Dual-pixel collaboration scheme for enhanced physics-based bathymetry from single multispectral imagery

The limited number of spectral bands is one of the primary factors contributing to the uncertainty in physics‑based satellite-derived bathymetry (SDB) when applied to single multispectral imagery. This study proposes an enhanced physics-based SDB method that addresses this limitation through a dual-pixel collaboration scheme (DPCS)‌. Instead of independent pixel-wise retrieval, DPCS addresses the ill-posed nature of physics-based SDB by conjointly estimating the depths of spatially adjacent pixels. The proposed DPCS represents a paradigm shift in physics-based SDB from single-pixel optimization to multipixel collaborative retrieval, leveraging the spatial homogeneity of inherent optical properties (IOPs) as additional physical constraints across neighboring pixels. Then, a post-processing step is utilized to generate the final depth at each pixel by averaging all DPCS-derived depth candidates weighted by the inverse of their spectral fitting errors, further mitigating optimization-induced anomalies. Different from simply utilizing spatial information as training features or post spatial smoothing, DPCS embeds the spatial consistency of IOPs as an intrinsic physics-driven constraint within the radiative transfer inversion process, directly strengthens the mathematical conditioning of the inverse problem by increasing the observation to unknown ratio at the stage of model formulation. The proposed scheme features a concise structure, strong extensibility, and a clear underlying physical mechanism. Experimental results on four coral reefs in the Xisha Islands and two coastal regions around the Oahu Island using a series of Landsat-8 OLI images demonstrate that the proposed method outperformed the traditional hyperspectral optimization process exemplar (HOPE) method. Specifically, DPCS achieved higher R² by 0.02–0.13, while reducing the root-mean-square error (RMSE) by 0.07–0.75 m and the mean absolute error (MAE) by 0.07–0.25 m across the six study areas, with the most significant improvements observed in deeper waters (>8 m). This study demonstrates that the proposed DPCS framework improves the robustness and accuracy of physics-based SDB, enabling high-precision bathymetry mapping in challenging single multispectral scenarios without supplementary data acquisitions.