JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (6): 92-98.doi: 10.6040/j.issn.1671-9352.4.2015.004

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Application of a new accelerating Bregman iterative algorithm in the sparse least squares problems

WANG Wen-shu1,2, LI Wei-guo1, QIN Shu-lan2   

  1. 1. College of Science, China University of Petroleum, Qingdao 266580, Shandong, China;
    2. Qingdao Binhai University, Qingdao 266580, Shandong, China
  • Received:2015-01-21 Online:2016-06-20 Published:2016-06-15

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Abstract: Based on the residual Bregman iterative algorithm and fixed point iteration, a novel Bregman iterative algorithm is proposed. Then, inspired by the equivalence of the linearized Bregman and the gradient descent algorithm of the dual problem, a new algorithm by introducing Nesterov accelerating technique into the predictor-corrector method is put forward for solving the sparse least squares problems. Simultaneously, It is proved that the solution sequence obtained by the new method is the optimal solution of the sparse least squares problems. Finally, we use the new method to the sparse signal recovery problem. The numerical results show that the new method is faster and more efficientthan the old ones.

Key words: Nesterov accelerating technique, Bregman iteration, the sparse least squares problems

CLC Number: 

  • O242
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