University of Oulu

Zhang, Y., Li, X., Zhao, G. et al. Signal Reconstruction of Compressed Sensing Based on Alternating Direction Method of Multipliers. Circuits Syst Signal Process 39, 307–323 (2020).

Signal reconstruction of compressed sensing based on alternating direction method of multipliers

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Author: Zhang, Yanliang1; Li, Xingwang1; Zhao, Guoying2;
Organizations: 1School of Physics and Electrical Information Engineering, Henan Polytechnic University, Jiaozuo, China
2Center for Machine Vision and Signal Analysis, University of Oulu, Oulu, Finland
3Wireless Telecommunications Research Group, Federal University of Ceará Campus do Pici, Fortaleza, Brazil
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.2 MB)
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Language: English
Published: Springer Nature, 2020
Publish Date: 2020-06-15


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.

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Series: Circuits, systems and signal processing
ISSN: 0278-081X
ISSN-E: 1531-5878
ISSN-L: 0278-081X
Volume: 39
Pages: 307 - 323
DOI: 10.1007/s00034-019-01174-2
Type of Publication: A1 Journal article – refereed
Field of Science: 113 Computer and information sciences
Funding: This work was supported by Ph.D. Fund of Henan Polytechnic University with Grant Number B2012-100 and Open Fund of Network and Exchange Technology State Key Laboratory with Grant Number SKLNST-2016-1-02.
Copyright information: © Springer Science+Business Media, LLC, part of Springer Nature 2019. This is a post-peer-review, pre-copyedit version of an article published in Circuits, Systems, and Signal Processing. The final authenticated version is available online at: