Compressive sensing of a superposition of pulses

Chinmay Hegde, Richard G. Baraniuk

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

    Abstract

    Compressive Sensing (CS) has emerged as a potentially viable technique for the efficient acquisition of high-resolution signals and images that have a sparse representation in a fixed basis. The number of linear measurements M required for robust polynomial time recovery of S-sparse signals of length N can be shown to be proportional to S logN. However, in many real-life imaging applications, the original S-sparse image may be blurred by an unknown point spread function defined over a domain Ω; this multiplies the apparent sparsity of the image, as well as the corresponding acquisition cost, by a factor of |Ω|. In this paper, we propose a new CS recovery algorithm for such images that can be modeled as a sparse superposition of pulses. Our method can be used to infer both the shape of the two-dimensional pulse and the locations and amplitudes of the pulses. Our main theoretical result shows that our reconstruction method requires merely M = O(S + |Ω|) linear measurements, so that M is sublinear in the overall image sparsity S|Ω|. Experiments with real world data demonstrate that our method provides considerable gains over standard state-of-the-art compressive sensing techniques in terms of numbers of measurements required for stable recovery.

    Original languageEnglish (US)
    Title of host publication2010 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2010 - Proceedings
    Pages3934-3937
    Number of pages4
    DOIs
    StatePublished - 2010
    Event2010 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2010 - Dallas, TX, United States
    Duration: Mar 14 2010Mar 19 2010

    Publication series

    NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
    ISSN (Print)1520-6149

    Other

    Other2010 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2010
    CountryUnited States
    CityDallas, TX
    Period3/14/103/19/10

    Keywords

    • Blind deconvolution
    • Compressive sensing
    • Sparse approximation

    ASJC Scopus subject areas

    • Software
    • Signal Processing
    • Electrical and Electronic Engineering

    Fingerprint Dive into the research topics of 'Compressive sensing of a superposition of pulses'. Together they form a unique fingerprint.

  • Cite this

    Hegde, C., & Baraniuk, R. G. (2010). Compressive sensing of a superposition of pulses. In 2010 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2010 - Proceedings (pp. 3934-3937). [5495801] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). https://doi.org/10.1109/ICASSP.2010.5495801