LOFAR sparse image reconstruction

¹ Laboratoire AIM, Université Paris Diderot Paris 7/CNRS/CEA-Saclay, DSM/IRFU/SAp 91191 Gif-sur-Yvette France
² Department of Physics and Electronics, Rhodes University, PO Box 94, 6140 Grahamstown, South Africa
³ SKA South Africa, 3rd Floor, The Park, Park Road, 7405 Pinelands, South Africa
⁴ Sagem (Safran), 27 rue Leblanc, 75512 Paris Cedex 15, France
⁵ Netherlands Institute for Radio Astronomy (ASTRON), Postbus 2, 7990 AA Dwingeloo, The Netherlands
⁶ Helmholtz-Zentrum Potsdam, Deutsches GeoForschungsZentrum GFZ, Department 1: Geodesy and Remote Sensing, Telegrafenberg, A17, 14473 Potsdam, Germany
⁷ Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany
⁸ SRON Netherlands Institute for Space Research, PO Box 800, 9700 AV Groningen, The Netherlands
⁹ Kapteyn Astronomical Institute, PO Box 800, 9700 AV Groningen, The Netherlands
¹⁰ Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
¹¹ University of Twente, Drienerlolaan 5, 7522 Enschede, The Netherlands
¹² Institute for Astronomy, University of Edinburgh, Royal Observatory of Edinburgh, Blackford Hill, Edinburgh EH9 3HJ, UK
¹³ School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, UK
¹⁴ University of Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany
¹⁵ Research School of Astronomy and Astrophysics, Australian National University, Mt Stromlo Obs., via Cotter Road, Weston, A.C.T. 2611, Australia
¹⁶ Max Planck Institute for Astrophysics, Karl Schwarzschild Str. 1, 85741 Garching, Germany
¹⁷ SmarterVision BV, Oostersingel 5, 9401 JX Assen, The Netherlands
¹⁸ Thüringer Landessternwarte, Sternwarte 5, 07778 Tautenburg, Germany
¹⁹ Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany
²⁰ Department of Astrophysics/IMAPP, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands
²¹ Astrophysics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK
²² Laboratoire Lagrange, UMR7293, Université de Nice Sophia-Antipolis, CNRS, Observatoire de la Côte d’Azur, 06300 Nice, France
²³ Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
²⁴ LPC2E – Universite d’Orléans/CNRS, 45071 Orléans Cedex 2, France
²⁵ Station de Radioastronomie de Nançay, Observatoire de Paris – CNRS/INSU, USR 704 – Univ. Orléans, OSUC, route de Souesmes, 18330 Nançay, France
²⁶ Jodrell Bank Center for Astrophysics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK
²⁷ Astronomical Institute “Anton Pannekoek”, University of Amsterdam, Postbus 94249, 1090 GE Amsterdam, The Netherlands
²⁸ Astronomisches Institut der Ruhr-Universität Bochum, Universitaetsstrasse 150, 44780 Bochum, Germany
²⁹ Astro Space Center of the Lebedev Physical Institute, Profsoyuznaya str. 84/32, 117997 Moscow, Russia
³⁰ Sodankylä Geophysical Observatory, University of Oulu, Tähteläntie 62, 99600 Sodankylä, Finland
³¹ STFC Rutherford Appleton Laboratory, Harwell Science and Innovation Campus, Didcot OX11 0QX, UK
³² Center for Information Technology (CIT), University of Groningen, PO Box 11044, 9700 CA Groningen, The Netherlands
³³ Centre de Recherche Astrophysique de Lyon, Observatoire de Lyon, 9 av Charles André, 69561 Saint Genis Laval Cedex, France
³⁴ Fakultät für Physik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
³⁵ LESIA, UMR CNRS 8109, Observatoire de Paris, 92195 Meudon, France
³⁶ Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA

^⋆ J. N. Girard, e-mail: julien.girard@cea.fr

Received: 30 June 2014
Accepted: 18 December 2014

Abstract

Context. The LOw Frequency ARray (LOFAR) radio telescope is a giant digital phased array interferometer with multiple antennas distributed in Europe. It provides discrete sets of Fourier components of the sky brightness. Recovering the original brightness distribution with aperture synthesis forms an inverse problem that can be solved by various deconvolution and minimization methods.

Aims. Recent papers have established a clear link between the discrete nature of radio interferometry measurement and the “compressed sensing” (CS) theory, which supports sparse reconstruction methods to form an image from the measured visibilities. Empowered by proximal theory, CS offers a sound framework for efficient global minimization and sparse data representation using fast algorithms. Combined with instrumental direction-dependent effects (DDE) in the scope of a real instrument, we developed and validated a new method based on this framework.

Methods. We implemented a sparse reconstruction method in the standard LOFAR imaging tool and compared the photometric and resolution performance of this new imager with that of CLEAN-based methods (CLEAN and MS-CLEAN) with simulated and real LOFAR data.

Results. We show that i) sparse reconstruction performs as well as CLEAN in recovering the flux of point sources; ii) performs much better on extended objects (the root mean square error is reduced by a factor of up to 10); and iii) provides a solution with an effective angular resolution 2−3 times better than the CLEAN images.

Conclusions. Sparse recovery gives a correct photometry on high dynamic and wide-field images and improved realistic structures of extended sources (of simulated and real LOFAR datasets). This sparse reconstruction method is compatible with modern interferometric imagers that handle DDE corrections (A- and W-projections) required for current and future instruments such as LOFAR and SKA.