Efficient compression of QRS complexes using Hermite expansion

IEEE Transactions on Signal Processing

Volumn 60, Issue 2, 2012, Pages 947-955

  Sandryhaila, Aliaksei ^a   Saba, Samir ^b   Püschel, Markus ^c   Kovacevic, Jelena ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b UNIVERSITY OF PITTSBURGH MEDICAL CENTER   (United States)

^c ETH ZURICH   (Switzerland)

Author keywords

Compression; ECG signal; Hermite function; Hermite transform; orthogonal polynomials; QRS complex; signal model

Indexed keywords

ECG SIGNAL; HERMITE FUNCTIONS; HERMITE TRANSFORMS; ORTHOGONAL POLYNOMIAL; QRS COMPLEXES; SIGNAL MODELS;

COMPACTION; COSINE TRANSFORMS; DISCRETE COSINE TRANSFORMS; DISCRETE FOURIER TRANSFORMS; DISCRETE WAVELET TRANSFORMS; ELECTROCARDIOGRAPHY; ORTHOGONAL FUNCTIONS;

ALGORITHMS;

EID: 84855960358     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2011.2173336     Document Type: Article

References (26)

1. P. Libby, R. O. Bonow, D. L. Mann, and D. P. Zipes, Braunwald's Heart Disease: A Textbook of Cardiovascular Medicine, Single Volume,8th ed. New York: Saunders, 2007.
2. A. Sandryhaila, J. Kovacevic, and M. Püschel, "Compression of QRS complexes using Hermite expansion," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process., 2011, pp. 581-584.
3. M. Püschel and J. M. F. Moura, "Algebraic signal processing theory" [Online]. Available: Http://arxiv.org/abs/cs.IT/0612077
4. A. Sandryhaila, "Algebraic Signal Processing: Modeling and Subband Analysis," Ph.D., Carnegie Mellon Univ., Pittsburgh, PA, 2010.
5. A. Sandryhaila, J. Kovacevic, and M. Püschel, "Algebraic signal processing theory: 1-D nearest-neighbor models," IEEE Trans. Signal Process., submitted for publication.
6. P. Laguna, R. Jané, S. Olmos, N. V. Thakor, H. Rix, and P. Caminal, "Adaptive estimation of QRS complex wave features of ECG signal by the Hermite model," J. Med. Biol. Eng. Comput., vol. 34, no. 1, pp. 58-68, 1996. (Pubitemid 26058861)
7. L. Sörnmo, P. O. Börjesson, P. Nygards, and O. Pahlm, "A method for evaluation of QRS shape features using a mathematical model for the ECG," IEEE Trans. Biomed. Eng., vol. BME-28, no. 10, pp. 713-717, 1981.
8. L. R. L. Conte, R. Merletti, and G. V. Sandri, "Hermite expansion of compact support waveforms: Applications to myoelectric signals," IEEE Trans. Biomed. Eng., vol. 41, no. 12, pp. 1147-1159, 1994. (Pubitemid 24381462)
9. M. Lagerholm, C. Peterson, G. Braccini, L. Edenbranhdt, and L. Sörnmo, "Clustering ECG complexes using Hermite functions and self-organizing maps," IEEE Trans. Biomed. Eng., vol. 47, no. 7, pp. 838-848, 2000. (Pubitemid 30421818)
10. G. Szegö, Orthogonal Polynomials, 3rd ed. New York: Amer. Math. Soc. Colloq., 1967.
11. R. Askey, Orthogonal Polynomials and Special Functions. Philadelphia, PA: SIAM, 1966.
12. B. S. Kashin and A. A. Saakyan, Orthogonal Series. New York: Amer. Math. Soc., 1989.
13. W. Gautschi, Orthogonal Polynomials: Computation and Approximation. Oxford, U.K.: Oxford Univ. Press, 2004.
14. M. Püschel, "Cooley-Tukey FFT like algorithms for the DCT," Proc. ICASSP, vol. 2, pp. 501-504, 2003.
15. M. Püschel and J. M. F. Moura, "The algebraic approach to the discrete cosine and sine transforms and their fast algorithms," SIAM J. Comput., vol. 32, no. 5, pp. 1280-1316, 2003.
16. M. Püschel and J. M. F. Moura, "Algebraic signal processing theory: Foundation and 1-D time," IEEE Trans. Signal Process., vol. 56, no. 8, pp. 3572-3585, 2008.
17. M. Püschel and J. M. F. Moura, "Algebraic signal processing theory: 1-D space," IEEE Trans. Signal Process., vol. 56, no. 8, pp. 3586-3599, 2008.
18. M. Püschel and J. M. F. Moura, "Algebraic signal processing theory: Cooley-Tukey type algorithms for DCTs and DSTs," IEEE Trans. Signal Process., vol. 56, no. 4, pp. 1502-1521, 2008. (Pubitemid 351493845)
19. J.-B. Martens, "The Hermite transform-Theory," IEEE Trans. Acoust., Speech, Signal Process., vol. 38, no. 9, pp. 1595-1605, 1990.
20. J.-B. Martens, "The Hermite transform-Applications," IEEE Trans. Acoust., Speech, Signal Process., vol. 38, no. 9, pp. 1607-1618, 1990.
21. A. Jerri, Integral and Discrete Transforms with Applications and Error Analysis. Boca Raton, FL: CRC, 1992.
22. J. R. Driscoll, D. M. Healy, Jr,, and D. Rockmore, "Fast discrete polynomial transforms with applications to data analysis for distance transitive graphs," SIAM J. Comput., vol. 26, pp. 1066-1099, 1997. (Pubitemid 127599137)
23. A. Sandryhaila, J. Kovacevic, and M. Püschel, "Algebraic signal processing theory: Cooley-Tukey type algorithms for polynomial transforms based on induction," SIAM J. Matrix Analysis Appl., vol. 32, no. 2, pp. 364-384, 2011.
24. S. Mallat, A Wavelet Tour of Signal Processing: The Sparse Way, 3rd ed. New York: Academic, 2008.
25. MIT-BIH ECG Compression Test Database [Online]. Available: Http:// www.physionet.org/physiobank/database/cdb
26. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.