Sparse representations and convex optimization as tools for LOFAR radio interferometric imaging

TL;DR

This paper explores the use of sparse representations and convex optimization techniques, specifically proximal algorithms, to enhance radio interferometric imaging, demonstrating improvements in resolution, photometry, and extended source reconstruction.

Contribution

It introduces a novel application of convex optimization and sparse representations to radio interferometry, showing significant improvements over traditional methods like CLEAN.

Findings

Achieved super-resolution of approximately 2x over CLEAN.

Attained accurate photometry in high dynamic range fields.

Improved fidelity in imaging extended sources.

Abstract

Compressed sensing theory is slowly making its way to solve more and more astronomical inverse problems. We address here the application of sparse representations, convex optimization and proximal theory to radio interferometric imaging. First, we expose the theory behind interferometric imaging, sparse representations and convex optimization, and second, we illustrate their application with numerical tests with SASIR, an implementation of the FISTA, a Forward-Backward splitting algorithm hosted in a LOFAR imager. Various tests have been conducted in Garsden et al., 2015. The main results are: i) an improved angular resolution (super resolution of a factor ~2) with point sources as compared to CLEAN on the same data, ii) correct photometry measurements on a field of point sources at high dynamic range and iii) the imaging of extended sources with improved fidelity. SASIR provides better reconstructions (five time less residuals) of the extended emission as compared to CLEAN. With the advent of large radiotelescopes, there is scope for improving classical imaging methods with convex optimization methods combined with sparse representations.