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Greedy Block Coordinate Descent under Restricted Isometry Property

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Abstract

Exact support recovery of K-group sparse matrices X from the multiple measurement vectors (MMV) model Y = A X arises from many applications and has been extensively studied. In this paper, we investigate the restricted isometry property (RIP) based condition that guarantees exact support recovery of K-group sparse matrices X from the MMV model with greedy block coordinate descent (GBCD) algorithm in K iterations. We show that if A satisfies the RIP with \(\delta _{K+1}<1/\sqrt {K+1}\), then GBCD recovers the support of any K-group sparse matrix X in K iterations. This RIP condition is sharp since GBCD may fail to recover the support of a K-group sparse matrix in K iterations if \(\delta _{K+1}\geq 1/\sqrt {K+1}\). As far as we know, this is the first sharp condition for GBCD.

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Authors and Affiliations

  1. ENS de Lyon, Laboratoire LIP (U. Lyon, CNRS, ENSL, INRIA, UCBL), Lyon, 69007, France

    Jinming Wen

  2. School of Electronic and Information Engineering, South China University of Technology, Guangzhou, China

    Jie Tang

  3. College of Economics, Shenzhen University, Shenzhen, 518060, China

    Fumin Zhu

Authors
  1. Jinming Wen
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  2. Jie Tang
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  3. Fumin Zhu
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Corresponding author

Correspondence to Fumin Zhu.

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Wen, J., Tang, J. & Zhu, F. Greedy Block Coordinate Descent under Restricted Isometry Property. Mobile Netw Appl 22, 371–376 (2017). https://doi.org/10.1007/s11036-016-0774-9

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  • DOI: https://doi.org/10.1007/s11036-016-0774-9

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