PolyCLEAN: Atomic Optimization for Super-Resolution Imaging and Uncertainty Estimation in Radio Interferometry

Abstract

Aims: We address two issues for the adoption of convex optimization in radio interferometric imaging. First, a method for a fine resolution setup is proposed which scales naturally in terms of memory usage and reconstruction speed. Second, a new tool to localize a region of uncertainty is developed, paving the way for quantitative imaging in radio interferometry. Methods: The classical ${\ell }_1$ penalty is used to turn the inverse problem into a sparsity-promoting optimization. For efficient implementation, the so-called Frank-Wolfe algorithm is used together with a \textit{polyatomic} refinement. The algorithm naturally produces sparse images at each iteration, leveraged to reduce memory and computational requirements. In that regard, PolyCLEAN reproduces the numerical behavior of CLEAN while guaranteeing that it solves the minimization problem of interest. Additionally, we introduce the concept of the \textit{dual certificate image}, which appears as a numerical byproduct of the Frank-Wolfe algorithm. This image is proposed as a tool for uncertainty quantification on the location of the recovered sources. Results: PolyCLEAN demonstrates good scalability performance, in particular for fine-resolution grids. On simulations, the Python-based implementation is competitive with the fast numerically-optimized CLEAN solver. This acceleration does not affect image reconstruction quality: PolyCLEAN images are consistent with CLEAN-obtained ones for both point sources and diffuse emission recovery. We also highlight PolyCLEAN reconstruction capabilities on observed radio measurements. Conclusions: PolyCLEAN can be considered as an alternative to CLEAN in the radio interferometric imaging pipeline, as it enables the use of Bayesian priors without impacting the scalability and numerical performance of the imaging method.

References in corpus (28)

• LOFAR: The LOw-Frequency ARray
• WSClean: an implementation of a fast, generic wide-field imager for radio astronomy
• The solution path of the generalized lasso
• Multi-Scale CLEAN deconvolution of radio synthesis images
• An optimized algorithm for multi-scale wideband deconvolution of radio astronomical images
• Compressed sensing imaging techniques for radio interferometry
• LOFAR 150-MHz observations of the Boötes field: Catalogue and Source Counts
• High Resolution Linear Polarimetric Imaging for the Event Horizon Telescope
• Imaging the Schwarzschild-radius-scale Structure of M87 with the Event Horizon Telescope using Sparse Modeling
• Sparsity Averaging Reweighted Analysis (SARA): a novel algorithm for radio-interferometric imaging
• The application of compressive sampling to radio astronomy I: Deconvolution
• LOFAR Sparse Image Reconstruction
• Scale sensitive deconvolution of interferometric images I. Adaptive Scale Pixel (Asp) decomposition
• Advances in Calibration and Imaging Techniques in Radio Interferometry
• Uncertainty quantification for radio interferometric imaging: I. proximal MCMC methods
• RESOLVE: A new algorithm for aperture synthesis imaging of extended emission in radio astronomy
• Image reconstruction algorithms in radio interferometry: from handcrafted to learned regularization denoisers
• Comparison of classical and Bayesian imaging in radio interferometry
• Uncertainty quantification for radio interferometric imaging: II. MAP estimation
• Deep Learning-based Imaging in Radio Interferometry
• An accelerated splitting algorithm for radio-interferometric imaging: when natural and uniform weighting meet
• Cygnus A super-resolved via convex optimisation from VLA data
• Parallel faceted imaging in radio interferometry via proximal splitting (Faceted HyperSARA): I. Algorithm and simulations
• Wideband Super-resolution Imaging in Radio Interferometry via Low Rankness and Joint Average Sparsity Models (HyperSARA)
• Multi-scale and Multi-directional VLBI Imaging with CLEAN
• Dynamic and polarimetric VLBI imaging with a multiscalar approach
• Parallel faceted imaging in radio interferometry via proximal splitting (Faceted HyperSARA): II. Code and real data proof of concept
• A Fast and Scalable Polyatomic Frank-Wolfe Algorithm for the LASSO

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• A Decentralized Framework for Radio-interferometric Image Reconstruction
• Accelerating the CLEAN algorithm of radio interferometry with convex optimization