的光学数据稀疏场景下，融合方法展现出显著更强的鲁棒性。