Hybrid data- and model-driven three-dimensional ocean sound speed field super-resolution: Diffusion model meets low-rank tensor

Accurate, high-resolution three-dimensional (3D) sound speed fields (SSFs) are crucial for characterizing ocean sound propagation, enabling environment-aware underwater acoustic detection and communications. However, SSF data gathered by current observation systems often suffer from low resolution and noise, diminishing their effectiveness in subsequent tasks and necessitating advanced methods to restore their intricate details-referred to as super-resolution (SR) methods. Existing SR methods are either model-based or data-driven. Both paradigms, however, have their limitations in restoring the subtle variations within SSFs, particularly in challenging scenarios with sparse and noisy measurements. To tackle these challenges, we propose a hybrid SR algorithm, named Hybrid-DOT, which combines the strengths of both data-driven and model-driven approaches. Specifically, we employ a pre-trained diffusion model as the data-driven prior to exploit the information inside the data distribution, and a low-rank tensor (LRT) modeling as the model-based prior to integrate domain knowledge. The incorporation of the LRT not only enhances SR performance but also saves the sampling steps of the diffusion model. Experimental results using 3D SSF datasets demonstrate that Hybrid-DOT surpasses state-of-the-art methods across various SR factors and noise levels, enabling accurate characterizations of fine-grained acoustic transmission losses.