Rank Awareness in Joint Sparse Recovery

Abstract : This paper revisits the sparse multiple measurement vector (MMV) problem, where the aim is to recover a set of jointly sparse multichannel vectors from incomplete measurements. This problem is an extension of single channel sparse recovery, which lies at the heart of compressed sensing. Inspired by the links to array signal processing, a new family of MMV algorithms is considered that highlight the role of rank in determining the difficulty of the MMV recovery problem. The simplest such method is a discrete version of MUSIC which is guaranteed to recover the sparse vectors in the full rank MMV setting, under mild conditions. This idea is extended to a rank aware pursuit algorithm that naturally reduces to Order Recursive Matching Pursuit (ORMP) in the single measurement case while also providing guaranteed recovery in the full rank setting. In contrast, popular MMV methods such as Simultaneous Orthogonal Matching Pursuit (SOMP) and mixed norm minimization techniques are shown to be rank blind in terms of worst case analysis. Numerical simulations demonstrate that the rank aware techniques are significantly better than existing methods in dealing with multiple measurements.
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Article dans une revue
Information Theory, IEEE Transactions on, IEEE Signal Processing Society, 2012, 58 (2), pp.1135 -1146. 〈10.1109/TIT.2011.2173722〉
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https://hal.inria.fr/hal-00706058
Contributeur : Rémi Gribonval <>
Soumis le : vendredi 8 juin 2012 - 18:03:14
Dernière modification le : dimanche 31 décembre 2017 - 09:44:02

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Mike Davies, Yonina Eldar. Rank Awareness in Joint Sparse Recovery. Information Theory, IEEE Transactions on, IEEE Signal Processing Society, 2012, 58 (2), pp.1135 -1146. 〈10.1109/TIT.2011.2173722〉. 〈hal-00706058〉

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