Circuits, Systems, and Signal Processing

, Volume 39, Issue 1, pp 307–323 | Cite as

Signal Reconstruction of Compressed Sensing Based on Alternating Direction Method of Multipliers

  • Yanliang Zhang
  • Xingwang LiEmail author
  • Guoying Zhao
  • Bing Lu
  • Charles C. Cavalcante


The sparse signal reconstruction of compressive sensing can be accomplished by \({l_1}\)-norm minimization, but in many existing algorithms, there are the problems of low success probability and high computational complexity. To overcome these problems, an algorithm based on the alternating direction method of multipliers is proposed. First, using variable splitting techniques, an additional variable is introduced, which is tied to the original variable via an affine constraint. Then, the problem is transformed into a non-constrained optimization problem by means of the augmented Lagrangian multiplier method, where the multipliers can be obtained using the gradient ascent method according to dual optimization theory. The \({l_1}\)-norm minimization can finally be solved by cyclic iteration with concise form, where the solution of the original variable could be obtained by a projection operator, and the auxiliary variable could be solved by a soft threshold operator. Simulation results show that a higher signal reconstruction success probability is obtained when compared to existing methods, while a low computational cost is required.


Compressive sensing (CS) Signal reconstruction \({l_1}\)-Norm minimization Alternating direction method of multipliers Dual optimization 



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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Physics and Electrical Information EngineeringHenan Polytechnic UniversityJiaozuoChina
  2. 2.Center for Machine Vision and Signal AnalysisUniversity of OuluOuluFinland
  3. 3.Wireless Telecommunications Research GroupFederal University of Ceará Campus do PiciFortalezaBrazil

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