Physics-driven deep low-rank and sparse priors for airborne LiDAR bathymetry signal denoising

Extracting weak seafloor echoes from airborne LiDAR bathymetry (ALB) waveforms remains challenging due to heterogeneous environmental noise and scattering-induced attenuation, which obscure bottom returns and destabilize depth retrieval. To improve interpretability beyond conventional black-box deep denoisers while enhancing bathymetric stability, we propose ALB-DLSR-Net, a physics-driven deep unfolding framework. Specifically, we cast ALB waveform denoising as a physically constrained optimization problem with low-rank and sparse priors, capturing correlated background trends and transient echoes, respectively. By unrolling the iterative shrinkage-thresholding algorithm (ISTA) into interpretable neural layers, ALB-DLSR-Net incorporates physical constraints into the learning process. Within this framework, a depth-adaptive learned singular value thresholding (LSVT) module dynamically approximates the attenuation of deep-water signals while a multi-scale residual (MSR) block precisely suppresses non-stationary impulsive noise. Extensive experiments demonstrate consistent gains over state-of-the-art baselines, achieving 29.60 dB PSNR and 0.962 SSIM on measurements, which translate into improved recovery of weak bottom returns and enhanced bathymetric accuracy in turbid waters.