Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Efficient coding of natural sounds

Abstract

The auditory system encodes sound by decomposing the amplitude signal arriving at the ear into multiple frequency bands whose center frequencies and bandwidths are approximately exponential functions of the distance from the stapes. This organization is thought to result from the adaptation of cochlear mechanisms to the animal's auditory environment. Here we report that several basic auditory nerve fiber tuning properties can be accounted for by adapting a population of filter shapes to encode natural sounds efficiently. The form of the code depends on sound class, resembling a Fourier transformation when optimized for animal vocalizations and a wavelet transformation when optimized for non-biological environmental sounds. Only for the combined set does the optimal code follow scaling characteristics of physiological data. These results suggest that auditory nerve fibers encode a broad set of natural sounds in a manner consistent with information theoretic principles.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Auditory filters derived from efficient coding of different natural sounds classes.
Figure 2: Filter power spectra.
Figure 3: Efficient coding of a combined sound ensemble.
Figure 4: Principal components of natural sounds.
Figure 5: Control analyses.
Figure 6: Time–frequency analysis.
Figure 7: Comparison of filter population characteristics to physiological data.
Figure 8: Predicted bandwidth versus frequency curves assuming equalization of spectral power across bandwidths.

Similar content being viewed by others

References

  1. Barlow, H. B. Possible principles underlying the transformation of sensory messages. in Sensory Communication (ed. Rosenbluth, W. A.) 217–234 (MIT Press, Cambridge, 1961).

    Google Scholar 

  2. Kiang, N. Y.-S., Watanabe, T., Thomas, E. C. & Clark, L. F. Discharge Patterns of Single Fibers in the Cat's Auditory Nerve (MIT Press, Cambridge, Massachusetts, 1965).

    Google Scholar 

  3. Evans, E. F. Frequency selectivity at high signal levels of single units in cochlear nerve and nucleus. in Psychophysics and Physiology of Hearing (eds. Evans, E. F. & Wilson, J. P.) 185–192 (Academic, New York, 1977).

    Google Scholar 

  4. de Boer, E. & de Jongh, H. R. On cochlear encoding: potentialities and limitations of the reverse-correlation technique. J. Acoust. Soc. Am. 63, 115–135 (1978).

    Article  CAS  PubMed  Google Scholar 

  5. Carney, L. H. & Yin, T. C. T. Temporal coding of resonances by low-frequency auditory nerve fibers: single-fiber responses and a population model. J. Neurophys. 60, 1653–1677 (1988).

    Article  CAS  Google Scholar 

  6. Field, D. J. Relations between the satistics of natural images and the response properties of cortical cells. J. Optical Soc. Am. A 12, 2379–2394 (1987).

    Article  Google Scholar 

  7. Field, D. J. What is the goal of sensory coding? Neural Comp. 6, 559–601 (1994).

    Article  Google Scholar 

  8. Linsker, R. Perceptual neural organization—some approaches based on network models and information-theory. Annu. Rev. Neuro. 13, 257–281 (1990).

    Article  CAS  Google Scholar 

  9. Atick, J. J. Could information-theory provide an ecological theory of sensory processing. Network Comp. Neural Sys. 3, 213–251 (1992).

    Article  Google Scholar 

  10. Rieke, F., Bodnar, D. A. & Bialek, W. Naturalistic stimuli increase the rate and efficiency of information transmission by primary auditory afferents. Proc. R. Soc. Lond. B Biol. Sci. 262, 259–265 (1995).

    Article  CAS  Google Scholar 

  11. Olshausen, B. A. & Field, D. J. Emergence of simple-cell receptive-field properties by learning a sparse code for natural images. Nature 381, 607–609 (1996).

    Article  CAS  Google Scholar 

  12. Bell, A. J. & Sejnowski, T. J. The 'independent components' of natural scenes are edge filters. Vision Res. 37, 3327–3338 (1997).

    Article  CAS  PubMed  Google Scholar 

  13. van Hateren, J. H. & Ruderman, D. L. Independent component analysis of natural images sequences yield spatiotemporal filters similar to simple cells in primary visual cortex. Proc. R. Soc. Lond. B Biol. Sci. 265, 2315–2320 (1998).

    Article  CAS  Google Scholar 

  14. Lewicki, M. S. & Olshausen, B. A. A probabilistic framework for the adaptation and comparison of image codes. J. Opt. Soc. Am. A 16, 1587–1601 (1999).

