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The design approaches of two-dimensional digital filters based on metaheuristic optimization algorithms: a review of the literature

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Abstract

Recently, the design of the two-dimensional digital filter has become a subject of interest in the field of two-dimensional signal processing. The two-dimensional digital filter has been applied in many important areas such as image processing, television systems and seismic signal processing. In digital filter design, there are several indispensable aims such as stability, reduced computational complexity and computational time. Thus, researchers and practitioners have investigated various advanced methods based on metaheuristic optimization algorithms for the design of the two-dimensional digital filter. Metaheuristic optimization algorithms have been applied to solve different complicated problems in various fields and they have also been successfully used in digital filter design. This paper presents a review of the design approaches of two-dimensional digital filters based on metaheuristic optimization algorithms such as the genetic algorithm, differential evolution and particle swarm optimization. By comparing the proposed design approaches based on metaheuristic optimization algorithms, it is observed that the genetic algorithm is the most preferred algorithm and emerging novel algorithms using metaheuristic optimization algorithms have better performance in terms of computational complexity and computational time. It is hoped that this review will be helpful for researchers and practitioners studying the design of two-dimensional digital filters.

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References

  • Abo-Zahhad M, Ahmed SM, Al-Ajlouni AF, Sabor N (2010) Design of two-dimensional recursive digital filters with specified magnitude and group-delay characteristics using taguchi-based immune algorithm. Int J Signal Imaging Syst Eng 3(4):222–235. doi:10.1504/IJSISE.2010.038018

    Article  Google Scholar 

  • Abo-Zahhad M, Ahmed SM, Sabor N, Al-Ajlouni AF (2011) Design of immune algorithm based two-dimensional recursive digital filters using multi-level orthogonal arrays. In: 28th national radio science conference (NRSC), pp 1–8. doi:10.1109/NRSC.2011.5873608

  • Antoniou A (1979) Digital filters: analysis and design. McGraw-Hill, New York

    Google Scholar 

  • Antoniou A (1993) Digital filters: analysis, design and applications. McGraw-Hill, Singapore

    Google Scholar 

  • Boashash B (2003) Time frequency signal analysis and processing a comprehensive reference. Elsevier, Amsterdam

    Google Scholar 

  • Bose NK (1982) Applied multidimensional systems theory. Van Nostrand Reinhold Company, New York

    MATH  Google Scholar 

  • Boudjeleba K, Chikouche D, Ros F (2011a) Evolutionary techniques for the synthesis of 2-d fir filters. In: IEEE statistical signal processing workshop (SSP), pp 601–604. doi:10.1109/SSP.2011.5967771

  • Boudjeleba K, Ros F, Chikouche D (2011b) An advanced genetic algorithm for designing 2-d fir filters. In: IEEE Pacific rim conference on communications, computers and signal processing (PacRim), pp 60–65. doi:10.1109/PACRIM.2011.6032868

  • Bovik A (2005) Handbook of image and video processing. Elsevier, USA

    Google Scholar 

  • Chen WK (2009) Passive, active and digital filters. CRC Press, USA

    Google Scholar 

  • Constantinides AG (1970) Spectral transformations for digital filters. Proc Inst Electr Eng 117(8):1585–1590. doi:10.1049/piee.1970.0281

    Article  Google Scholar 

  • Costa JM, Venetsanopoulos AN (1974) Design of circularly symmetric two-dimensional recursive filters. IEEE Trans Acoust Speech Signal Process 22(6):432–443. doi:10.1109/TASSP.1974.1162616

    Article  Google Scholar 

  • Das S, Dey D (2005) Design of two-dimensional iir filters using an improved de algorithm. Pattern Recognit Mach Intell Lect Notes Comput Sci 3776:369–375. doi:10.1007/11590316_56

  • Das S, Konar A (2006) Two-dimensional iir filter design with modern search heuristics: a comparative study. Int J Comput Intell Appl 6(3):329–355. doi:10.1142/S1469026806001848

    Article  MATH  Google Scholar 

  • Das S, Konar A (2007) A swarm intelligence approach to the synthesis of two-dimensional iir filters. Eng Appl Artif Intell 20(8):1086–1096. doi:10.1016/j.engappai.2007.02.004

