Journal of Signal Processing Systems

, Volume 64, Issue 2, pp 205–221 | Cite as

Localizing Lung Sounds: Eigen Basis Decomposition for Localizing Sources Within a Circular Array of Sensors

  • S. M. A. SalehinEmail author
  • Thushara D. Abhayapala


Lung disorders or injury can result in changes in the production of lung sounds both spectrally and regionally. Localizing these lung sounds can provide information to the extent and location of the disorder. Difference in arrival times at a set of sensors and triangulation were previously proposed for acoustic imaging of the chest. We propose two algorithms for acoustic imaging using a set of eigen basis functions of the Helmholtz wave equation. These algorithms remove the sensor location contribution from the multi sensor recordings using either an orthogonality property or a least squares based estimation after which a spatial minimum variance (MV) spectrum is applied to estimate the source locations. The use of these eigen basis functions allows possible extension to a lung sound model consisting of layered cylindrical media. Theoretical analysis of the relationship of resolution to frequency and noise power was derived and simulations verified the results obtained. Further, a Nyquist’s criteria for localizing sources within a circular array shows that the radius of region where sources can be localized is inversely proportional to the frequency of sound.The resolution analysis and modified Nyquist criteria can be used for determining the number of sensors required at a given noise level, for a required resolution, frequency range, and radius of region for which sources need to be localized.


Localization Lung sounds Helmholtz equation Basis decomposition Cylindrical harmonics Nyquist’s criteria Resolution 


