Abstract
Time-frequency atom decomposition (TFAD) provides a flexible representation for non-stationary signals, but the extremely high computational effort greatly blocks its practical applications. Quantum-inspired evolutionary algorithms (QEA) are efficient optimization methods with strong search capability and rapid convergence. This paper proposes the application of a modified variant of QEA to the TFAD problem. The problem on TFAD with evolutionary algorithms is formulated. By using gray coding, elite groups, and an appropriate termination criterion, the modified QEA is developed to search the suboptimal time-frequency atoms from a very large and redundant time-frequency dictionary. Also, this paper discusses the reduction of the computational time in terms of parameter setting, and presents an application example of radar emitter signals. Extensive experiments show the effectiveness and practicability of the presented algorithm.
Similar content being viewed by others
References
M.R. Akbarzadeh-T, A.R. Khorsand, Evolutionary quantum algorithms for structural design, in Proc. of IEEE Int. Conf. on Systems, Man and Cybernetics, vol. 4 (2005), pp. 3077–3082
C.H. Bennett, D.P. DiVincenzo, Quantum information and computation. Nature 404, 247–255 (2000)
S.S. Chen, Basis pursuit, Ph.D. thesis, Stanford University, November 1995
R.R. Coifman, M.V. Wickerhauser, Entropy based methods for best basis selection. IEEE Trans. Inf. Theory 38, 719–746 (1992)
P. Czerepinski, C. Davies, N. Canagarajah, D. Bull, Matching pursuits video coding: dictionaries and fast implementation. IEEE Trans. Circuits Syst. Video Technol. 10, 1103–1115 (2000)
G. Davis, S. Mallat, M. Avellaneda, Adaptive greedy approximation. J. Constr. Approx. 13, 57–98 (1997)
A.R. Ferreira da Silva, Evolutionary-based methods for adaptive signal representation. Signal Process. 81, 927–944 (2001)
A.R. Ferreira da Silva, Atomic decomposition with evolutionary pursuit. Dig. Signal Process. 13, 317–337 (2003)
A.R. Ferreira da Silva, Approximations with evolutionary pursuit. Signal Process. 83, 465–481 (2003)
R.M. Figueras i Ventura, P. Vandergheynst, Matching pursuit through genetic algorithms. LTS-EPFL Tech. Report, 2001, pp. 1–14
R. Gribonval, Fast matching pursuit with a multiscale dictionary of Gaussian chirps. IEEE Trans. Signal Process. 49, 994–1001 (2001)
R. Gribonval, E. Bacry, Harmonic decomposition of audio signals with matching pursuit. IEEE Trans. Signal Process. 51, 101–111 (2003)
L.K. Grover, Quantum computation, in Proc. of the 12th International Conference on VLSI Design (1999), pp. 548–553
K.H. Han, J.H. Kim, Genetic quantum algorithm and its application to combinatorial optimization problem, in Proc. of the 2000 IEEE Congress on Evolutionary Computation, vol. 2 (2000), pp. 1354–1360
K.H. Han, J.H. Kim, Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Trans. Evol. Comput. 6, 580–593 (2002)
K.H. Han, J.H. Kim, Quantum-inspired evolutionary algorithms with a new termination criterion, H ε gate, and two-phase scheme. IEEE Trans. Evol. Comput. 8, 156–169 (2004)
T. Hey, Quantum computing: an introduction. Comput. Control Eng. J. 10, 105–112 (1999)
J.S. Jang, K.H. Han, J.H. Kim, Face detection using quantum-inspired evolutionary algorithm, in Proc. of the 2004 Congress on Evolutionary Computation, vol. 2 (2004), pp. 2100–2106
B. Jeon, S. Oh, Fast matching pursuit with vector norm comparison. IEEE Trans. Circuits Syst. Video Technol. 13, 338–342 (2003)
A.R. Khorsand, M.R. Akbarzadeh-T, Quantum gate optimization in a meta-level genetic quantum algorithm, in Proc. of IEEE Int. Conf. on Systems, Man and Cybernetics, vol. 4 (2005), pp. 3055–3062
A.R. Khorsand, M.R. Akbarzadeh-T, Genetic quantum algorithm for voltage and pattern design of piezoelectric actuator, in Proc. of IEEE Congress on Evolutionary Computation (2006), pp. 2593–2600
K.H. Kim, J.Y. Hwang, K.H. Han, J.H. Kim, K.H. Park, A quantum inspired evolutionary computing algorithm for disk allocation method. IEICE Trans. Inf. Syst. vol. E86-D, 645–649 (2003)
Y. Kim, J.H. Kim, K.H. Han, Quantum-inspired multiobjective evolutionary algorithm for multiobjective 0/1 knapsack problems, in Proc. of IEEE Congress on Evolutionary Computation (2006), pp. 2601–2606
Y. Li, Y.N. Zhang, R.C. Zhao, L.C. Jiao, An edge detector based on parallel quantum-inspired evolutionary algorithm, in Proc. of the 3rd Int. Conf. on Machine Learning and Cybernetics (2004), pp. 4062–4066
Q.S. Liu, Q. Wang, L.N. Wu, Size of the dictionary in matching pursuit algorithm. IEEE Trans. Signal Process. 52(12), 3403–3408 (2004)