    Article  Google Scholar 

  • Das S, Suganthan PN (2011) Differential evolution: a survey of the state-of-the-art. IEEE Trans Evol Comput 15(1):4–31. doi:10.1109/TEVC.2010.2059031

    Article  Google Scholar 

  • Das S, Konar A, Chakraborty UK (2005a) An efficient evolutionary algorithm applied to the design of two-dimensional iir filters. In: Proceedings of the 2005 conference on genetic and evolutionary computation, pp 2157–2163. doi:10.1145/1068009.1068364

  • Das S, Konar A, Chakraborty UK (2005b) Design of two-dimensional iir filters with self-organizing hierarchical pso algorithm. In: Proceedings of the 8th joint conference on information sciences, pp 550–553

  • De Carlo RA, Murray J, Saeks R (1977) Multivariable nyquist theory. Int J Control 25(5):657–675. doi:10.1080/00207177708922261

    Article  Google Scholar 

  • De Castro LN, von Zuben VJ (2002) Learning and optimization using the clonal selection principle. IEEE Trans Evol Comput 6(3):239–251. doi:10.1109/TEVC.2002.1011539

    Article  Google Scholar 

  • Dorigo M, Birattari M (2007) Swarm intelligence. Scholarpedia 2(9):1462. doi:10.4249/scholarpedia.1462

    Article  Google Scholar 

  • Dudgeon DE, Mersereau RM (1983) Multidimensional digital signal processing. Prentice Hall, New Jersey

    Google Scholar 

  • Elkarami B, Ahmadi M (2011) An efficient design of 2-d fir digital filters by using singular value decomposition and genetic algorithm with canonical signed digit (csd) coefficients. In: IEEE 54th international midwest symposium on circuits and systems (MWSCAS), pp 1–4. doi:10.1109/MWSCAS.2011.6026659

  • Fang W, Sun J, Xu W (2006) Design of two-dimensional recursive filters by using quantum-behaved particle swarm optimization. In: International conference on intelligent information hiding and multimedia signal processing (IIH-MSP’06), pp 240–243. doi:10.1109/IIH-MSP.2006.84

  • Farmer JD, Packard NH, Perelson AS (1986) The immune system, adaptation, and machine learning. Physica 22:187–204. doi:10.1016/0167-2789(86)90240-X

    MathSciNet  Google Scholar 

  • Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68. doi:10.1177/003754970107600201

    Article  Google Scholar 

  • Ghosh S, Kundu D, Suresh K, Das S, Abraham A (2009) Design of optimal digital IIR filters by using a bandwidth adaptive harmony search algorithm. In: World congress on nature and biologically inspired computing (NaBIC 2009), pp 481–486. doi:10.1109/NABIC.2009.5393362

  • Ghosh P, Das S, Zafar H (2012) Adaptive differential evolution based design of two-channel quadrature mirror filter banks for sub-band coding and data transmission. IEEE Trans Syst Man Cybern Part C 42(6):1613–1623. doi:10.1109/TSMCC.2012.2212007

    Article  Google Scholar 

  • Glover F (1986) Future paths for integer programming and links to artificial intelligence. Comput Oper Res 13(5):533–549. doi:10.1016/0305-0548(86)90048-1

    Article  MathSciNet  MATH  Google Scholar 

  • Glover F (1989) Tabu search-part I. ORSA J Comput 1(3):190–206. doi:10.1287/ijoc.1.3.190

    Article  MATH  Google Scholar 

  • Glover F (1990) Tabu search-part II. ORSA J Comput 2(1):4–32. doi:10.1287/ijoc.2.1.4

    Article  MATH  Google Scholar 

  • Glover F, Taillard E, De Werra D (1993) A user’s guide to tabu search. Ann Oper Res 41:3–28. doi:10.1007/BF02078647

    Article  MATH  Google Scholar 

  • Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison Wesley, MA

    MATH  Google Scholar 

  • Gonzales RC, Woods RE (2007) Digital image processing. Prentice Hall, New Jersey

