Signal, Image and Video Processing

, Volume 12, Issue 1, pp 133–140 | Cite as

Mixed \({L}_{1}\) norm and \({L}_{2}\) norm regularized sparsity adaptive matching pursuit algorithm

  • Nian CaiEmail author
  • Qian Ye
  • Jing Wang
  • Guandong Cen
  • Junchi Liu
  • Han Wang
  • Bingo Wing-Kuen
Original Paper


The sparsity adaptive matching pursuit (SAMP) algorithm has an advantage of reconstructing signals without the prior information of the sparsity level. However, the required computational power is high and the reconstruction performance is not satisfied for perturbed systems. This is because this algorithm is based on the expectation maximization algorithm. Also, a pseudo-inverse operation of the matrix is employed to select the element candidates of the sensing matrix in each iteration. In this paper, a mixed \(L_{1}\) norm and \(L_{2}\) norm regularized algorithm is proposed to address these issues. Similar to the SAMP algorithm, the regularized algorithm also reconstructs the signals without the prior information of the sparsity level. Different from the SAMP algorithm, the element candidates of the sensing matrix are selected by the \(L_{2}\) norm strategy in each iteration. Experiments are performed on an ideal simulation system, a perturbed simulation system and real image reconstruction. Simulation and real image reconstruction experimental results indicate that the regularized algorithm has lower computational power than the SAMP algorithm. Also, the proposed algorithm has better reconstruction performance on the perturbed system compared to the SAMP algorithm.


Sparsity adaptive matching pursuit Mixed \(L_{1}\) norm and \(L_{2}\) norm regularized algorithm Signal reconstruction 



This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 61001179, 91648108 and 61471132), Guangdong Science and Technology Plan (Grant Nos. 2015B010104006, 2015B090903017 and 2015B010102014), Guangdong Natural Science Foundation (Grant No. 2015A030312008), and Key Project of Industry-University-Research Collaborative Innovation in Guangzhou, China (Nos. 201604016064, 201604016022 and 201508010001).


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Copyright information

© Springer-Verlag London Ltd. 2017

Authors and Affiliations

  • Nian Cai
    • 1
    Email author
  • Qian Ye
    • 1
  • Jing Wang
    • 1
  • Guandong Cen
    • 1
  • Junchi Liu
    • 1
  • Han Wang
    • 2
  • Bingo Wing-Kuen
    • 1
  1. 1.School of Information EngineeringGuangdong University of TechnologyGuangzhouChina
  2. 2.School of Electromechanical EngineeringGuangdong University of TechnologyGuangzhouChina

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