Deterministic sea wave reconstruction techniques are critical for enhancing maritime safety and disaster warnings. Coherent radar remote sensing captures sea surface velocity information to enable more precise wave reconstruction. Existing difference matrix methods address rank-deficient systems through artificial boundary processing, which distorts local hydrodynamic characteristics and propagates errors to global features, thereby limiting the accuracy and stability of reconstructions. To resolve this limitation, this study proposes a physics-constrained deterministic wave reconstruction methodology. We introduce the Data-Anchored Projection model for the differential matrix, extracting hydrodynamic constraints directly from radar backscatter data. This approach achieves stable solutions for rank-deficient systems without artificial boundaries. The model’s performance was rigorously validated through both simulated and real-sea experiments. The simulation results demonstrate a minimum 13% accuracy improvement over conventional methods and high stability under various sea states and at different range resolutions. In a real-sea trial under sea states 3 to 5, reconstruction errors remained below 10%, with consistent stability observed across varying sea states.