Causal SAR ATR with Limited Data via Dual Invariance

Synthetic aperture radar automatic target recognition (SAR ATR) with limited data has recently been a hot research topic to enhance weak generalization. Despite many excellent methods being proposed, a fundamental theory is lacked to explain what problem the limited SAR data causes, leading to weak generalization of ATR. In this paper, we establish a causal ATR model demonstrating that noise $N$ that could be blocked with ample SAR data, becomes a confounder with limited data for recognition. As a result, it has a detrimental causal effect damaging the efficacy of feature $X$ extracted from SAR images, leading to weak generalization of SAR ATR with limited data. The effect of $N$ on feature can be estimated and eliminated by using backdoor adjustment to pursue the direct causality between $X$ and the predicted class $Y$. However, it is difficult for SAR images to precisely estimate and eliminated the effect of $N$ on $X$. The limited SAR data scarcely powers the majority of existing optimization losses based on empirical risk minimization (ERM), thus making it difficult to effectively eliminate $N$'s effect. To tackle with difficult estimation and elimination of $N$'s effect, we propose a dual invariance comprising the inner-class invariant proxy and the noise-invariance loss. Motivated by tackling change with invariance, the inner-class invariant proxy facilitates precise estimation of $N$'s effect on $X$ by obtaining accurate invariant features for each class with the limited data. The noise-invariance loss transitions the ERM's data quantity necessity into a need for noise environment annotations, effectively eliminating $N$'s effect on $X$ by cleverly applying the previous $N$'s estimation as the noise environment annotations. Experiments on three benchmark datasets indicate that the proposed method achieves superior performance.