Q.S. Liu, Q. Wang, L.N. Wu, Improvement of encoder for matching pursuit-based video coding. Electron. Lett. 36(6), 548–549 (2000)
G. Lopez-Risueno, J. Grajal, Unknown signal detection via atomic decomposition, in Proceedings of the 11th IEEE Signal Processing Workshop on Statistical Signal Processing (2001), pp. 174–177
G. Lopez-Risueno, J. Grajal, O. Yeste-Ojeda, Atomic decomposition-based radar complex signal interception. IEE Proc. Radar Sonar Navig. 150(4), 323–331 (2003)
S.G. Mallat, Z.F. Zhang, Matching pursuits with time-frequency dictionaries. IEEE Trans. Signal Process. 41(12), 3397–3415 (1993)
K.E. Mathias, L.D. Whitley, Transforming the search space with gray coding, in Proceedings of the First IEEE Conference on Evolutionary Computation (1994), pp. 513–518
S. Meshoul, K. Mahdi, M. Batouche, A quantum inspired evolutionary framework for multi-objective optimization, in Proc. of 12th Portuguese Conference on Artificial Intelligence. Lecture Notes in Artificial Intelligence, vol. 3808 (Springer, Berlin, 2005), pp. 190–201
M. Moore, A. Narayanan, Quantum-inspired computing. Department of Computer Science, University of Exeter, Exeter, UK, 1995
A. Narayanan, Quantum computing for beginners, in Proc. of the 1999 Congress on Evolutionary Computation (1999), pp. 2231–2238
A. Narayanan, M. Moore, Quantum-inspired genetic algorithm, in Proc. of IEEE International Conference on Evolutionary Computation (1996), pp. 61–66
R. Neff, A. Zakhor, Very low bit rate video coding based on matching pursuit. IEEE Trans. Circuits Syst. Video Technol. 7, 158–171 (1997)
S. Qian, D. Chen, Signal representation using adaptive normalized Gaussian functions. Signal Process. 36(1), 1–11 (1994)
D. Stefanoiu, F. Ionescu, A genetic matching pursuit algorithm, in Proceedings of 7th International Symposium on Signal Processing and Its Applications (2003), pp. 577–580
D. Stefanoiu, F. Ionescu, A time-frequency-scale approach to fractal data denoising and compression, in Proceedings of the First South-East European Symposium on Interdisciplinary Approaches in Fractal Analysis (2003), pp. 79–84
D. Stefanoiu, F. Ionescu, Faults diagnosis through genetic matching pursuit, in Proceedings of 7th International Conference on Knowledge-Based Intelligent Information and Engineering Systems. Lecture Notes in Computer Science, vol. 2773 (Springer, Berlin, 2003), pp. 733–740
H. Talbi, M. Batouche, A. Draa, A quantum-inspired genetic algorithm for multi-source affine image registration, in Proceedings of International Conference on Image Analysis and Recognition. Lecture Notes in Computer Science, vol. 3211 (Springer, Berlin, 2004), pp. 147–154
M.P. Tcheou, L. Lovisolo, E.A.B. da Silva, M.A.M. Rodrigues, P.S.R. Diniz, Optimum rate-distortion dictionary selection for compression of atomic decompositions of electric disturbance signals. IEEE Trans. Signal Process. Lett. 14(2), 81–84 (2007)
J. Vesin, Efficient implementation of matching pursuit using a genetic algorithm in the continuous space, in Proceedings of 10th European Signal Processing Conference (2000), pp. 2–5
H.L. Wang, O.K. Ersoy, Parallel gray code optimization for high dimensional problems, in Proceedings of the Sixth International Conference on Computational Intelligence and Multimedia Applications (2005), pp. 1–6
D. Whitley, S. Rana, R. Heckendorn, Representation issues in neighborhood search and evolutionary algorithms, in Genetic Algorithms and Computer Science, ed. by D. Quagliarelli et al. (Wiley, New York, 1997)
G.X. Zhang, L.Z. Hu, W.D. Jin, Resemblance coefficient and a quantum genetic algorithm for feature selection, in Proceedings of the 7th International Conference on Discovery Science. Lecture Notes in Artificial Intelligence, vol. 3245 (Springer, Berlin, 2004), pp. 155–168
G.X. Zhang, W.D. Jin, L.Z. Hu, A novel parallel quantum genetic algorithm, in Proceedings of the 4th Int. Conf. on Parallel and Distributed Computing, Applications and Technologies (2003), pp. 693–697
Author information
Authors and Affiliations
Corresponding author
Additional information
This work is supported by the National Natural Science Foundation of China grants 60702026, the Scientific and Technological Funds for Young Scientists of Sichuan grants 09ZQ026-040, and the Open Research Fund of Key Laboratory of Sichuan, Xihua University.
Rights and permissions
About this article
Cite this article
Zhang, GX. Time-Frequency Atom Decomposition with Quantum-Inspired Evolutionary Algorithms. Circuits Syst Signal Process 29, 209–233 (2010). https://doi.org/10.1007/s00034-009-9142-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00034-009-9142-3