  1. 1.
    Ward, D. B., & Williamson, R. C. (1999). Beamforming for a source located in the interior of a sensor array. In Proceedings of the fifth international symposium on signal processing and its applications, 1999. ISSPA ’99 (Vol. 2, pp. 873–876). doi: 10.1109/ISSPA.1999.815810.
  2. 2.
    Moussavi, Z. (2007). Acoustic mapping and imaging of thoracic sounds. In Fundamentals of respiratory sounds and analysis (Ch. 8, pp. 51–52). Morgan and Claypool.Google Scholar
  3. 3.
    Mansy, H. A., Hoxie, S. J., Warren, W. H., Balk, R. A., Sandler, R. H., & Hassaballa, H. A. (2004). Detection of pneumothorax by computerized breath sound analysis. Chest, 126(4), 881S.Google Scholar
  4. 4.
    Kompis, M., Pasterkamp, H., & Wodicka, G. R. (2001). Acoustic imaging of the human chest. Chest, 120(4), 1309–1321. doi: 10.1378/chest.120.4.1309.CrossRefGoogle Scholar
  5. 5.
    Charleston-Villalobos, S., Cortés-Rubiano, S., González-Camerena, R., Chi-Lem, G., & Aljama-Corrales, T. (2004). Respiratory acoustic thoracic imaging (rathi): Assessing deterministic interpolation techniques. Medical & Biological Engineering & Computing, 42(5), 618–626.CrossRefGoogle Scholar
  6. 6.
    Charleston-Villalobos, S., Gonzalez-Camarena, R., Chi-Lem, G., & Aljama-Corrales, T. (2007). Acoustic thoracic images for transmitted glottal sounds. In Engineering in medicine and biology society, 2007. EMBS 2007. 29th annual international conference of the IEEE (pp. 3481–3484). doi: 10.1109/IEMBS.2007.4353080.
  7. 7.
    Harris, F. J. (1978). On the use of windows for harmonic analysis with the discrete fourier transform. Proceedings of the IEEE, 66(1), 51–83.CrossRefGoogle Scholar
  8. 8.
    Murphy, Jr., R. L. H. (1996). Method and apparatus for locating the origin of intrathoracic sounds. U.S. patent, 729,272.Google Scholar
  9. 9.
    McKee, A. M., & Goubran, R. A. (2005). Sound localization in the human thorax. In Instrumentation and measurement technology conference, 2005. IMTC 2005. Proceedings of the IEEE (Vol. 1, pp. 117–122). doi: 10.1109/IMTC.2005.1604082.
  10. 10.
    Ozer, M. B., Acikgoz, S., Royston, T. J., Mansy, H. A., & Sandler, R. (2007). Boundary element model for simulating sound propagation and source localization within the lungs. Journal of the Acoustical Society of America, 122(1), 657–661.CrossRefGoogle Scholar
  11. 11.
    Barshinger, J. N., & Rose, J. L. (2004). Guided wave propagation in an elastic hollow cylinder coated with a viscoelastic material. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 51(11), 1547–1556. doi: 10.1109/TUFFC.2004.1367496.CrossRefGoogle Scholar
  12. 12.
    Valle, C., Qu, J., & Jacobs, L. J. (1999). Guided circumferential waves in layered cylinders. International Journal of Engineering Science, 37(11), 1369–1387.CrossRefGoogle Scholar
  13. 13.
    Yao, G.-J., Wang, K.-X., Ma, J., & White, J. E. (2005). Sh wavefields in cylindrical double-layered elastic media excited by a shear stress source applied to a borehole wall. Journal of Geophysics and Engineering, 2(2), 169–175. Scholar
  14. 14.
    Abhayapala, T. D. (2006). Broadband source localization by modal space processing. In S. Chandran (Ed.), Advances in direction-of-arrival estimation (Ch. 4, pp. 71–86). Norwood: Artech House.Google Scholar
  15. 15.
    Wodicka, G., Stevens, K., Golub, H., Cravalho, E., & Shannon, D. (1989). A model of acoustic transmission in the respiratory system. IEEE Transactions on Biomedical Engineering, 36(9), 925–934.CrossRefGoogle Scholar
  16. 16.
    Garbacz, R., & Pozar, D. (1982). Antenna shape synthesis using characteristic modes. IEEE Transactions on Antennas and Propagation [legacy, pre-1988], 30(3), 340–350.CrossRefGoogle Scholar
  17. 17.
    Harackiewicz, F., & Pozar, D. (1986). Optimum shape synthesis of maximum gain omnidirectional antennas. IEEE Transactions on Antennas and Propagation [legacy, pre-1988], 34(2), 254–258.CrossRefGoogle Scholar
  18. 18.
    Abhayapala, T. D., Kennedy, R. A., & Williamson, R. C. (2000). Nearfield broadband array design using a radially invariant modal expansion. Journal of the Acoustical Society of America, 107, 392–403.CrossRefGoogle Scholar
  19. 19.
    Ward, D. B., & Abhayapala, T. D. (2004). Range and bearing estimation of wideband sources using an orthogonal beamspace processing structure. In Proc. IEEE int. conf. acoust., speech, signal processing, ICASSP 2004 (Vol. 2(2), pp. 109–112).Google Scholar
  20. 20.
    Abhayapala, T. D., & Ward, D. B. (2002). Theory and design of high order sound field microphones using spherical microphone array. In IEEE international conference on acoustics, speech, and signal processing, 2002. Proceedings. (ICASSP ’02) (Vol. 2, pp. 1949–1952).Google Scholar
  21. 21.
    Ward, D. B., & Abhayapala, T. D. (2001). Reproduction of a plane-wave sound field using an array of loudspeakers. IEEE Transactions on Speech and Audio Processing, 9(6), 697–707. doi: 10.1109/89.943347.CrossRefGoogle Scholar
  22. 22.
    Colton, D., & Kress, R. (1998). Inverse acoustic and electromagnetic scattering theory (2nd ed.). New York: Springer.zbMATHGoogle Scholar
  23. 23.
    Jones, H. M., Kennedy, R. A., & Abhayapala, T. D. (2002). On dimensionality of multipath fields: Spatial extent and richness. In IEEE international conference on acoustics, speech, and signal processing, 2002. Proceedings. (ICASSP ’02) (Vol. 3, pp. 2837–2840). doi: 10.1109/ICASSP.2002.1005277.
  24. 24.
    Schmidt, R. (1986). Multiple emitter location and signal parameter estimation. IEEE Transactions on Antennas and Propagation [legacy, pre-1988], 34(3), 276–280.CrossRefGoogle Scholar
  25. 25.
    Owsley, N. L. (1985). Sonar array processing. In S. Haykin (Ed.), Array signal processing. Englewood Cliffs: Prentice Hall.Google Scholar
  26. 26.
    Stewart, G. W. (1977). On the perturbation of pseudo-inverses, projections and linear least squares problems. SIAM Review, 19(4), 634–662. Scholar
  27. 27.
    Li, F., & Vaccaro, R. J. (1992). Performance degradation of doa estimators due to unknown noise fields. IEEE Transactions on Signal Processing, 40(3), 686–690. doi: 10.1109/78.120813.CrossRefGoogle Scholar
  28. 28.
    Oppenheim, A. V. (1993). Array signal processing: Concepts and techniques. Englewood Cliffs: PTR Prentice Hall.Google Scholar
  29. 29.
    Dudgeon, D. E. (1977). Fundamentals of digital array processing. Proceedings of the IEEE, 65(6), 898–904.CrossRefGoogle Scholar
  30. 30.
    Kummer, W. H. (1992). Basic array theory. Proceedings of the IEEE, 80(1), 127–140. doi: 10.1109/5.119572.CrossRefGoogle Scholar
  31. 31.
    Heinz, G., Peterson, L. J., Johnson, R. W., & Kerk, C. J. (2003). Exploring relationships in body dimensions. Journal of Statistics Education, 11(2).Google Scholar
  32. 32.
    Bresler, Y., & Macovski, A. (1986). On the number of signals resolvable by a uniform linear array. IEEE Transactions on Acoustics, Speech, and Signal Processing, 34(6), 1361–1375 (see also IEEE Transactions on Signal Processing).Google Scholar
  33. 33.
    Li, F., Liu, H., & Vaccaro, R. J. (1993). Performance analysis for doa estimation algorithms: Unification, simplification, and observations. IEEE Transactions on Aerospace and Electronic Systems, 29(4), 1170–1184. doi: 10.1109/7.259520.CrossRefGoogle Scholar
  34. 34.
    Rice, D. A. (1983). Sound speed in pulmonary parenchyma. Journal of Applied Physiology, 54(1), 304–308.Google Scholar
  35. 35.
    Gavriely, N., Palti, Y., & Alroy, G. (1981). Spectral characteristics of normal breath sounds. Journal of Applied Physiology, 50(2), 307–314.Google Scholar
  36. 36.
    Gavriely, N., Nissan, M., Rubin, A. H., & Cugell, D. W. (1995). Spectral characteristics of chest wall breath sounds in normal subjects. Thorax, 50(12), 1292–1300.CrossRefGoogle Scholar
  37. 37.
    Royston, T. J., Zhang, X., Mansy, H. A., & Sandler, R. H. (2002). Modeling sound transmission through the pulmonary system and chest with application to diagnosis of a collapsed lung. Journal of the Acoustical Society of America, 111(4), 1931–1946.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Applied Signal Processing Group, Research School of Information Sciences and Engineering (RSISE)Australian National UniversityCanberraAustralia
  2. 2.National ICT AustraliaCanberraAustralia

Personalised recommendations