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Rapport (Rapport De Recherche) Année : 2011

Tightening information theoretic constraints on noisy compressive sensing

Résumé

Recently, information-theoretic barriers of compressive sensing (CS) have been studied by several authors. Sarvotham et al. derived a bound on the number of measurements m using the source-channel separation theorem. Similar bounds were derived by Wainwright and Aeron et al. using Fano’s inequality and the source-channel separation theorem. In these papers, the noisy CS is modeled as a communication system and an upper bound on the system capacity is used to derive the bounds. However, for the derivation of these bounds, the signal source memory was not considered. Furthermore, the derived bounds only exhibits a minor dependence on m when m is large. In this paper, we derive tighter bounds on m by looking at the information rate (IR) of noisy CS. We derive a lower bound on m based on an upper bound on the IR for wide-sense stationary sparse signals and Gaussian sampling matrices, taking into account the memory of the sparse signal. We also consider the expected value of the IR for the ensemble of Gaussian sampling matrices and derive a sufficient condition on m to recover the signal.
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Dates et versions

hal-00724800 , version 1 (22-08-2012)

Identifiants

  • HAL Id : hal-00724800 , version 1

Citer

Behrooz Kamary Aliabadi. Tightening information theoretic constraints on noisy compressive sensing. [Rapport de recherche] Dépt. Electronique (Institut Mines-Télécom-Télécom Bretagne-UEB); Laboratoire en sciences et technologies de l'information, de la communication et de la connaissance (UMR CNRS 6285 - Télécom Bretagne - Université de Bretagne Occidentale - Université de Bretagne Sud); Pôle de Recherche Avancée en Communications (Institut Mines-Télécom-Télécom Bretagne-UEB). 2011, pp.12. ⟨hal-00724800⟩
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