Plug-and-play imaging with model uncertainty quantification in radio astronomy

Plug-and-Play (PnP) algorithms are appealing alternatives to proximal algorithms when solving inverse imaging problems. By learning a Deep Neural Network (DNN) behaving as a proximal operator, one waives the computational complexity of optimisation algorithms induced by sophisticated image priors, and the sub-optimality of handcrafted priors compared to DNNs. At the same time, these methods inherit the versatility of optimisation algorithms allowing the minimisation of a large class of objective functions. Such features are highly desirable in radio-interferometric (RI) imaging in astronomy, where the data size, the ill-posedness of the problem and the dynamic range of the target reconstruction are critical. In a previous work, we introduced a class of convergent PnP algorithms, dubbed AIRI, relying on a forward-backward algorithm, with a differentiable data-fidelity term and dynamic range-specific denoisers trained on highly pre-processed unrelated optical astronomy images. Here, we show that AIRI algorithms can benefit from a constrained data fidelity term at the mere cost of transferring to a primal-dual forward-backward algorithmic backbone. Moreover, we show that AIRI algorithms are robust to strong variations in the nature of the training dataset: denoisers trained on MRI images yield similar reconstructions to those trained on astronomical data. We additionally quantify the model uncertainty introduced by the randomness in the training process and suggest that AIRI algorithms are robust to model uncertainty. Finally, we propose an exhaustive comparison with methods from the radio-astronomical imaging literature and show the superiority of the proposed method over the current state-of-the-art.