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 from visibility data, inherits the robustness and interpretability of optimization, and the learning power and speed of networks. Our approach relies on three steps. First, we design a low dynamic range training data base from optical intensity images. Secondly, we train a DNN denoiser at a noise level inferred from the signal-to-noise ratio of the data. We use training losses enhanced with a non-expansiveness term ensuring algorithm convergence, and including on-the-fly data base 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. We have validated AIRI against clean, optimization algorithms of the SARA family, and a DNN trained to reconstruct the image directly from visibility data. Simulation results show that AIRI is competitive in imaging quality with SARA and its unconstrained forward–backward-based version uSARA, while providing significant acceleration. clean remains faster but offers lower quality. The end-to-end DNN offers further acceleration, but with far lower quality than AIRI.
Catalyst Acceleration for First-order Convex Optimization: from Theory to Practice
We introduce a generic scheme for accelerating gradient-based optimization methods in the sense of Nesterov. The approach, called Catalyst, builds upon the inexact accelerated proximal point algorithm for minimizing a convex objective function, and consists of approximately solving a sequence of well-chosen auxiliary problems, leading to faster convergence. One of the keys to achieve acceleration in theory and in practice is to solve these sub-problems with appropriate accuracy by using the right stopping criterion and the right warm-start strategy. We give practical guidelines to use Catalyst and present a comprehensive analysis of its global complexity. We show that Catalyst applies to a large class of algorithms, including gradient descent, block coordinate descent, incremental algorithms such as SAG, SAGA, SDCA, SVRG, MISO/Finito, and their proximal variants. For all of these methods, we establish faster rates using the Catalyst acceleration, for strongly convex and non-strongly convex objectives. We conclude with extensive experiments showing that acceleration is useful in practice, especially for ill-conditioned problems.
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- Award ID(s):
- 1740551
- NSF-PAR ID:
- 10066994
- Date Published:
- Journal Name:
- Journal of machine learning research
- Volume:
- 18
- ISSN:
- 1533-7928
- Page Range / eLocation ID:
- 1−54
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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