Integrating the special electromagnetic characteristics of Synthetic Aperture Radar (SAR) in deep neural networks is essential in order to enhance the explainability and physics awareness of deep learning. In this paper, we first propose a novel physically explainable convolutional neural network for SAR image classification, namely physics guided and injected learning (PGIL). It comprises three parts: (1) explainable models (XM) to provide prior physics knowledge, (2) physics guided network (PGN) to encode the knowledge into physics-aware features, and (3) physics injected network (PIN) to adaptively introduce the physics-aware features into classification pipeline for label prediction. A hybrid Image-Physics SAR dataset format is proposed for evaluation, with both Sentinel-1 and Gaofen-3 SAR data being experimented. The results show that the proposed PGIL substantially improve the classification performance in case of limited labeled data compared with the counterpart data-driven CNN and other pre-training methods. Additionally, the physics explanations are discussed to indicate the interpretability and the physical consistency preserved in the predictions. We deem the proposed method would promote the development of physically explainable deep learning in SAR image interpretation field.

将合成孔径雷达 (SAR) 的特殊电磁特性集成到深度神经网络中对于增强深度学习的可解释性和物理意识至关重要。在本文中，我们首先提出了一种新的用于 SAR 图像分类的物理可解释卷积神经网络，即物理引导和注入学习 (PGIL)。它包括三个部分：（1）可解释模型（XM）提供先验物理知识，（2）物理引导网络（PGN）将知识编码为物理感知特征，（3）物理注入网络（PIN）自适应将物理感知特征引入分类管道以进行标签预测。提出了一种混合 Image-Physics SAR 数据集格式进行评估，同时对 Sentinel-1 和高分 3 SAR 数据进行了实验。结果表明，与对应的数据驱动的 CNN 和其他预训练方法相比，所提出的 PGIL 在有限标记数据的情况下显着提高了分类性能。此外，还讨论了物理解释以表明预测中保留的可解释性和物理一致性。我们认为所提出的方法将促进物理可解释深度学习在 SAR 图像解释领域的发展。