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21 July 2010 Spectral regularization and sparse representation bases for interferometric imaging
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Abstract
This paper presents some methods being developped for relaxing the underdetermination of the image reconstruction from interferometric data. We consider, in a first part, the advantages of using spectro-differential data for having a more accurate and complete set of complexe visibilities. We formulate some regularization criteria along the spectral dimension, in order to express some prior knowledge on the correlation between the brightness distributions in different wavelength. These spectral prior terms are inspired by, and combinable with, some spatial regularization functions already in use in existing Image Reconstruction sofwares. We also show that the interferometric image reconstruction problem can benefit from being reformulated as a sparse approximation problem in redundant dictionaries. The dictionary is composed from union of representation bases, whose atoms correspond to geometric features of the image. Different bases (e.g. impulsions, wavelets, discrete cosine transform) correspond to different features. The sparse approximation approach consists in selecting the geometrical features that best explain the interferometric data, by imposing that only a few such features should be necessary to reconstruct the image. Simulations showing images reconstructed using this method are presented.
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M. Vannier, D. Mary, F. Millour, R. G. Petrov, S. Bourguignon, and C. Theys "Spectral regularization and sparse representation bases for interferometric imaging", Proc. SPIE 7734, Optical and Infrared Interferometry II, 77342J (21 July 2010); https://doi.org/10.1117/12.858098
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