Advertisement

Signal Processing for Radio Astronomy

  • Alle-Jan van der Veen
  • Stefan J. Wijnholds
  • Ahmad Mouri Sardarabadi
Chapter

Abstract

Radio astronomy is known for its very large telescope dishes but is currently making a transition towards the use of a large number of small antennas. For example, the Low Frequency Array, commissioned in 2010, uses about 50 stations each consisting of 96 low band antennas and 768 or 1536 high band antennas. The low-frequency receiving system for the future Square Kilometre Array is envisaged to initially consist of over 131,000 receiving elements and to be expanded later. These instruments pose interesting array signal processing challenges. To present some aspects, we start by describing how the measured correlation data is traditionally converted into an image, and translate this into an array signal processing framework. This paves the way to describe self-calibration and image reconstruction as estimation problems. Self-calibration of the instrument is required to handle instrumental effects such as the unknown, possibly direction dependent, response of the receiving elements, as well a unknown propagation conditions through the Earth’s troposphere and ionosphere. Array signal processing techniques seem well suited to handle these challenges. Interestingly, image reconstruction, calibration and interference mitigation are often intertwined in radio astronomy, turning this into an area with very challenging signal processing problems.

References

  1. 1.
    Barrett, R., Berry, M., Chan, T.F., Demmel, J., Donato, J., Dongarra, J., Eijkhout, V., Pozo, R., Romine, C., der Vorst, H.V.: Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd Edition. SIAM, Philadelphia, PA (1994)CrossRefGoogle Scholar
  2. 2.
    Bartholomew, D.J., Knott, M., Moustaki, I.: Latent Variable Models and Factor Analysis: A Unified Approach. John Wiley and Sons (2011)Google Scholar
  3. 3.
    Ben-David, C., Leshem, A.: Parametric high resolution techniques for radio astronomical imaging. IEEE Journal of Selected Topics in Signal Processing 2(5), 670–684 (2008)CrossRefGoogle Scholar
  4. 4.
    Blahut, R.E.: Theory of remote image formation. Cambridge University Press (2004). ISBN 0521553733Google Scholar
  5. 5.
    Boonstra, A.J.: Radio frequency interference mitigation in radio astronomy. Ph.D. thesis, TU Delft, Dept. EEMCS (2005). ISBN 90-805434-3-8Google Scholar
  6. 6.
    Boonstra, A.J., van der Veen, A.J.: Gain calibration methods for radio telescope arrays. IEEE Transactions on Signal Processing 51(1), 25–38 (2003)CrossRefGoogle Scholar
  7. 7.
    Boonstra, A.J., Wijnholds, S.J., van der Tol, S., Jeffs, B.: Calibration, sensitivity and RFI mitigation requirements for LOFAR. In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Philadelphia (Penn.), USA (2005)Google Scholar
  8. 8.
    Borgiotti, G.B., Kaplan, L.J.: Superresolution of uncorrelated interference sources by using adaptive array techniques. IEEE Transactions on Antennas and Propagation 27, 842–845 (1979)CrossRefGoogle Scholar
  9. 9.
    Bridle, A.H., Schwab, F.R.: Bandwidth and Time-Average Smearing. In: G.B. Taylor, C.L. Carilli, R.A. Perley (eds.) Synthesis Imaging in Radio Astronomy II, Astronomical Society of the Pacific Conference Series, vol. 180, chap. 18, pp. 371–382. Astronomical Society of the Pacific (1999)Google Scholar
  10. 10.
    Briggs, D.S.: High fidelity deconvolution of moderately resolved sources. Ph.D. thesis, New Mexico Inst. of Mining and Technology, Socorro (NM) (1995)Google Scholar
  11. 11.
