Zero-shot reconstruction of ocean sound speed field tensors: A deep plug-and-play approach

Reconstructing a three-dimensional ocean sound speed field (SSF) from limited and noisy measurements presents an ill-posed and challenging inverse problem. Existing methods used a number of pre-specified priors (e.g., low-rank tensor and tensor neural network structures) to address this issue. However, the SSFs are often too complex to be accurately described by these pre-defined priors. While utilizing neural network-based priors trained on historical SSF data may be a viable workaround, acquiring SSF data remains a nontrivial task. This work starts with a key observation: Although natural images and SSFs admit fairly different characteristics, their denoising processes appear to share similar traits-as both remove random components from more structured signals. This observation allows us to incorporate deep denoisers trained using extensive natural images to realize zero-shot SSF reconstruction, without any extra training or network modifications. To implement this idea, an alternating direction method of multipliers (ADMM) algorithm using such a deep denoiser is proposed, which is reminiscent of the plug-and-play scheme from medical imaging. Our plug-and-play framework is tailored for SSF recovery such that the learned denoiser can be simultaneously used with other handcrafted SSF priors. Extensive numerical studies show that the new framework largely outperforms state-of-the-art baselines, especially under widely recognized challenging scenarios, e.g., when the SSF samples are taken as tensor fibers. The code is available at https://github.com/OceanSTARLab/DeepPnP.