Advertisement

Pure and Applied Geophysics

, Volume 176, Issue 1, pp 335–344 | Cite as

Comparing Signal Waveforms and Their Use in Estimating Signal Lag Time

  • Alexey I. ChulichkovEmail author
  • Sergey N. Kulichkov
  • Nadezda D. Tsybulskaya
  • Elena V. Golikova
Article
  • 54 Downloads

Abstract

Mathematical methods are proposed for comparing the waveforms of signals with amplitudes distorted by unknown monotonic transformations and random noise. These methods are based on solving the problems of the best approximation of the signal under analysis to signals of a specified class and used in estimating the lag time of one fragment of signal with respect to another. Such problems arise, for example, in determining the direction of propagation of a sound wave in the atmosphere. The solution to this problem is based on the assumption that the conditions of the signal detection are different at different spatial points; as a result, the measured signals differ not only in their lag time, but also in nonlinear distortions, such that only the general waveform of the signal is preserved: if the amplitude of one signal is the result of a strictly monotonic transformation of the amplitude of another signal, then their waveforms are equivalent. In addition, the measurements are accompanied by an additive noise with an unknown dispersion.

Keywords

Signal waveform Lag time Estimate of signal parameters/best approximation problem 

Notes

Acknowledgements

This work was supported by the Russian Foundation for Basic Research (projects nos. 17-07-00832 and 18-05-00576) and the program of the Presidium of Russian Academy of Science no. 56.

