H. Garsden et al., "LOFAR sparse image reconstruction," Astronomy & Astrophysics, V575, no. A90, pp1-18, March 2015.
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.
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