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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. 

Spectrum cartography (SC) techniques craft multi-domain (e.g., space and frequency) radio maps from limited measurements, which is an ill-posed inverse problem. Recent works used low-dimensional priors such as a low tensor rank structure and a deep generative model to assist radio map estimation---with provable guarantees. However, a premise of these approaches is that the sensors are able to send real-valued feedback to a fusion center for SC---yet practical communication systems often use (heavy) quantization for signaling. This work puts forth a limited feedback-based SC framework. Similar to a prior work, a generative adversarial network (GAN)-based deep prior is used in our framework for fending against heavy shadowing. However, instead of using real-valued feedback, a random quantization strategy is adopted and a maximum likelihood estimation (MLE) criterion is proposed. Analysis shows that the MLE provably recovers the radio map, under reasonable conditions. Simulations are conducted to showcase the effectiveness of the proposed approach.