  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.
