A Novel Distributed Jointly Sparse Optimization Algorithm

Abstract:

This paper develops a novel distributed jointly sparse optimization algorithm to recover the sparse signal, in which the joint sparse structure is used to improve the quality of recovery. In distributed networked multi-agent system, each agent collects measurement vectors and aims to recover its own sparse signal collaboratively in a distributed manner. We propose to use the factored gradient approach to calculate the solution iteratively, and introduce a energy vector of the current estimates as the consensus constrain which is updated by inexact consensus optimization for its distributed implementation. This algorithm does not require excessive data transmissions from distributed agents to fusion center, which reduces communication overhead and the computational complexity of the agents. Simulation results demonstrate that the proposed distributed algorithm has strong recovery performance and can reach global convergence as well as fast convergence rate.

• Periodical: Applied Mechanics and Materials (Volumes 519-520)
• Pages: 747-751
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.519-520.747
• Online since: February 2014
• Authors: Di Wu, Tian Li Jiang, Lin Dong Ge, Hua Peng
• Keywords: Consensus Optimization, Distributed Jointly Sparse Optimization, Gradient Factorization, Multiple Measurement Vectors

References

[1] S. Ilarri, E. Mena, A. Illarramendi, Using cooperative mobile agents to monitor distributed and dynamic environments, Information Sciences, vol. 178, no. 9, pp.2105-2127, (2008).

DOI: 10.1016/j.ins.2007.12.015

[2] I. D. Schizas, G. Mateos, G. B. Giannakis, Distributed LMS for consensus-based in network adaptive processing, IEEE Transactions on Signal Processing , vol. 57, no. 6, pp.2365-2382, (2009).

DOI: 10.1109/tsp.2009.2016226

[3] A. Rakotomamonjy, Surveying and comparing simultaneous sparse approximation (or group-lasso) algorithms, Signal processing, vol. 91, no. 7, pp.1505-1526, (2011).

DOI: 10.1016/j.sigpro.2011.01.012

[4] Z. Qin, K. Scheinberg, D. Goldfarb, Efficient block-coordinate descent algorithms for the Group Lasso., Mathematical programming computation, vol. 5, no. 2, pp.143-169, (2013).

DOI: 10.1007/s12532-013-0051-x

[5] F. Zeng, C. Li, Z, Tian, Distributed compressive spectrum sensing in cooperative multihop cognitive networks, IEEE Journal of Selected Topics in Signal Processing, vol. 5, no. 1, pp.37-48, (2011).

DOI: 10.1109/jstsp.2010.2055037

[6] J. A. Bazerque, G. Mateos, G. B. Giannakis, Group-lasso on splines for spectrum cartography, IEEE Transactions on Signal Processing, vol. 59, no. 10, pp.4648-4663, (2011).

DOI: 10.1109/tsp.2011.2160858

[7] Q. Ling, Z. Tian, Decentralized support detection of multiple measurement vectors with joint sparsity, in 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.2996-2999, (2011).

DOI: 10.1109/icassp.2011.5946288

[8] J. Zhu, Y. Li, M. Xue, et al. A lightweight decentralized algorithm for jointly sparse optimization, in IEEE 2013 32nd Chinese Control Conference (CCC), pp.4666-4670, (2013).

[9] Q. Ling, Z. Wen, and W. Yin, Decentralized Jointly Sparse Recovery by Reweighted Lq Minimization, IEEE Transactions on Signal Processing, vol. 61, no. 5, pp.1165-70, (2013).

DOI: 10.1109/tsp.2012.2236830

[10] E. Candes, M. Wakin, S. Boyd, Enhancing sparsity by reweighted ℓ1 minimization, Journal of Fourier Analysis and Applications, vol. 14, pp.877-905, (2008).

DOI: 10.1007/s00041-008-9045-x

[11] S. F. Cotter, B. D. Rao, K. Engan, et al., Sparse solutions to linear inverse problems with multiple measurement vectors, IEEE Transactions on Signal Processing, vol. 53, no. 7, pp.2477-2488, (2005).

DOI: 10.1109/tsp.2005.849172

[12] M. Yuan, Y. Lin, Model selection and estimation in regression with grouped variables, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol. 68, no. 1, pp.49-67, (2006).

DOI: 10.1111/j.1467-9868.2005.00532.x

[13] D. P. Bertsekas, J. N. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods, Englewood Cliffs, NJ: Prentice-Hall, 1989, Mass. Inst. of Technol.

DOI: 10.1177/109434208900300408

[14] B. D. Rao, K. Engan, S. F. Cotter, et al., Subset selection in noise based on diversity measure minimization, IEEE Transactions on Signal Processing, vol. 51, no. 3, pp.760-770, (2003).

DOI: 10.1109/tsp.2002.808076