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). https://doi.org/10.1007/s00034-019-01174-2

### 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)
Language: English
Published: Springer Nature, 2020
Publish Date: 2020-06-15
Description:

# Abstract

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