Latent Variable-Mediated Cross-Learning for Few-Shot Acoustic Impedance Imaging

Acoustic impedance imaging is a fundamental yet severely ill-posed problem in subsurface analysis: the seismic wavelet is unknown, observations are band-limited, and labeled well-log samples are extremely scarce (typically <1% of all traces). Existing semi-supervised deep learning methods mitigate few-shot problem by incorporating forward modeling, yet they either rely on inaccurate prior wavelet assumptions or introduce auxiliary networks, leading to unstable optimization and degraded performance. We propose RD-SCL, a novel framework that integrates regularized deconvolution with semi-supervised cross-learning. At its core lies a differentiable, closed-form first-order Tikhonov deconvolution operator that dynamically estimates the latent wavelet in the frequency domain during training, providing stable physics-guided feedback without explicit auxiliary networks and fixed wavelet priors. Building on this operator, we design a symmetric cross-learning that enforces consistency between predictions on labeled and unlabeled data, thereby effectively exploiting abundant unlabeled traces. Extensive experiments on the SEAM and Marmousi 2 benchmarks demonstrate that RD-SCL consistently outperforms state-of-the-art supervised and semi-supervised methods, achieving substantial gains with lower computational cost. With only 56.5k learnable parameters and competitive runtime, RD-SCL offers a practical, physically consistent, and efficient solution for acoustic impedance imaging.