    Carrillo, R.E., McEwen, J.D., Wiaux, Y.: Sparsity averaging reweighted analysis (SARA): a novel algorithm for radio-interferometric imaging. Monthly Notices of the Royal Astronomical Society 426(2), 1223–1234 (2012)CrossRefGoogle Scholar
  12. 12.
    Carrillo, R.E., McEwen, J.D., Wiaux, Y.: PURIFY: a new approach to radio-interferometric imaging. Monthly Notices of the Royal Astronomical Society 439(4), 3591–3604 (2014)CrossRefGoogle Scholar
  13. 13.
    Cornwell, T., Braun, R., Brigss, D.S.: Deconvolution. In: G.B. Taylor, C.L. Carilli, R.A. Perley (eds.) Synthesis Imaging in Radio Astronomy II, Astronomical Society of the Pacific Conference Series, vol. 180, pp. 151–170. Astronomical Society of the Pacific (1999)Google Scholar
  14. 14.
    Cornwell, T.J.: Multiscale CLEAN deconvolution of radio synthesis images. IEEE Journal of Selected Topics in Signal Processing 2(5), 793–801 (2008)CrossRefGoogle Scholar
  15. 15.
    Cornwell, T.J., Wilkinson, P.N.: A new method for making maps with unstable radio interferometers. Monthly Notices of the Royal Astronomical Society 196, 1067–1086 (1981)CrossRefGoogle Scholar
  16. 16.
    Cotton, W.D., et al.: Beyond the isoplanatic patch in the VLA Low-frequency Sky Survey. In: Proceedings of the SPIE, vol. 5489, pp. 180–189. Glasgow (2004)Google Scholar
  17. 17.
    Dewdney, P.E., Braun, R.: SKA1-low configuration coordinates - complete set. Tech. Rep. SKA-TEL-SKO-0000422, SKA Office, Manchester (UK) (2016)Google Scholar
  18. 18.
    Dewdney, P.E., Hall, P.J., Schilizzi, R.T., Lazio, T.J.L.W.: The square kilometre array. Proceedings of the IEEE 97(8), 1482–1496 (2009)CrossRefGoogle Scholar
  19. 19.
    Duijndam, A.J.W., Schonewille, M.A.: Nonuniform fast Fourier transform. Geophysics 64(2), 539–551 (1999)CrossRefGoogle Scholar
  20. 20.
    Foucart, S., Koslicki, D.: Sparse recovery by means of nonnegative least squares. IEEE Signal Processing Letters 21(4), 498–502 (2014)CrossRefGoogle Scholar
  21. 21.
    Frieden, B.: Restoring with maximum likelihood and maximum entropy. Journal of the Optical Society of America 62, 511–518 (1972)CrossRefGoogle Scholar
  22. 22.
    Fuhrmann, D.R.: Estimation of sensor gain and phase. IEEE Transactions on Signal Processing 42(1), 77–87 (1994)CrossRefGoogle Scholar
  23. 23.
    Garsden, H., et al.: LOFAR sparse image reconstruction. Astronomy & Astrophysics 575(A90), 1–18 (2015)Google Scholar
  24. 24.
    van Haarlem, M.P., et al.: LOFAR: The low frequency array. Astronomy & Astrophysics 556(A2), 1–53 (2013)Google Scholar
  25. 25.
    Hamaker, J.P.: Understanding radio polarimetry - iv. the full-coherency analogue of scalar self-calibration: Self-alignment, dynamic range and polarimetric fidelity. Astronomy & Astrophysics Supplement 143(3), 515–534 (2000)CrossRefGoogle Scholar
  26. 26.
    Hayes, M.H.: Statistical Digital Signal Processing and Modeling. John Wiley and Sons (1996)Google Scholar
  27. 27.
    Hogbom, J.A.: Aperture synthesis with non-regular distribution of interferometer baselines. Astronomy and Astrophysics Suppl. 15, 417–426 (1974)Google Scholar
  28. 28.
    Intema, H.T., et al.: Ionospheric calibration of low frequency radio interferometric observations using the peeling scheme. I. Method description and first results. Astronomy & Astrophysics 501(3), 1185–1205 (2009)Google Scholar
  29. 29.
    Jongerius, R.: Exascale computer system design: The square kilometre array. Ph.D. thesis, Eindhoven University of Technology (2016). ISBN 978-90-386-4136-2Google Scholar
  30. 30.
    Jongerius, R., Wijnholds, S., Nijboer, R., Corporaal, H.: An end-to-end computing model for the square kilometre array. IEEE Computer 47(9), 48–54 (2014)CrossRefGoogle Scholar
  31. 31.
