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Reconstruction of low-rank jointly sparse signals from multiple measurement vectors

  • Mehrrad Mehrkam
  • Mohammad Ali TinatiEmail author
  • Tohid Yousefi Rezaii
Original Paper
  • 44 Downloads

Abstract

The multiple measurement vectors problem approximates a set of signals sharing a common sparsity pattern simultaneously, using different linear combinations of those signals obtained through a sensing matrix. In a situation where the signal matrix has full row-rank, MUltiple SIgnal Classification (MUSIC) algorithm guarantees to recover the jointly sparse signals, but for the rank-defective case, the MUSIC performance is voided. To address such a rank deficient case, our proposed method, line search low-rank jointly sparse signals (LS-LRJSS), provides a geometric analysis of the problem by characterizing the linear dependence of the measurements with the linear coefficients that permit the reconstruction of each point from its neighbors. Moreover, a subspace analysis has been done on a Grassmann manifold to obtain the subspace that the signal matrix belongs to. Several numerical experiments evidence that the proposed method is more accurate and less time-consuming compared to existing approaches especially wherever the sparsity level of the signals increases or the number of measurement vectors decreases.

Keywords

Compressive sensing Multiple measurement vectors Joint sparsity Rank deficiency 

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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  • Mehrrad Mehrkam
    • 1
  • Mohammad Ali Tinati
    • 1
    Email author
  • Tohid Yousefi Rezaii
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of TabrizTabrizIran

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