    Google Scholar 

  • Goodman DM (1978) A design technique for circularly symmetric low-pass filters. IEEE Trans Acoust Speech Signal Process 26(4):290–304. doi:10.1109/TASSP.1978.1163095

    Article  MATH  Google Scholar 

  • Hirano K, Aggarwal JK (1978) Design of two-dimensional recursive digital filters. IEEE Trans Circuits Syst 25(12):1066–1076. doi:10.1109/TCS.1978.1084426

    Article  Google Scholar 

  • Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor

    Google Scholar 

  • Huang TS (1972) Stability of two-dimensional recursive filters. IEEE Transaction Audio Electroacoust 20(2):158–163. doi:10.1109/TAU.1972.1162364

    Article  Google Scholar 

  • Hunt JE, Cooke DE (1996) Learning using an artificial immune system. J Netw Comput Appl 19:189–212. doi:10.1006/jnca.1996.0014

    Article  Google Scholar 

  • Jury EI (1978) Stability of multidimensional scalar and matrix polynominals. Proc IEEE 66(9):1018–1047. doi:10.1109/PROC.1978.11079

    Article  MathSciNet  Google Scholar 

  • Kaczorek T (1985) Two-dimensional linear system. Springer, Berlin

    Google Scholar 

  • Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical report, Computer Engineering Department, Engineering Faculty, Erciyes University, Turkey

  • Kawamata M, Imakubo J, Higuchi T (1994) Optimal design method of 2-d iir digital filters based on a simple genetic algorithm. In: IEEE international conference image processing, pp 780–784. doi:10.1109/ICIP.1994.413421

  • Kawamata M, Imakubo J, Higuchi T (1995) Optimal design method of separable-denominator two-dimensional digital filters based on a genetic algorithm. Electron Commun Jpn Part III Fundam Electron Sci 78(12):70–80. doi:10.1002/ecjc.4430781208

    Article  Google Scholar 

  • Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, pp 1942–1948. doi:10.1109/ICNN.1995.488968

  • Kenneth VP (1999) An introduction to differential evolution, in new ideas in optimization. McGraw-Hill, New York, pp 79–108

  • Kirkpatrcik S, Gelatt CD, Vecchi PM (1983) Optimization by simulated annealing. Science 220:671–680

    Article  MathSciNet  Google Scholar 

  • Kishida M, Hamada N (1996) Design of 2-d iir filter using the genetic algorithm. IEICE Trans Fundam Electron Commun Comput Sci 79(1):131–133

    Google Scholar 

  • Kockanat S, Karaboga N, Koza T (2012) Image denoising with 2-d fir filter by using artificial bee colony algorithm. In: International symposium on innovations in intelligent systems and applications (INISTA), pp 1–4. doi:10.1109/INISTA.2012.6247041

  • Kuang W, Hua J, Zheng Z, Meng L, Xu Z (2012) Frequency sampling design of 2-d fir filters based on depso. In: 8th international conference on natural computation (ICNC), pp 1119–1122. doi:10.1109/ICNC.2012.6234611

  • Kumar R, Kumar A (2010) Design of two-dimensional infinite impulse response recursive filters using hybrid multiagent particle swarm optimization. Appl Artif Intell Int J 24(4):295–312. doi:10.1080/08839511003715204

    Article  Google Scholar 

  • Liang L, Ahmadi M, Sid-Ahmed M (2003) Design of 2-d iir filters with canonical signed-digit coefficients using genetic algorithm. In: IEEE 46th Midwest symposium on circuits and systems, pp 633–635. doi:10.1109/MWSCAS.2003.1562366

  • Lim JS (1990) Two-dimensional signal and image processing. Prentice Hall, New Jersey

    Google Scholar 

  • Liu JC, Tai YL (2011) Design of 2-d wideband circularly symmetric fir filters by multiplierless high-order transformation. IEEE Trans Circuits Syst I Regul Pap 58(4):746–754. doi:10.1109/TCSI.2010.2078730

    Article  MathSciNet  Google Scholar 

  • Lu WS, Antoniou A (1992) Two-dimensional digital filters. Marcel Dekker, New York

