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A Novel Underdetermined Source Recovery Algorithm Based on k-Sparse Component Analysis

Authors
  • Eqlimi, Ehsan1, 2, 3
  • Makkiabadi, Bahador1, 3
  • Samadzadehaghdam, Nasser1, 3
  • Khajehpour, Hassan1, 3
  • Mohagheghian, Fahimeh4
  • Sanei, Saeid5
  • 1 Tehran University of Medical Sciences (TUMS), Department of Medical Physics and Biomedical Engineering, School of Medicine, Tehran, Iran , Tehran (Iran)
  • 2 Ghent University (UGent), WAVES Research Group, Department of Information Technology (INTEC), Ghent, Belgium , Ghent (Belgium)
  • 3 TUMS, Research Center for Biomedical Technology and Robotics (RCBTR), Institute of Advanced Medical Technologies (IAMT), Tehran, Iran , Tehran (Iran)
  • 4 Shahid Beheshti University of Medical Sciences (SBMU), Department of Medical Physics and Biomedical Engineering, School of Medicine, Tehran, Iran , Tehran (Iran)
  • 5 Nottingham Trent University (NTU), School of Science and Technology, Nottingham, UK , Nottingham (United Kingdom)
Type
Published Article
Journal
Circuits, Systems, and Signal Processing
Publisher
Springer US
Publication Date
Aug 03, 2018
Volume
38
Issue
3
Pages
1264–1286
Identifiers
DOI: 10.1007/s00034-018-0910-9
Source
Springer Nature
Keywords
License
Yellow

Abstract

Sparse component analysis (SCA) is a popular method for addressing underdetermined blind source separation in array signal processing applications. We are motivated by problems that arise in the applications where the sources are densely sparse (i.e. the number of active sources is high and very close to the number of sensors). The separation performance of current underdetermined source recovery (USR) solutions, including the relaxation and greedy families, reduces with decreasing the mixing system dimension and increasing the sparsity level (k). In this paper, we present a k-SCA-based algorithm that is suitable for USR in low-dimensional mixing systems. Assuming the sources is at most (m-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(m-1$$\end{document}) sparse where m is the number of mixtures; the proposed method is capable of recovering the sources from the mixtures given the mixing matrix using a subspace detection framework. Simulation results show that the proposed algorithm achieves better separation performance in k-SCA conditions compared to state-of-the-art USR algorithms such as basis pursuit, minimizing norm-L1, smoothed L0, focal underdetermined system solver and orthogonal matching pursuit.

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