Abstract
Radio astronomy is known for its very large telescope dishes, but is currently making a transition towards the use of large numbers of small elements. For example, the Low Frequency Array, commissioned in 2010, uses about 50 stations, each consisting of at least 96 low band antennas and 768 high band antennas. For the Square Kilometre Array, planned for 2024, the numbers will be even larger. 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 for a number of alternative image reconstruction techniques, such as a Weighted Least Squares approach. 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. The fact that the noise power at each antenna element may be different motivates the use of Factor Analysis, as a more appropriate alternative to the eigenvalue decomposition that is commonly used in array processing. Factor Analysis also proves to be very useful for interference mitigation. Interestingly, image reconstruction, calibration and interference mitigation are often intertwined in radio astronomy, turning this into an area with very challenging signal processing problems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
With abuse of notation, as m, n are not related to the time variables used earlier.
References
Ben-David, C., Leshem, A.: Parametric high resolution techniques for radio astronomical imaging. IEEE J. Sel. Topics in Signal Processing 2(5), 670–684 (2008)
Blahut, R.E.: Theory of remote image formation. Cambridge University Press (2004). ISBN 0521553733
Boonstra, A.J.: Radio frequency interference mitigation in radio astronomy. Ph.D. thesis, TU Delft, Dept. EEMCS (2005). ISBN 90-805434-3-8
Boonstra, A.J., van der Veen, A.J.: Gain calibration methods for radio telescope arrays. IEEE Trans. Signal Processing 51(1), 25–38 (2003)
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)
Borgiotti, G.B., Kaplan, L.J.: Superresolution of uncorrelated interference sources by using adaptive array techniques. IEEE Trans. Antennas Propagat. 27, 842845 (1979)
Briggs, D.S.: High fidelity deconvolution of moderately resolved sources. Ph.D. thesis, New Mexico Inst. of Mining and Technology, Socorro (NM) (1995). URL http://www.aoc.nrao.edu/dissertations/dbriggs/
Cornwell, T., Braun, R., Briggs, 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 (1999)
Cornwell, T.J.: Multiscale CLEAN deconvolution of radio synthesis images. IEEE J. Sel. Topics in Signal Processing 2(5), 793–801 (2008)
Cornwell, T.J., Wilkinson, P.N.: A new method for making maps with unstable radio interferometers. Mon. Not. R. Astron. Soc. 196, 1067–1086 (1981)
Cotton, W.D., Condon, J.J., Perley, R.A., Kassim, N., Lazio, J., Cohen, A.S., Lane, W., Erickson, W.C.: Beyond the isoplanatic patch in the VLA Low-frequency Sky Survey. In: Proc. SPIE, vol. 5489, pp. 180–189. Glasgow (2004)
Dewdney, P., Hall, P., Schilizzi, R., Lazio, T.: The square kilometre array. Proceedings of the IEEE 97(8), 1482–1496 (2009)
Fuhrmann, D.R.: Estimation of sensor gain and phase. IEEE Trans. Signal Processing 42(1), 77–87 (1994)
Hayes, M.H.: Statistical Digital Signal Processing and Modeling. John Wiley and Sons (1996)
Hogbom, J.A.: Aperture synthesis with non-regular distribution of interferometer baselines. Astronomy and Astrophysics Suppl. 15, 417–426 (1974)
Intema, H.T., van der Tol, S., Cotton, W.D., Cohen, A.S., van Bemmel, I.M., Rottgering, H.J.A.: 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)
Kay, S.M.: Fundamentals of Statistical Signal Processing. Volume II: Detection Theory. Prentice Hall PTR, Upper Saddle River, NJ (1998)
Lawley, D.N., Maxwell, A.E.: Factor Analysis as a Statistical Method. Butterworth & Co, London (1971)
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)
Leshem, A., van der Veen, A.J., Boonstra, A.J.: Multichannel interference mitigation techniques in radio astronomy. Astrophysical Journal Supplements 131(1), 355–374 (2000)
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)
