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

• Published in: Journal of instrumentation Vol. 10; no. 8; p. C08013
• Main Authors: Girard, J.N., Garsden, H., Starck, J.L., Corbel, S., Woiselle, A., Tasse, C., McKean, J.P., Bobin, J.
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.08.2015
• Subjects: Astrophysics; Instrumentation and Methods for Astrophysic; Physics; Image processing; Antennas; Interferometry
• ISSN: 1748-0221; 1748-0221
• DOI: 10.1088/1748-0221/10/08/C08013

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 illustratetheir application with numerical tests with SASIR, an implementation of the FISTA, a ForwardBackward 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 photometrymeasurements 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.