Image reconstruction algorithms in radio interferometry: from handcrafted to learned denoisers

We introduce a new class of iterative image reconstruction algorithms for radio interferometry, at the interface of convex optimization and deep learning, inspired by plug-and-play methods. The approach consists in learning a prior image model by training a deep neural network (DNN) as a denoiser, and substituting it for the handcrafted proximal regularization operator of an optimization algorithm. The proposed AIRI ("AI for Regularization in Radio-Interferometric Imaging") framework, for imaging complex intensity structure with diffuse and faint emission, inherits the robustness and interpretability of optimization, and the learning power and speed of networks. Our approach relies on three steps. Firstly, we design a low dynamic range database for supervised training from optical intensity images. Secondly, we train a DNN denoiser with basic architecture ensuring positivity of the output image, at a noise level inferred from the signal-to-noise ratio of the data. We use either $\ell_2$ or $\ell_1$ training losses, enhanced with a nonexpansiveness term ensuring algorithm convergence, and including on-the-fly database dynamic range enhancement via exponentiation. Thirdly, we plug the learned denoiser into the forward-backward optimization algorithm, resulting in a simple iterative structure alternating a denoising step with a gradient-descent data-fidelity step. The resulting AIRI-$\ell_2$ and AIRI-$\ell_1$ were validated against CLEAN and optimization algorithms of the SARA family, propelled by the "average sparsity" proximal regularization operator. Simulation results show that these first AIRI incarnations are competitive in imaging quality with SARA and its unconstrained forward-backward-based version uSARA, while providing significant acceleration. CLEAN remains faster but offers lower reconstruction quality.