Levanda, R., Leshem, A.: Image formation in radio astronomy. IEEE Signal Processing Magazine 27(1) (2010)
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)
Lonsdale, C., et al.: The Murchison Widefield Array: Design overview. Proceedings of the IEEE 97(8), 1497–1506 (2009)
Mallat, S., Zhang, Z.: Matching pursuits with time-frequency dictionaries. IEEE Tr. Signal Processing 41(12), 3397–3415 (1993)
Mardia, K.V., Kent, J.T., Bibby, J.M.: Multivariate Analysis. Academic Press (1979)
Marsh, K.A., Richardson, J.M.: The objective function implicit in the CLEAN algorithm. Astronomy and Astrophysics 182(1), 174–178 (1987)
Mitchell, D.A., Greenhill, L.J., Wayth, R.B., Sault, R.J., Lonsdale, C.J., Cappallo, R.J., Morales, M.F., Ord, S.M.: Real-time calibration of the Murchison Widefield Array. IEEE Journal of Selected Topics in Signal Processing 2(5), 707–717 (2008)
Moon, T.K., Stirling, W.C.: Mathematical Methods and Algorithms for Signal Processing. Prentice Hall (2000). ISBN 0201361868
Noordam, J.E.: Generalized self-calibration for LOFAR. In: XXVIIth General Assembly of the International Union of Radio Science (URSI). Maastricht (The Netherlands) (2002)
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)
Pearson, T.J., Readhead, A.C.S.: Image formation by self-calibration in radio astronomy. Annual Rev. Astronomy and Astrophysics 22, 97–130 (1984)
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)
Raza, J., Boonstra, A.J., van der Veen, A.J.: Spatial filtering of RF interference in radio astronomy. IEEE Signal Processing Letters 9(2), 64–67 (2002)
Schwardt, L.C.: Compressed sensing imaging with the KAT-7 array. In: Int. Conf. on Electromagnetics in Adv. Appl. (ICEAA), pp. 690–693. IEEE (2012)
Seghouane, A.K.: An iterative projections algorithm for ML factor analysis. In: IEEE Workshop on Machine Learning for Signal Processing (MLSP08), pp. 333–338 (2008)
Thompson, A.R., Moran, J.M., Swenson, G.W.: Interferometry and Synthesis in Radio Astronomy, 2nd edn. Wiley, New York (2001)
van der Tol, S.: Bayesian estimation for ionospheric calibration in radio astronomy. Ph.D. thesis, TU Delft, Dept. EEMCS (2009)
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)
van der Tol, S., van der Veen, A.J.: Performance analysis of spatial filtering of RF interference in radio astronomy. IEEE Transactions on Signal Processing 53(3), 896–910 (2005)
van der Veen, A.J., Leshem, A., Boonstra, A.J.: Array signal processing for radio astronomy. Experimental Astronomy 17(1–3), 231–249 (2004)
de Vos, M., Gunst, A., Nijboer, R.: The LOFAR telescope: System architecture and signal processing. Proceedings of the IEEE 97(8), 1431–1437 (2009)
Wiaux, Y., Jacques, L., Puy, G., Scaife, A., Vandergheynst, P.: Compressed sensing imaging techniques for radio interferometry. Monthly Notices of the Royal Astronomical Society 395, 17331742 (2009)
Wijnholds, S.J.: Fish-eye observing with phased array radio telescopes. Ph.D. thesis, TU Delft, Dept. EEMCS (2010). ISBN 978-90-9025180-6
Wijnholds, S.J., Boonstra, 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)
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)
Wijnholds, S.J., van der Veen, A.J.: Fundamental imaging limits of radio telescope arrays. IEEE J. Sel. Topics in Signal Processing 2(5), 613–623 (2008)
Wijnholds, S.J., van der Veen, A.J.: Multisource self-calibration for sensor arrays. IEEE Tr. Signal Processing 57(9), 3512–3522 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
van der Veen, AJ., Wijnholds, S.J. (2013). Signal Processing Tools for Radio Astronomy. In: Bhattacharyya, S., Deprettere, E., Leupers, R., Takala, J. (eds) Handbook of Signal Processing Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6859-2_14
Download citation
DOI: https://doi.org/10.1007/978-1-4614-6859-2_14
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-6858-5
Online ISBN: 978-1-4614-6859-2
eBook Packages: EngineeringEngineering (R0)