    MATH  Google Scholar 

  • Lu WS, Lee EB (1985) Stability analysis for two-dimensional systems via lyapunov approach. IEEE Trans Circuits Syst 32(1):61–68. doi:10.1109/TCS.1985.1085596

    Article  MathSciNet  MATH  Google Scholar 

  • Lu HC, Tzeng ST (1998) Design of 2-d fir filters using mcclellan transformation with genetic algorithms. In: IEEE international conference on evolutionary computation proceedings, pp 265–270. doi:10.1109/ICEC.1998.699723

  • Lu HC, Tzeng ST (2000) Design of two-dimensional fir digital filters for sampling structure conversion by genetic algorithm approach. Signal Process 80(8):1445–1458. doi:10.1016/S0165-1684(00)00048-7

    Article  Google Scholar 

  • Manuel M, Elias E (2012) Design of sharp 2-d multiplier-less circularly symmetric fir filter using harmony search algorithm and frequency transformation. J Signal Inf Process 3(3):344–351. doi:10.4236/jsip.2012.33044

    Google Scholar 

  • Manuel M, Krishnan R, Elias E (2012) Design of multiplierless 2-d sharp wideband using frm and gsa. Glob J Res Eng Electr Electron Eng 12(5):41–49

  • Mastorakis NE, Gonos IF, Swamy MNS (2003) Design of two-dimensional recursive filters using genetic algorithms. IEEE Trans Circuits Syst I Fundam Theory Appl 50(5):634–639. doi:10.1109/TCSI.2003.811019

    Article  MathSciNet  Google Scholar 

  • McClellan JH (1973) The design of two-dimensional filters by transformation. In: Proceeding 7th annual princeton conference information sciences and systems, pp 247–251

  • Oppenheim AV, Schafer RW (1975) Digital signal processing. Prentice Hall, USA

    MATH  Google Scholar 

  • Oppenheim AV, Willsky AS, Young IT (1983) Signals and systems. Prentice Hall, USA

    MATH  Google Scholar 

  • Oppenheim AV, Schafer RW, Buck JR (1999) Discrete-time signal processing. Prentice Hall, New Jersey

    Google Scholar 

  • Pham DT, Koc E (2010) Design of a two-dimensional recursive filter using the bees algorithm. Int J Autom Comput 7(3):399–402. doi:10.1007/s11633-010-0520-x

    Article  Google Scholar 

  • Pham DT, Ghanbarzadeh A, Koc E, Otri S, Rahim S, Zaidi M (2005) The bees algorithm. Technical Report MEC0501, Manufacturing Engineering Centre, Cardiff University, Cardiff, UK

  • Priemer R (1991) Introductory signal processing. World Scientific, Singapore

    Google Scholar 

  • Proakis JG, Manolakis DG (1996) Digital signal processing. Prentice Hall, New Jersey

    Google Scholar 

  • Proakis JG, Manolakis DK (2007) Digital signal processing principles, algorithms and applications. Pearson Prentice Hall, New Jersey

    Google Scholar 

  • Radecki J, Konrad J, Dubois E (1992) Design of finite wordlength 2-d iir filters using simulated annealing. In: Proceedings 6th European signal processing conference, pp 953–956. doi:10.1.1.50.7699

  • Radecki J, Konrad J, Dubois E (1995) Design of multidimensional finite-wordlength fir and iir filters by simulated annealing. IEEE Trans Circuits Syst II Analog Digit Signal Process 42(6):424–431. doi:10.1109/82.392318

    Article  MATH  Google Scholar 

  • Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) Gsa: a gravitational search algorithm. Inf Sci 179(13):2232–2248. doi:10.1016/j.ins.2009.03.004

    Article  MATH  Google Scholar 

  • Shanks JL, Treitel S, Justice JH (1972) Stability and synthesis of two-dimensional recursive filters. IEEE Trans Audio Electroacoust 20(2):115–128. doi:10.1109/TAU.1972.1162358

    Article  Google Scholar 

  • Sriranganathan D, Bull DR, Redmill DW (1995) Design of 2-d multiplierless fir filters using genetic algorithms. In: 1st International conference on genetic algorithms in engineering systems: innovations and applications (GALESIA), pp 282–286. doi:10.1049/cp:19951063

  • Sriranganathan D, Bull DR, Redmill DW (1996) Low complexity two-dimensional digital filters using unconstrained spt term allocation. In: IEEE international symposium on circuits and systems (ISCAS’96), pp 762–765. doi:10.1109/ISCAS.1996.541837

  • Storn R (1997) Differential evolution: a simple and efficient heuristic strategy for global optimization over continuous spaces. J Glob Optim 11:341–359. doi:10.1023/A:1008202821328

    Article  MathSciNet  MATH  Google Scholar 

  • Stranneby D, Walker W (2004) Digital signal processing and applications. Elsevier, Oxford

    Google Scholar 

  • Strintzis MG (1977) Tests of stability of multidimensional filters. IEEE Trans Circuits Syst 24(8):432–437. doi:10.1109/TCS.1977.1084368

    Article  MathSciNet  MATH  Google Scholar 

  • Su TJ, Yang TC, Tsai WP, Liu JW (2007) Design two-dimensional iir filters based on clonal selection algorithm with singular value decomposition. Res Lett Signal Process 2007:1–5. doi:10.1155/2007/32081

    Article  MathSciNet  Google Scholar 

  • Su TJ, Kuo CH, Tsai WP, Hou CC (2008) A hybrid of clonal selection algorithm and frequency sampling method for designing a 2-d fir filter. In: 4th IEEE international symposium on electronic design, test and applications, pp 274–278. doi:10.1109/DELTA.2008.15

  • Sun J, Fang W, Chen W, Xu W (2008) Design of two-dimensional iir digital filters using an improved quantum-behaved particle swarm optimization algorithm. In: American control conference, pp 2603–2608. doi:10.1109/ACC.2008.4586884

  • Sun J, Fang W, Xu W (2010) A quantum-behaved particle swarm optimization with diversity-guided mutation for the design of two-dimensional iir digital filters. IEEE Trans Circuits Syst II Express Briefs 57(2):141–145. doi:10.1109/TCSII.2009.2038514

    Article  Google Scholar 

  • Thamvichai R, Bose T, Haupt RL (2001) Design of 2-d multiplierless filters using the genetic algorithm. In: Conference record of the thirty-fifth asilomar conference on signals, systems and computers, pp 588–591. doi:10.1109/ACSSC.2001.986991

  • Thamvichai R, Bose T, Haupt RL (2002) Design of 2-d multiplierless iir filters using the genetic algorithm. IEEE Trans Circuits Syst I Fundam Theory Appl 49(6):878–882. doi:10.1109/TCSI.2002.1010045

    Article  Google Scholar 

  • Timmis J, Andrews P, Hart E (2010) On artificial immune systems and swarm intelligence. Swarm Intell 4(4):247–273. doi:10.1007/s11721-010-0045-5

    Article  Google Scholar 

  • Tsai JT, Chou JH, Liu TK, Chen CH (2005) Design of two-dimensional recursive filters by using a novel genetic algorithm. In: IEEE international symposium on circuits and systems, pp 2603–2606. doi:10.1109/ISCAS.2005.1465159

  • Tsai JT, Ho WH, Chou JH (2008) Design of two-dimensional recursive filters by using taguchi-based immune algorithm. IET Signal Process 2(2):110–117. doi:10.1049/iet-spr:20070165

    Article  Google Scholar 

  • Tsai JT, Ho WH, Chou JH (2009) Design of two-dimensional iir digital structure-specified filters by using an improved genetic algorithm. Expert Syst Appl 36(3):6928–6934. doi:10.1016/j.eswa.2008.08.065

    Article  Google Scholar 

  • Tzafestas ST (1986) Multidimensional systems, techniques and applications. Marcel Dekker, New York

    MATH  Google Scholar 

  • Tzeng ST (2004a) Genetic algorithm approach for designing 2-d fir digital filters with 2-d symmetric properties. Signal Process 84(10):1883–1893. doi:10.1016/j.sigpro.2004.06.018

