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A Simple Recovery Framework for Signals with Time-Varying Sparse Support

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Advances in Data Science

Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 26))

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Abstract

Sparse recovery methods have been developed to solve multiple measurement vector (MMV) problems. These methods seek to reconstruct a collection of sparse signals from a small number of linear measurements, exploiting not only the sparsity but also certain correlations between the signals. Typically, the assumption is that the collection of signals shares a common joint support, allowing the problem to be solved more efficiently (or with fewer measurements) than solving many individual, single measurement vector (SMV) subproblems. Here, we relax this stringent assumption so that the signals may exhibit a changing support, a behavior that is much more prominent in applications. We propose a simple windowed framework that can utilize any traditional MMV method as a subroutine, and exhibits improved recovery when the MMV method incorporates prior information on signal support. In doing so, our framework enjoys natural extensions of existing theory and performance of such MMV methods. We demonstrate the value of this approach by using different MMV methods as subroutines within the proposed framework and applying it to both synthetic and real-world data.

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Acknowledgements

Shuang Li was supported by NSF CAREER CCF #1149225. Deanna Needell was partially supported by NSF CAREER DMS #1348721, NSF DMS #2011140, and NSF BIGDATA #1740325. Jing Qin was supported by the NSF DMS #1941197.

Author information

Authors and Affiliations

  1. Spiceworks, Austin, TX, USA

    Natalie Durgin

  2. Wofford College, Spartanburg, SC, USA

    Rachel Grotheer

  3. Yale University, New Haven, CT, USA

    Chenxi Huang

  4. University of California, Los Angeles, CA, USA

    Shuang Li & Deanna Needell

  5. University of California, Irvine, CA, USA

    Anna Ma

  6. University of Kentucky, Lexington, KY, USA

    Jing Qin

Authors
  1. Natalie Durgin
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  2. Rachel Grotheer
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  3. Chenxi Huang
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  4. Shuang Li
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  5. Anna Ma
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  6. Deanna Needell
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  7. Jing Qin
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Corresponding author

Correspondence to Rachel Grotheer .

Editor information

Editors and Affiliations

  1. Intel (United States), Hermosa Beach, CA, USA

    Ilke Demir

  2. School of Natural Sciences & Mathematics, The University of Texas at Dallas, Richardson, TX, USA

    Yifei Lou

  3. Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada

    Xu Wang

  4. Fakultät für Maschinenbau, Helmut Schmidt University, Hamburg, Germany

    Kathrin Welker

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Durgin, N. et al. (2021). A Simple Recovery Framework for Signals with Time-Varying Sparse Support. In: Demir, I., Lou, Y., Wang, X., Welker, K. (eds) Advances in Data Science. Association for Women in Mathematics Series, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-030-79891-8_9

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