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.

Deep network series for large-scale high-dynamic range imaging

We propose a new approach for large-scale high-dynamic range computational imaging. Deep Neural Networks (DNNs) trained end-to-end can solve linear inverse imaging problems almost instantaneously. While unfolded architectures provide necessary robustness to variations of the measurement setting, embedding large-scale measurement operators in DNN architectures is impractical. Alternative Plug-and-Play (PnP) approaches, where the denoising DNNs are blind to the measurement setting, have proven effective to address scalability and high-dynamic range challenges, but rely on highly iterative algorithms. We propose a residual DNN series approach, where the reconstructed image is built as a sum of residual images progressively increasing the dynamic range, and estimated iteratively by DNNs taking the back-projected data residual of the previous iteration as input. We demonstrate on simulations for radio-astronomical imaging that a series of only few terms provides a high-dynamic range reconstruction of similar quality to state-of-the-art PnP approaches, at a fraction of the cost.

Parallel faceted imaging in radio interferometry via proximal splitting (Faceted HyperSARA): II. Code and real data proof of concept

In a companion paper, a faceted wideband imaging technique for radio interferometry, dubbed Faceted HyperSARA, has been introduced and validated on synthetic data. Building on the recent HyperSARA approach, Faceted HyperSARA leverages the splitting functionality inherent to the underlying primal-dual forward-backward algorithm to decompose the image reconstruction over multiple spatio-spectral facets. The approach allows complex regularization to be injected into the imaging process while providing additional parallelization flexibility compared to HyperSARA. The present paper introduces new algorithm functionalities to address real datasets, implemented as part of a fully fledged MATLAB imaging library made available on Github. A large scale proof-of-concept is proposed to validate Faceted HyperSARA in a new data and parameter scale regime, compared to the state-of-the-art. The reconstruction of a 15 GB wideband image of Cyg A from 7.4 GB of VLA data is considered, utilizing 1440 CPU cores on a HPC system for about 9 hours. The conducted experiments illustrate the reconstruction performance of the proposed approach on real data, exploiting new functionalities to set, both an accurate model of the measurement operator accounting for known direction-dependent effects (DDEs), and an effective noise level accounting for imperfect calibration. They also demonstrate that, when combined with a further dimensionality reduction functionality, Faceted HyperSARA enables the recovery of a 3.6 GB image of Cyg A from the same data using only 91 CPU cores for 39 hours. In this setting, the proposed approach is shown to provide a superior reconstruction quality compared to the state-of-the-art wideband CLEAN-based algorithm of the WSClean software.