Compressive sampling of pulse trains: spread the spectrum !

Farid Movahedi Naini (1) , Rémi Gribonval (2) , Laurent Jacques (1, 3) , Pierre Vandergheynst (1)

1 LTS2 - EPFL
2 METISS - Speech and sound data modeling and processing
3 TELE - Laboratoire de Télécommunications et Télédétection [Louvain]

In this paper we consider the problem of sampling far below the Nyquist rate signals that are sparse linear superpositions of shifts of a known, potentially wide-band, pulse. This signal model is key for applications such as Ultra Wide Band (UWB) communications or neural signal processing. Following the recently proposed Compressed Sensing methodology, we study several acquisition strategies and show that the approximations recovered via l1 minimization are greatly enhanced if one uses Spread Spectrum modulation prior to applying random Fourier measurements. We complement our experiments with a discussion of possible hardware implementation of our technique.

Mots clés: Compressive sampling; compressed sensing; pulse trains; Ultra Wide Band; shift-invariant dictionary

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Farid Movahedi Naini, Rémi Gribonval, Laurent Jacques, Pierre Vandergheynst. Compressive sampling of pulse trains: spread the spectrum !. ICASSP 2009, Apr 2009, Taipei city, Taiwan. pp. 2877-2880, ⟨10.1109/ICASSP.2009.4960224⟩. ⟨hal-00481954⟩