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-Loéve (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 $92\,km \times 92\,km$ 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：本文开发了一套融合光学与合成孔径雷达（SAR）数据的森林砍伐检测流程。该流程的关键组成部分是基于离散Karhunen-Loéve（KL）展开的残差空间构建光学数据异常图。异常量化采用森林名义状态下残差分量分布的浓度界，该界无需预先知晓数据分布信息，这与需要数据分布先验知识的统计参数方法形成对比——后者对本文所述高维数据尤其不可行。生成光学异常图后，将其与SAR数据融合，通过隐马尔科夫模型（HMM）对森林状态进行分类。我们在亚马逊森林92公里×92公里区域，使用Sentinel-1（SAR）与Sentinel-2（光学）数据对方法进行验证。结果表明，光学-雷达混合方法与纯光学方法均实现了优于最新混合方法的准确率，且混合方法在高云量区域常见的光学数据稀疏场景中表现出显著更强的鲁棒性。