Compressive sensing of streams of pulses

Chinmay Hegde, Richard G. Baraniuk

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    Compressive Sensing (CS) has developed as an enticing alternative to the traditional process of signal acquisition. For a length-N signal with sparsity K, merely M = O(K log N) ≪ N random linear projections (measurements) can be used for robust reconstruction in polynomial time. Sparsity is a powerful and simple signal model; yet, richer models that impose additional structure on the sparse nonzeros of a signal have been studied theoretically and empirically from the CS perspective. In this work, we introduce and study a sparse signal model for streams of pulses, i.e., S-sparse signals convolved with an unknown F-sparse impulse response. Our contributions are threefold: (i) we geometrically model this set of signals as an infinite union of subspaces; (ii) we derive a sufficient number of random measurements M required to preserve the metric information of this set. In particular this number is linear merely in the number of degrees of freedom of the signal S + F, and sublinear in the sparsity K = SF; (iii) we develop an algorithm that performs recovery of the signal from M measurements and analyze its performance under noise and model mismatch. Numerical experiments on synthetic and real data demonstrate the utility of our proposed theory and algorithm. Our method is amenable to diverse applications such as the high-resolution sampling of neuronal recordings and ultra-wideband (UWB) signals.

    Original languageEnglish (US)
    Title of host publication2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
    Pages44-51
    Number of pages8
    DOIs
    StatePublished - 2009
    Event2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 - Monticello, IL, United States
    Duration: Sep 30 2009Oct 2 2009

    Publication series

    Name2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009

    Conference

    Conference2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
    CountryUnited States
    CityMonticello, IL
    Period9/30/0910/2/09

    ASJC Scopus subject areas

    • Computer Science(all)
    • Control and Systems Engineering
    • Communication

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  • Cite this

    Hegde, C., & Baraniuk, R. G. (2009). Compressive sensing of streams of pulses. In 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 (pp. 44-51). [5394833] (2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009). https://doi.org/10.1109/ALLERTON.2009.5394833