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

Causal SAR ATR with Limited Data via Dual Invariance