Physics-informed online low-rank separation for weak target enhancement in rough seabed waveguides

We address weak bottom-target feature enhancement under strong rough-seabed reverberation with a physics-informed, online delay-spectrum (DS) separation framework. A roughness-aware ray model reveals that, in the DS domain, the stationary propagating field is low-rank while target returns are sparse. We develop two streaming algorithms: DS-incremental singular value decomposition (DS-iSVD) for single-pass, low-latency updates, and DS-Grassmannian optimization (DS-GO) for iterative refinement. Scaled-tank experiments with scaling factor (SF) 1000, peak signal-to-interference ratio (SIR peak ) − 20 . 9 dB, and signal-to-noise ratio (SNR) 14.2 dB show that both methods demonstrate recovery of targets 20 dB below interference. DS-GO achieves mean SIR improvement Δ SIR ≈ 14 . 6 dB and improves separation accuracy versus DS-iSVD: mean center offset distance (COD) decreases from 0.112 s to 0.092 s ( ℓ 1 ) and from 0.121 s to 0.100 s ( ℓ 2 ); the mean 1-Wasserstein distance (W1) is 0.173 s. Monte Carlo (MC) SNR sweeps (0–10 dB) confirm robustness: DS-GO attains the best overall ridge score (RS), lowest W1 and COD, and highest peak hit rate (PHR) consistency with small variance, while DS-iSVD is a close second with the lowest latency. The approach enables real-time, physically interpretable feature enhancement for autonomous underwater vehicles (AUVs) and synthetic aperture sonar (SAS) in rough-bottom environments. • Delay-spectrum (DS) embedding exposes low-rank propagating and sparse target returns. • Two algorithms: DS-iSVD (low latency) and DS-GO (high fidelity) for feature enhancement. • Scaled-tank validation: recover targets 20 dB below interference; DS-GO improves SIR ≈ 14 . 6 dB. • Localization: mean COD improved from 0.112 s to 0.092 s; mean W1 = 0 . 173 s. • Robust across 0–10 dB SNR; real-time AUV/SAS with accuracy-latency trade-offs.