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Spread spectrum for imaging techniques in radio interferometry

Wiaux, Y. ; Puy, G. ; Boursier, Y. ; Vandergheynst, P.

In: Monthly Notices of the Royal Astronomical Society, 2009, vol. 400, no. 2, p. 1029-1038

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    Title
    • Spread spectrum for imaging techniques in radio interferometry
    Author
    • Wiaux, Y.. Institute of Electrical Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
    • Puy, G.. Institute of Electrical Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
    • Boursier, Y.. Institute of Electrical Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
    • Vandergheynst, P.. Institute of Electrical Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
    Document Type
    • Postprint
    OAI-PMH Identifier
    • oai:doc.rero.ch:297724
    Summary
    We consider the probe of astrophysical signals through radio interferometers with a small field of view and baselines with a non-negligible and constant component in the pointing direction. In this context, the visibilities measured essentially identify with a noisy and incomplete Fourier coverage of the product of the planar signals with a linear chirp modulation. In light of the recent theory of compressed sensing and in the perspective of defining the best possible imaging techniques for sparse signals, we analyse the related spread spectrum phenomenon and suggest its universality relative to the sparsity dictionary. Our results rely both on theoretical considerations related to the mutual coherence between the sparsity and sensing dictionaries and on numerical simulations