Sparse Randomized Kaczmarz for Support Recovery of Jointly Sparse Corrupted Multiple Measurement Vectors

Natalie Durgin; Rachel Grotheer; Chenxi Huang; Shuang Li; Anna Ma; Deanna Needell; Jing Qin

doi:10.1007/978-3-030-11566-1_1

Sparse Randomized Kaczmarz for Support Recovery of Jointly Sparse Corrupted Multiple Measurement Vectors

Natalie Durgin, Rachel Grotheer, Chenxi Huang, Shuang Li, Anna Ma, Deanna Needell, Jing Qin

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

3 Scopus citations

Abstract

While single measurement vector (SMV) models have been widely studied in signal processing, there is a surging interest in addressing the multiple measurement vectors (MMV) problem. In the MMV setting, more than one measurement vector is available and the multiple signals to be recovered share some commonalities such as a common support. Applications in which MMV is a naturally occurring phenomenon include online streaming, medical imaging, and video recovery. This work presents a stochastic iterative algorithm for the support recovery of jointly sparse corrupted MMV. We present a variant of the sparse randomized Kaczmarz algorithm for corrupted MMV and compare our proposed method with an existing Kaczmarz type algorithm for MMV problems. We also showcase the usefulness of our approach in the online (streaming) setting and provide empirical evidence that suggests the robustness of the proposed method to the number of corruptions and the distribution from which the corruptions are drawn.

Original language	English
Title of host publication	Association for Women in Mathematics Series
Pages	1-14
Number of pages	14
DOIs	https://doi.org/10.1007/978-3-030-11566-1_1
State	Published - 2019

Publication series

Name	Association for Women in Mathematics Series
Volume	17
ISSN (Print)	2364-5733
ISSN (Electronic)	2364-5741

Bibliographical note

Publisher Copyright:
© 2019, The Author(s) and the Association for Women in Mathematics.

Funding

Acknowledgements The initial research for this effort was conducted at the Research Collaboration Workshop for Women in Data Science and Mathematics, July 17–21, held at ICERM. Funding for the workshop was provided by ICERM, AWM, and DIMACS (NSF Grant No. CCF-1144502). SL was supported by NSF CAREER Grant No. CCF−1149225. DN was partially supported by the Alfred P. Sloan Foundation, NSF CAREER #1348721, and NSF BIGDATA #1740325. JQ was supported by NSF DMS-1818374.

Funders	Funder number
ICERM
National Science Foundation Arctic Social Science Program	CCF-1144502, 1149225
Alfred P Sloan Foundation	DMS-1818374, 1740325, 1348721
Association for Women in Mathematics

ASJC Scopus subject areas

Gender Studies
General Mathematics

Access to Document

10.1007/978-3-030-11566-1_1

Cite this

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abstract = "While single measurement vector (SMV) models have been widely studied in signal processing, there is a surging interest in addressing the multiple measurement vectors (MMV) problem. In the MMV setting, more than one measurement vector is available and the multiple signals to be recovered share some commonalities such as a common support. Applications in which MMV is a naturally occurring phenomenon include online streaming, medical imaging, and video recovery. This work presents a stochastic iterative algorithm for the support recovery of jointly sparse corrupted MMV. We present a variant of the sparse randomized Kaczmarz algorithm for corrupted MMV and compare our proposed method with an existing Kaczmarz type algorithm for MMV problems. We also showcase the usefulness of our approach in the online (streaming) setting and provide empirical evidence that suggests the robustness of the proposed method to the number of corruptions and the distribution from which the corruptions are drawn.",

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AU - Grotheer, Rachel

AU - Huang, Chenxi

AU - Li, Shuang

AU - Ma, Anna

AU - Needell, Deanna

AU - Qin, Jing

PY - 2019

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Sparse Randomized Kaczmarz for Support Recovery of Jointly Sparse Corrupted Multiple Measurement Vectors

Abstract

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Bibliographical note

Funding

ASJC Scopus subject areas

Access to Document

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