    Kazemi, S., Yatawatta, S., Zaroubi, S., Lampropoulos, P., de Bruyn, A.G., Koopmans, L.V.E., Noordam, J.: Radio interferometric calibration using the sage algorithm. Monthly Notices of the Royal Astronomical Society 414(2), 1656 (2011)CrossRefGoogle Scholar
  32. 32.
    Lawley, D.N., Maxwell, A.E.: Factor Analysis as a Statistical Method. Butterworth & Co, London (1971)zbMATHGoogle Scholar
  33. 33.
    Leshem, A., van der Veen, A.J.: Radio-astronomical imaging in the presence of strong radio interference. IEEE Transactions on Information Theory 46(5), 1730–1747 (2000)CrossRefGoogle Scholar
  34. 34.
    Leshem, A., van der Veen A. J., Boonstra, A.J.: Multichannel interference mitigation technique in radio astronomy. Astrophysical Journal Supplements 131(1), 355–374 (2000)CrossRefGoogle Scholar
  35. 35.
    Levanda, R., Leshem, A.: Radio astronomical image formation using sparse reconstruction techniques. In: IEEE 25th convention of Elec. Electron. Eng. in Israel (IEEEI 2008), pp. 716–720 (2008)Google Scholar
  36. 36.
    Levanda, R., Leshem, A.: Synthetic aperture radio telescopes. IEEE Signal Processing Magazine 27(1), 14–29 (2010)CrossRefGoogle Scholar
  37. 37.
    Li, F., Cornwell, T.J., de Hoog, F.: The application of compressive sampling to radio astronomy; I deconvolution. Astronomy and Astrophysics 528(A31), 1–10 (2011)Google Scholar
  38. 38.
    Lonsdale, C., et al.: The Murchison Widefield Array: Design overview. Proceedings of the IEEE 97(8), 1497–1506 (2009)CrossRefGoogle Scholar
  39. 39.
    Mallat, S.G., Zhang, Z.: Matching pursuits with time-frequency dictionaries. IEEE Transactions on Signal Processing 41(12), 3397–3415 (1993)CrossRefGoogle Scholar
  40. 40.
    Mardia, K.V., Kent, J.T., Bibby, J.M.: Multivariate Analysis. Academic Press, New York (1979)zbMATHGoogle Scholar
  41. 41.
    Marsh, K.A., Richardson, J.M.: The objective function implicit in the CLEAN algorithm. Astronomy and Astrophysics 182(1), 174–178 (1987)Google Scholar
  42. 42.
    Mitchell, D.A., et al.: Real-time calibration of the Murchison Widefield Array. IEEE Journal of Selected Topics in Signal Processing 2(5), 707–717 (2008)CrossRefGoogle Scholar
  43. 43.
    Moon, T.K., Stirling, W.C.: Mathematical Methods and Algorithms for Signal Processing. Prentice Hall (2000). ISBN 0201361868Google Scholar
  44. 44.
    Mouri Sardarabadi, A.: Covariance matching techniques for radio astronomy calibration and imaging. Ph.D. thesis, TU Delft, Dept. EEMCS (2016)Google Scholar
  45. 45.
    Mouri Sardarabadi, A., Leshem, A., van der Veen, A.J.: Radio astronomical image formation using constrained least squares and Krylov subspaces. Astronomy & Astrophysics 588, A95 (2016)CrossRefGoogle Scholar
  46. 46.
    Noordam, J.E.: Generalized self-calibration for LOFAR. In: XXVIIth General Assembly of the International Union of Radio Science (URSI). Maastricht (The Netherlands) (2002)Google Scholar
  47. 47.
    Ottersten, B., Stoica, P., Roy, R.: Covariance matching estimation techniques for array signal processing applications. Digital Signal Processing, A Review Journal 8, 185–210 (1998)CrossRefGoogle Scholar
  48. 48.
    Pearson, T.J., Readhead, A.C.S.: Image formation by self-calibration in radio astronomy. Annual Review of Astronomy and Astrophysics 22, 97–130 (1984)CrossRefGoogle Scholar
  49. 49.
    Perley, R.A., Schwab, F.R., Bridle, A.H.: Synthesis Imaging in Radio Astronomy, Astronomical Society of the Pacific Conference Series, vol. 6. BookCrafters Inc. (1994)Google Scholar
  50. 50.
    Salvini, S., Wijnholds, S.J.: Fast gain calibration in radio astronomy using alternating direction implicit methods: Analysis and applications. Astronomy & Astrophysics 571(A97), 1–14 (2014)Google Scholar
