Decentralised seismic tomography computing in cyber-physical sensor systems

This paper presents an innovative decentralised seismic tomography computing paradigm in cyber-physical sensor systems, where each sensor node computes the tomography based on its partial information and through gossip with local neighbours only. The key challenge is the potential high communication overhead due to limited knowledge of each node about the entire network topology and information. The aim of this paper is to develop efficient algorithms for maximising the quality of tomography resolution while minimising the communication cost. We reformulate the conventional seismic tomography problem and exploit the alternating direction method of multipliers method to design two distributed algorithms. One is a synchronous algorithm and the other is asynchronous and more fault-tolerant and scalable. We theoretically prove that both proposed algorithms can reach their convergent solutions in a linear rate in terms of the number of communication rounds. Extensive evaluations on both synthetic and real data-sets validate the superior efficiency of the proposed algorithms. They not only achieve near-optimal (compare to centralised solution) high-quality tomography but also retain low communication cost even in sparse networks.

[1]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[2]  Qing Ling,et al.  EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimization , 2014, 1404.6264.

[3]  Per Christian Hansen,et al.  AIR Tools - A MATLAB package of algebraic iterative reconstruction methods , 2012, J. Comput. Appl. Math..

[4]  Ioannis D. Schizas,et al.  Performance Analysis of the Consensus-Based Distributed LMS Algorithm , 2009, EURASIP J. Adv. Signal Process..

[5]  Emiliano Dall'Anese,et al.  Fast Consensus by the Alternating Direction Multipliers Method , 2011, IEEE Transactions on Signal Processing.

[6]  Lei Shi,et al.  Imaging seismic tomography in sensor network , 2013, 2013 IEEE International Conference on Sensing, Communications and Networking (SECON).

[7]  Antonio Possolo,et al.  Spatial Statistics and Imaging , 1992 .

[8]  Stephen P. Boyd,et al.  Fast linear iterations for distributed averaging , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[9]  Goutham Kamath,et al.  Real-time In-situ Seismic Imaging: Overview and Case Study , 2015 .

[10]  Lei Shi,et al.  Component-Average Based Distributed Seismic Tomography in Sensor Networks , 2013, 2013 IEEE International Conference on Distributed Computing in Sensor Systems.

[11]  Stephen P. Boyd,et al.  Fastest Mixing Markov Chain on a Graph , 2004, SIAM Rev..

[12]  VangelistaLorenzo,et al.  Fast Consensus by the Alternating Direction Multipliers Method , 2011 .

[13]  Jun Ye Yu,et al.  Networked optimization with adaptive communication , 2013, 2013 IEEE Global Conference on Signal and Information Processing.

[14]  J. Lees Seismic tomography of magmatic systems , 2007 .

[15]  Jeff Ahrenholz Comparison of CORE network emulation platforms , 2010, 2010 - MILCOM 2010 MILITARY COMMUNICATIONS CONFERENCE.

[16]  Dimitri P. Bertsekas,et al.  On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators , 1992, Math. Program..

[17]  Ioannis D. Schizas,et al.  Distributed LMS for Consensus-Based In-Network Adaptive Processing , 2009, IEEE Transactions on Signal Processing.

[18]  José M. F. Moura,et al.  Fast Distributed Gradient Methods , 2011, IEEE Transactions on Automatic Control.

[19]  R. P. Bording,et al.  Applications of seismic travel-time tomography , 1987 .

[20]  Jonathan M. Lees,et al.  Bayesian ART versus conjugate gradient methods in tomographic seismic imaging: an application at Mount St. Helens, Washington , 1991 .

[21]  I. Daubechies,et al.  Tomographic inversion using L1-norm regularization of wavelet coefficients , 2006, physics/0608094.

[22]  A.H. Sayed,et al.  Distributed Recursive Least-Squares Strategies Over Adaptive Networks , 2006, 2006 Fortieth Asilomar Conference on Signals, Systems and Computers.

[23]  Qing Ling,et al.  On the Convergence of Decentralized Gradient Descent , 2013, SIAM J. Optim..

[24]  Rosemary A. Renaut,et al.  A parallel multisplitting solution of the least squares problem , 1998, Numer. Linear Algebra Appl..

[25]  Rosemary A. Renaut A Parallel Multisplitting Solution of the Least Squares Problem , 1998 .

[26]  Jeffrey S. Rosenthal,et al.  Convergence Rates for Markov Chains , 1995, SIAM Rev..

[27]  Gonzalo Mateos,et al.  Distributed Sparse Linear Regression , 2010, IEEE Transactions on Signal Processing.

[28]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .