SASIR

SASIR is a deconvolution algorithm (written in C++ and Python) dedicated to radio interferometric imaging and based on the convex optimization using sparse representations (refered to the framework of Compressed Sensing).

As an alternative to CLEAN, it allows a robust reconstruction of the sky brightness composed of a mix of extended emission and point sources, with improved image resolution and fidelity.

It has been developped and tested in the context of the giant radio interferometer LOFAR. It is being adapted on recent imagers use for LOFAR and other SKA pathfinders/precursors.

 

Super-resolved image of the radiosource Cygnus A (real data), reconstructed by the new Sparse imager (SASIR).

Super-resolved image of the radiosource Cygnus A (real data), reconstructed by the new Sparse imager (SASIR).

Sparse Aperture Synthesis Image Reconstruction

The correct reconstruction of radio images from visibility data is an intense field of research since the coming of new generation radio interferometers such as LOFAR (LOw Frequency Array) and SKA (Square Kilometre Array). These instruments require a correct approach taking into account Direction-(in)Dependent Effects  (such as variation of the beam, polarization, ...).  The mathematical framework for calibration is provided by the RIME, the Radio Interferometer Measurement Equation, (refer to Hamaker, Sault, Bregman series of papers and Smirnov 2011 series) enables a proper handling for data modelling and calibration.

In spite of the high angular/time/frequency resolutions and the large variety of baselines, these interferometers measure a finite number of visibilities over the course of an observation, giving an incomplete frequency sampling of the sky Fourier Transform. This incomplete knowledge of the sky FT creates distorted images when the visibility data are gridded and projected back to the image plane. These images are distorted by the instrumental Point Spread Function (PSF) which encode this lack of information. A robust imaging of radio interferometric data resides in the robustness of the deconvolution algorithm used to remove the effect of this PSF. CLEAN and its derivatives (see family of CLEAN algorithms and associated papers) have been performing this task for decades on point sources will relatively good performance and robustness.

However, Sparse data and the existence of multi-scale radio emission (mix of point source and extended emissions) are obstacles to the deconvolution. The framework of Compressed Sensing offer us an opportunity to redefine the deconvolution problem as an optimization problem (inpainting problem) targeting solutions close to the real sky brightness with the lowest reconstruction bias.

Our approach was to construct an alternative to CLEAN with the implementation of another deconvolution method based on the FISTA algorithm (Beck et Teboulle, 2009).

SASIR (Sparse Aperture Synthesis Image Reconstruction) is an in-painting imager which combines sparse representation with l_1-minimization.

SASIR 2D-1D is a spin-off of SASIR (based on Condat-Vu algorithm) applied to the reconstruction of transient sources in the image plane.

Project contributorsDr. Julien N. Girard, Ming Jiang, Jean-Luc Starck, Stéphane Corbel and formerly Dr. H. Garsden and Dr. A. Woiselle.

Software

Sparse Aperture Synthesis Image Reconstruction - 2D

SASIR 2D comes in two versions:

  • A C++ stand-alone in the ISAP package (not connected to an imager but using fits files as input/output).
  • A C++ "LOFAR" version integrated in LWimager (check out the github repository) and using Docker containers to facilitate the compilation.
  • A Python/C++ implementation pySASIR is currently being implemented on a separate github repository (to be released soon). Current efforts are focused on the implementation of this deconvolution algorithm as a minor cycle in WSCLEAN (Offringa et al., 2014)  and DDFacet (Tasse et al., to be submitted).

Sparse Aperture Synthesis Image Reconstruction for Radio Transients reconstruction - 2D-1D

SASIR 2D1D will come in one version:

  • A Python/C++ implementation pySASIR-2D1D is currently being implemented on a separate github repository (to be released soon). Its implementation as a minor cycle

Questions on compilation, the usage, access to the paper toy models and examples are available upon request to julien.girard [at] cea.fr.

 

Bibliography

Published

  • H. Garsden, J. N. Girard, J. L. Starck, S. Corbel, C. Tasse, A. Woiselle, J. P. McKean and 74 coauthors.
    LOFAR sparse image reconstruction. Astronomy & Astrophysics, 575:A90, March 2015 ADS
  • J. N. Girard, H. Garsden, J. L. Starck, S. Corbel, A. Woiselle, C. Tasse, J. P. McKean, and J. Bobin.
    Sparse representations and convex optimization as tools for LOFAR radio interferometric imaging. Journal
    of Instrumentation, 10:C8013, August 2015 ADS

Conferences Proceedings

  • M. Jiang, J. N. Girard, J. L. Starck, S. Corbel, and C. Tasse. Compressed sensing and radio interferometry.
    In Signal Processing Conference (EUSIPCO), 2015 23rd European, pages 1646-1650, August 2015 IEEE
  • M. Jiang, J. N. Girard, J.-L. Starck, S. Corbel, and C. Tasse. Interferometric Radio Transient Reconstruction
    in Compressed Sensing Framework. In F. Martins, S. Boissier, V. Buat, L. Cambresy, and P. Petit, editors,
    SF2A-2015: Proceedings of the Annual meeting of the French Society of Astronomy and Astrophysics. Eds.:
    F. Martins, S. Boissier, V. Buat, L. Cambresy, P. Petit, pp.231-236, pages 231-236, December 2015 (ADS)

To be published

  • J. N. Girard, M. Jiang, J. L. Starck, S. Corbel, Sparse spatio-temporal imaging of radio transients.

Acknowledgements: We acknowledge the financial support from the UnivEarthS Labex program of Sorbonne Paris Cité (ANR-10-LABX-0023 and ANR-11-IDEX-0005-02) and from the European Research Council grant SparseAstro (ERC-228261)

Results on simulated data

The following results are extracted from Garsden et al. 2015.

 

  • Photometry

Simulated LOFAR dataset containing a grid of 10 x 10 point sources over a field of 8°x8°.

bla

Fig 1 Output vs. input flux density of 100 point sources with Cotton-Schwab CLEAN (red) and SASIR (blue)

  • Effective angular resolution

- Two points sources (one at the phase center and one with a varying distance deltatheta from the phase center).

deltatheta=[30'' - 3'] by steps of 30''.

test

Fig. 2 Numerical test to show the super-resolution capability of SASIR (left) SASIR output image (center) Cotton-Schwab CLEAN components (right) CLEAN beam convolved image. The dash line marks the x coordinate of the phase center.

  • Extended emission (W50)

test

Fig. 3 Reconstruction comparison using CLEAN, MS-CLEAN and SASIR

 

Results on real LOFAR data

  • Reconstruction of Cygnus A

test

Fig. N  Comparison of Cygnus A reconstruction with CLEAN, MS-CLEAN and SASIR

 

test

Fig. N+1 (color map) LOFAR data at 150 MHz (contours) VLA at 325 MHz (Click the see the animated figure)

 

  • Other (to come)