  51. 51.
    Schwardt, L.C.: Compressed sensing imaging with the KAT-7 array. In: International Conference on Electromagnetics in Advanced Applications (ICEAA), pp. 690–693 (2012)Google Scholar
  52. 52.
    Thompson, A.R., Moran, J.M., Swenson, G.W.: Interferometry and Synthesis in Radio Astronomy, 2nd edn. Wiley, New York (2001)CrossRefGoogle Scholar
  53. 53.
    Tingay, S.J., et al.: The Murchison widefield array: The square kilometre array precursor at low radio frequencies. Publications of the Astronomical Society of Australia 30(7) (2013)Google Scholar
  54. 54.
    van der Tol, S.: Bayesian estimation for ionospheric calibration in radio astronomy. Ph.D. thesis, TU Delft, Dept. EEMCS (2009)Google Scholar
  55. 55.
    van der Tol, S., Jeffs, B.D., van der Veen, A.J.: Self-calibration for the LOFAR radio astronomical array. IEEE Transactions on Signal Processing 55(9), 4497–4510 (2007)MathSciNetCrossRefGoogle Scholar
  56. 56.
    Turner, W.: SKA phase 1 system requirements specification. Tech. Rep. SKA-TEL-SKO-0000008, SKA Office, Manchester (UK) (2016)Google Scholar
  57. 57.
    van der Veen, A.J., Leshem, A., Boonstra, A.J.: Array signal processing for radio astronomy. Experimental Astronomy 17(1–3), 231–249 (2004)CrossRefGoogle Scholar
  58. 58.
    de Vos, M., Gunst, A., Nijboer, R.: The LOFAR telescope: System architecture and signal processing. Proceedings of the IEEE 97(8), 1431–1437 (2009)CrossRefGoogle Scholar
  59. 59.
    Wiaux, Y., Jacques, L., Puy, G., Scaife, A.M.M., Vandergheynst, P.: Compressed sensing imaging techniques for radio interferometry. Monthly Notices of the Royal Astronomical Society 395, 1733–1742 (2009)CrossRefGoogle Scholar
  60. 60.
    Wijnholds, S.J.: Fish-eye observing with phased array radio telescopes. Ph.D. thesis, TU Delft, Dept. EEMCS (2010). ISBN 978-90-9025180-6Google Scholar
  61. 61.
    Wijnholds, S.J., Boosntra, A.J.: A multisource calibration method for phased array telescopes. In: Fourth IEEE Workshop on Sensor Array and Multi-channel Processing (SAM). Waltham (Mass.), USA (2006)Google Scholar
  62. 62.
    Wijnholds, S.J., van der Tol, S., Nijboer, R., van der Veen, A.J.: Calibration challenges for the next generation of radio telescopes. IEEE Signal Processing Magazine 27(1), 32–42 (2010)CrossRefGoogle Scholar
  63. 63.
    Wijnholds, S.J., van der Veen, A.J.: Fundamental imaging limits of radio telescope arrays. IEEE Journal of Selected Topics in Signal Processing 2(5), 613–623 (2008)CrossRefGoogle Scholar
  64. 64.
    Wijnholds, S.J., van der Veen, A.J.: Multisource self-calibration for sensor arrays. IEEE Transactions on Signal Processing 57(9), 3512–3522 (2009)MathSciNetCrossRefGoogle Scholar
  65. 65.
    Wise, M.W., Rafferty, D.A., McKean, J.P.: Feedback at the working surface: A joint X-ray and low-frequency radio spectral study of the Cocoon Shock in Cygnus A. In: 13th Meeting of the American Astronomical Society’s High Energy Astrophysics Division (HEAD), pp. 88–89 (2013)Google Scholar
  66. 66.
    Yatawatta, S.: Distributed radio interferometric calibration. Monthly Notices of the Royal Astronomical Society 449(4), 4506 (2015)CrossRefGoogle Scholar
  67. 67.
    Zatman, M.: How narrow is narrowband. IEE Proc. Radar, Sonar and Navig. 145(2), 85–91 (1998)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Alle-Jan van der Veen
    • 1
  • Stefan J. Wijnholds
    • 2
  • Ahmad Mouri Sardarabadi
    • 3
  1. 1.TU Delft, Faculty of EEMCSDelftThe Netherlands
  2. 2.Netherlands Institute for Radio Astronomy (ASTRON)DwingelooThe Netherlands
  3. 3.University of Groningen, Kapteyn Astronomical InstituteGroningenThe Netherlands

Personalised recommendations