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

Previous Articles     Next Articles

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

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
[1] DONOHOD L. De-noising by soft-thresholding[J]. IEEE Transactions Information Theory, 1995, 41(3):613-627.
[2] OSHER S, BURGER M, GOLDFARB D, et al. An iterative regularization method for total variation-based image restoration[J]. Multiscale Modeling and Simulation, 2005, 4(2):460-489.
[3] CAI Jianfeng, OSHER S, SHEN Zuowei. Linearized Bregman iterations for compressed sensing[J] Mathematics of Computation, 2009, 78(267):1515-1536.
[4] YIN Wotao, OSHERS Stanley, GOLDFARB D, et al. Bregman iterative algorithms forl1-minimization with applications to compressed sensing[J]. SIAM J Imaging Sciences, 2008, 1(1):143-168.
[5] VOGEL C R, OMAN M E. Iterative methods for total variation denoising[J]. SIAM Journal on Scientific Computing, 1996, 17(1):227-238.
[6] GOLUBG H, VAN LOAN C F. Matrix computations[M].4th ed.Baltimore: The Johns Hopkins University Press, 2013.
[7] 李娟, 李维国, 郑昭静. 求解稀疏最小二乘问题的新型Bregman迭代正则化算法[J]. 信号处理, 2012, 8:1164-1170. LI Juan, LI Weiguo, ZHENG Zhaojing. A New Bregman Iterative Regularization Algorithm forSparse Least Squares Problems[J]. Signal Processing, 2012, 8:1164-1170.
[8] 郑昭静,李维国. 基于Bregman迭代的稀疏最小二乘问题的预测校正法[J]. 高等学校计算数学学报, 2014, 36(2):167-182. ZHENG Zhaojing, LI Weiguo. Predictor-CorrectorAlgorithm Based onBregman Iterationfor Sparse LeastSquaresProblems[J]. Numerical Mathematics A Journal of Chinese Universities, 2014, 36(2):167-182.
[9] YIN Wotao. Analysis and generalization of linearized Bregmanmethod[J]. SIAM Journal on Imaging Sciences, 2010, 3(4):856-877.
[10] ZHANG Hui, YIN Wotao. Gradient methods for convex minimization: better rates under weaker conditions[EB/OL] //[2015-04].arXiv:1303.4645v2[math.OC]. http://arxiv.org/abs/1303.4645
[1] CAO Wei-dong, DAI Tao, YU Jin-biao, WANG Xiao-hong, SHI An-feng. Improvement on the solution of pressure equation based on alternating direction in chemical flooding model [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 88-94.
[2] . Interval algorithm for mixed integer nonlinear two-level programming problems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 9-17.
[3] SHI Zhang-lei, LI Wei-guo. A graded hard thresholding pursuit algorithm [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 58-64.
[4] ZHANG Jing-jing,YANG Xiu-ping,LIU Qing,ZHANG Chun-qiu*. Mechanics response analysis of lumbar intervertebral disc based on Biot theory [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(11): 93-98.
[5] CHEN Ling, MEN Yu-tao, WANG Jia-jiang. Reliability analysis of dental implantation and split-root technique joint repaired postoperative dental [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(5): 6-10.
[6] CUI An-gang, LI Hai-yang. Equivalence between the affine matrix rank minimization problem and the unconstrained matrix rank minimization problem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 86-89.
[7] DIAO Qun, SHI Dong-yang. New H 1-Galerkin mixed finite element analysis for quasi-linear viscoelasticity equation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 90-98.
[8] WANG Jia-jiang, CHEN Ling, MEN Yu-tao, JI Chen. The feasibility study on shorten treatment cycle of dental implantation and split-root technique joint repair [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(3): 40-43.
[9] ZHANG Hou-chao, ZHU Wei-jun, WANG Jun-jun. Superconvergence and extrapolation of a lower order mixed finite method for nonlinear fourth-order hyperbolic equation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(12): 35-46.
[10] LIU Chun-mei, ZHONG Liu-qiang, SHU Shi, XIAO Ying-xiong. Local multigrid method for higher-order finite element discretizations of elasticity problems in two dimensions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(08): 34-39.
[11] FAN Ming-zhi, WANG Fen-ling, SHI Dong-yang. High accuracy analysis of the lowest order new mixed finite element scheme for generalized nerve conductive equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(08): 78-89.
[12] JIANG Jun, YANG Xiu-ping, LIU Qing, ZHANG Chun-qiu. Simulating the solute diffusion in articular cartilage under compression loading [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(01): 85-89.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!