  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.
