An Interpretable Two-Stage Feature Decomposition Method for Deep Learning-Based SAR ATR

Synthetic aperture radar automatic target recognition (SAR ATR) has seen significant performance improvements with deep learning. However, the black-box nature of deep SAR ATR introduces low confidence and high risks in decision-critical SAR applications, hindering practical deployment. To address this issue, deep SAR ATR should provide an interpretable reasoning basis $r_{b}$ and weights $\lambda _{w}$ , forming the reasoning logic $\sum _{i} {{r_{b}^{i}} \times {\lambda _{w}^{i}}} = \mathrm {pred}$ behind the decisions. However, deep features are inherently abstract, high-dimensional, and entangled: standard DNN operations couple independent ASCs into uninterpretable representations, and directly decoupling them not only incurs large decomposition errors but also destroys discriminability. Therefore, this paper proposes a physics-based two-stage feature decomposition method for interpretable deep SAR ATR, which for the first time identifies and resolves the coupling-discriminability dilemma unique to SAR ATR by transforming entangled deep features into ASC components (ASCCs) with clear physical meanings. First, ASCCs are obtained through a clustering algorithm. To extract independent physical components from entangled deep features, we propose a two-stage decomposition method. In the first stage, a feature decoupling and discrimination module separates deep features into approximate ASCCs with global discriminability. In the second stage, a multilayer orthogonal non-negative matrix tri-factorization (MLO-NMTF) further decomposes the ASCCs into independent components with distinct physical meanings. The MLO-NMTF with orthogonal constraints is proved equivalent, in the relaxed sense, to spectral clustering, establishing a structural correspondence between the network's latent space and the physical scattering domain, and underpinning the verifiable reasoning logic $\sum _{i} r_{b}^{i} \times \lambda _{w}^{i} = \mathrm {pred}$ . Finally, this method ensures both a fully verifiable reasoning process and accurate recognition results. Extensive experiments on four benchmark datasets across 12 backbone architectures, compared against 9 interpretable SAR ATR methods, confirm its superior recognition performance and strong generalization capability.