References

  1. Averbuch, G., Assink, J. D., Smets, P. S. M., & Evers, L. G. (2018). Extracting low signal-to-noise ratio events with the Hough transform from sparse array data. Geophysics, 83, WC43-WC51.  https://doi.org/10.1190/geo2017-0490.1.CrossRefGoogle Scholar
  2. Bai, X. (2007). Heat kernel analysis on graphs. Ph.D. Thesis, The University of York.Google Scholar
  3. Belkin, M., & Niyogi, P. (2001). Laplacian eigenmaps and spectral techniques for embedding and clustering. Advances in Neural Information Processing Systems, 14, 585–591.Google Scholar
  4. Brianskiy, S. A., Sidyakin, S. V., & Vizilter, Y. V. (2015). Orientation spectrum algorithm development. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences.  https://doi.org/10.5194/isprsarchives-XL-5-W6-13-2015.
  5. Coifman, R., & Lafon, S. (2006). Diffusion maps. Applied and Computational Harmonic Analysis, 21(1), 5–30.CrossRefGoogle Scholar
  6. Coifman, R., Lafon, S., Maggioni, M., Keller, Y., Szlam, A., Warner, F., et al. (2006). Geometries of sensor outputs, inference and information processing. Storage and Retrieval for Image and Video Databases.  https://doi.org/10.1117/12.669723
  7. Dougherty, E. R. (1989). The dual representation of gray-scale morphological filters. Computer Vision, Graphics, & Image Processing.  https://doi.org/10.1109/CVPR.1989.37846.
  8. de Goes, F., Goldenstein, S., & Velho, L. (2008). A hierarchical segmentation of articulated bodies. Computer Graphics Forum. http://dblp.unitrier.de/db/journals/cgf/cgf27.html\(\sharp\)GoesGV08Google Scholar
  9. Gonzalez, R. C., & Woods, R. E. (2002). Digital Image Processing (2nd ed.). Upper Saddle River: Prentice-Hall.Google Scholar
  10. Gori, M., Maggini, M., & Sarti, L. (2005). Exact and approximate graph matching using random walks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27, 1100–1111.  https://doi.org/10.1109/TPAMI.2005.138.
  11. Hough, P. V. C. (1962). Method and means for recognizing complex patterns (p. 3069654). Patent no.: US.Google Scholar
  12. Huang, T. S. (1975). Picture Processing and Digital Filtering. Berlin: Springer.CrossRefGoogle Scholar
  13. Hussain, M., Chen, D., Cheng, A., Wei, H., & Stanley, D. (2013). Change detection from remotely sensed images: From pixel-based to objectbased ap-proaches. ISPRS Journal of Photogrammetry and Remote Sensing, 80, 91–106.CrossRefGoogle Scholar
  14. Kulichkov, S. N., Chulichkov, A. I., & Demin, D. S. (2011). On experience in using the method of morphological data analysis in atmospheric acoustics. Izvestiya, Atmospheric and Oceanic Physics, 47, 154–165.  https://doi.org/10.1134/S000143381102006X.CrossRefGoogle Scholar
  15. Kulichkov, S. N., Tsybulskaya, N. D., Chunchuzov, I. P., Gordinb, V. A., Bykovb, Ph L, & Chulichkova, A. I. (2017). Studying internal gravity waves generated by atmospheric fronts over the Moscow region. Izvestiya, Atmospheric and Oceanic Physics, 53, 402–412.  https://doi.org/10.1134/S0001433817040077.CrossRefGoogle Scholar
  16. La, S., Chandra, M., Upadhyay, G. K., & Gupta, D. (2011). Removal of additive Gaussian noise by complex double density dual tree discrete wavelet transform. MIT International Journal of Electronics and Communication Engineering, 1(1), 8–16.Google Scholar
  17. Lafon, S., Keller, Y., & Coifman, R. R. (2006). Data fusion and multicue data matching by diffusion maps. IEEE Transactions on Pattern Analysis and Machine Intelligence, 28, 1784–1797.  https://doi.org/10.1109/TPAMI.2006.223.CrossRefGoogle Scholar
  18. Lafon, S. (2004). Diffusion maps and geometric harmonics. Ph.D. Thesis, Department of Mathematics and Applied Mathematics, Yale University.Google Scholar
  19. Mohideen, S. K. (2012). Denoising of images using complex wavelet transform. International Journal of Advanced Scientific and Technical Research, 1(2), 176–184.Google Scholar
  20. Pyt’ev, Yu P. (1993). Morphological image analysis. Pattern Recognition Image Analysis, 3, 19–28.Google Scholar
  21. Pyt’ev, Yu P. (1997). The morphology of color (multispectral) images. Pattern Recognition Image Analysis, 7, 467–473.Google Scholar
  22. Pyt’ev, Yu P. (1998). Methods of morphological analysis of color images. Pattern Recognition Image Analysis, 8, 517–531.Google Scholar
  23. Pyt’ev, Yu P, Kalinin, A. V., Loginov, E. O., & Smolovik, V. V. (1998). On the problem of object detection by black-and-white and color morphologies. Pattern Recognition Image Analysis, 8, 532–536.Google Scholar
  24. Pyt’ev, Yu P, & Zhivotnikov, G. S. (2004). On the methods of possibility theory for morphological image analysis. Pattern Recognition Image Analysis, 14, 60–71.Google Scholar
  25. Pyt’ev, Yu P, & Chulichkov, A. I. (2010). Methods of Morphological Image Analysis. Moscow: Fizmatlit. (in Russian).Google Scholar
  26. Serra, J. (1982). Image Analysis and Mathematical Morphology. London: Academic Press.Google Scholar
  27. Urbach, E. R., Roerdink, J. B., & Wilkinson, M. H. (2007). Connected shape-size pattern apectra for rotation and scale-invariant classification of gray-scale images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29(2), 272–285.CrossRefGoogle Scholar
  28. Vizilter, Yu V, Gorbatsevich, V. S., Rubis, A Yu., & Zheltov, S Yu. (2014). Shape-based image matching using heat kernels and diffusion maps. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 40, 357.  https://doi.org/10.5194/isprsarchives-XL-3-357-2014.CrossRefGoogle Scholar
  29. Zhivotnikov, G. S., Pyt’ev, Yu P, & Falomkin, I. I. (2005). On the filtering algorithm for images. Pattern Recognition Image Analysis, 3(1), 19–28.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Alexey I. Chulichkov
    • 1
    Email author
  • Sergey N. Kulichkov
    • 2
  • Nadezda D. Tsybulskaya
    • 2
  • Elena V. Golikova
    • 2
  1. 1.Moscow State UniversityMoscowRussia
  2. 2.Obukhov Institute of Atmospheric Physics, Russian Academy of SciencesMoscowRussia

Personalised recommendations