  • Tzeng ST (2004b) Design of 2-d fir digital filters with symmetric properties by genetic algorithm approach. In: IEEE Asia-Pacific conference on circuits and systems, pp 417–420. doi:10.1109/APCCAS.2004.1412784

  • Tzeng ST (2007) Design of 2-d fir digital filters with specified magnitude and group delay responses by ga approach. Signal Process 87(9):2036–2044. doi:10.1016/j.sigpro.2007.01.034

    Article  MATH  Google Scholar 

  • Williams T, Ahmadi M, Hashemian R, Miller WC (2001) Design of high throughput 2-d fir filters using singular value decomposition (svd) and genetic algorithms. In: IEEE Pacific rim conference on communications, computers and signal processing (PACRIM), pp 571–574. doi:10.1109/PACRIM.2001.953697

  • Williams T, Ahmadi M, Miller WC (2005) High throughput rate 2-d fir filter design using singular value decomposition and genetic algorithms. In: Fifth international conference on information, communications and signal processing, pp 574–578. doi:10.1109/ICICS.2005.1689112

  • Williams T, Ahmadi M, Miller WC (2007) Design of 2-d fir and iir digital filters with canonical signed digit coefficients using singular value decomposition and genetic algorithms. Circuits Syst Signal Process 26(1):69–89. doi:10.1007/s00034-005-1015-9

    Article  MATH  Google Scholar 

  • Woods JW (2006) Multidimensional signal, image and video processing and coding. Elsevier, USA

    Google Scholar 

  • Wu LH, Wang YN, Yuan XF (2011) Design of 2-d recursive filters using self-adaptive mutation differential evolution algorithm. Int J Comput Intell Syst 4(4):644–654. doi:10.2991/ijcis.2011.4.4.20

    Article  Google Scholar 

  • Wysocka-Schillak F (2007a) Design of equiripple 2-d linear-phase fir digital filters using genetic algorithm. Numer Methods Appl Lect Notes Comput Sci 4310:263–270. doi:10.1007/978-3-540-70942-8_31

  • Wysocka-Schillak F (2007b) Design of 2-d fir half-band filters using genetic algorithm. In: International symposium on information technology convergence (ISITC), pp 198–202. doi:10.1109/ISITC.2007.17

  • Wysocka-Schillak F (2007c) Design of 2-d iir filters using two error criteria with genetic algorithm. Adapt Nat Comput Algorithms Lect Notes Comput Sci 4431:248–256. doi:10.1007/978-3-540-71618-1_28

  • Wysocka-Schillak F (2008a) Design of 2-d approximately zero-phase separable iir filters using genetic algorithms. Large-Scale Sci Comput Lect Notes Comput Sci 4818:626–633. doi:10.1007/978-3-540-78827-0_72

  • Wysocka-Schillak F (2008b) Design of separable 2-d iir filters with approximately linear phase in the passband using genetic algorithm. In: Conference on human system interactions, pp 66–70. doi:10.1109/HSI.2008.4581410

  • Yang XS (2011) Metaheuristic optimization. Scholarpedia 6(8):11472. doi:10.4249/scholarpedia.11472

  • Yeh KH, Tzeng ST (2008) Design of 2-d fir narrow transition band filters by double transformations using ga approach. Multidimens Syst Signal Process 19(2):199–218. doi:10.1007/s11045-007-0041-0

    Article  MATH  Google Scholar 

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Acknowledgments

The authors are indebted to the reviewers for their constructive suggestions which significantly helped in improving the quality of this paper. This work was supported by Research Fund of the Erciyes University. Project Number: FDK-2012-4156.

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  1. Sivas Vocational School, Electronic Communication Technology, Cumhuriyet University, 58140, Sivas, Turkey

    Serdar Kockanat

  2. Department of Electrical-Electronics Engineering, Faculty of Engineering, Erciyes University, 38039 , Melikgazi, Kayseri, Turkey

    Nurhan Karaboga

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Kockanat, S., Karaboga, N. The design approaches of two-dimensional digital filters based on metaheuristic optimization algorithms: a review of the literature. Artif Intell Rev 44, 265–287 (2015). https://doi.org/10.1007/s10462-014-9427-1

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