    Article  Google Scholar 

  15. Comon, P. Independent component analysis, a new concept? Signal Process. 36, 287–314 (1994).

    Article  Google Scholar 

  16. Bell, A. J. & Sejnowski, T. J. An information maximization approach to blind separation and blind deconvolution. Neural Comp. 7, 1129–1159 (1995).

    Article  CAS  Google Scholar 

  17. Laughlin, S. B. Matching coding to scenes to enhance coding efficiency. in Physical and Biological Processing of Images (eds. Braddick, O. J. & Sleigh, A. C.) 42–72 (Springer, Berlin, 1983).

    Chapter  Google Scholar 

  18. Bell, A. J. & Sejnowski, T. J. Learning the higher-order structure of a natural sound. Netw. Comput. Neural Syst. 7, 261–267 (1996).

    Article  CAS  Google Scholar 

  19. Irino, T. & Patterson, R. D. A time-domain, level-dependent auditory filter: the gammachirp. J. Acoust. Soc. Am. 101, 412–419 (1997).

    Article  Google Scholar 

  20. Zoharian, A. S. & Rothenberg, M. Principal-component analysis for low redundancy encoding of speech spectra. J. Acoust. Soc. Am. 69, 832–845 (1981).

    Article  Google Scholar 

  21. Mallat, S. A Wavelet Tour of Signal Processing 2nd edn. (Academic, London, 1999).

    Google Scholar 

  22. Lewicki, M. S. & Sejnowski, T. J. Learning overcomplete representations. Neural Comput. 12, 337–365 (2000).

    Article  CAS  PubMed  Google Scholar 

  23. Moore, B. C. J. (ed.) Frequency Selectivity in Hearing (Academic, London, 1986).

    Book  Google Scholar 

  24. Evans, E. F. Cochlear nerve and cochlear nucleus. in Handbook of Sensory Physiology Vol. 5/2 (eds. Keidel, W. D. & Neff, W. D.) 1–108 (Springer, Berlin, 1975).

    Google Scholar 

  25. Rhode, W. S. & Smith, P. H. Characteristics of tone-pip response patterns in relationship to spontaneous rate in cat auditory nerve fibers. Hearing Res. 18, 159–168 (1985).

    Article  CAS  Google Scholar 

  26. Voss, R. F. & Clarke, J. 1/f noise in music and speech. Nature 258, 317–318 (1975).

    Article  Google Scholar 

  27. Attias, H. & Schreiner, C. Low-order temporal statistics of natural sounds. in Advances in Neural and Information Processing Systems Vol. 9 (Morgan Kaufmann, San Mateo, California, 1997).

    Google Scholar 

  28. Furth, P. M. & Andreou, A. G. A design framework for low power analog filter banks. IEEE Trans. Circuits Syst. I 42, 966–971 (1995).

    Article  Google Scholar 

  29. Lewicki, M. S. & Sejnowski, T. J. Coding time-varying signals using sparse, shift-invariant representations. in Advances in Neural Information Processing Systems Vol. 11, 730–736 (MIT Press, Cambridge, Massachusetts, 1999).

    Google Scholar 

  30. Brenner, N., Bialek, W. & van Steveninck, R. D. Adaptive rescaling maximizes information transmission. Neuron 26, 695–702 (2000).

    Article  CAS  PubMed  Google Scholar 

  31. Schwartz, O. & Simoncelli, E. P. Natural signal statistics and sensory gain control. Nat. Neurosci. 4, 819–825 (2001).

    Article  CAS  PubMed  Google Scholar 

  32. Pearlmutter, B. A. & Parra, L. C. A context-senstive generalization of ICA. in Proceedings of the International Conference on Neural Information Processing 151–157 (Springer, Singapore, 1996).

    Google Scholar 

  33. Cardoso, J.-F. Infomax and maximum likelihood for blind source separation. IEEE Signal Process. Lett. 4, 109–111 (1997).

    Article  Google Scholar 

  34. Emmons, L. H., Whitney, B. M. & Ross, D. L. Sounds of the neotropical rainforest mammals [audio CD] (Library of Natural Sounds, Cornell Laboratory of Ornithology, Ithaca, New York, 1997).

  35. Amari, S., Cichocki, A. & Yang, H. H. A new learning algorithm for blind signal separation. in Advances in Neural and Information Processing Systems Vol. 8, 757–763 (Morgan Kaufmann, San Mateo, California, 1996).

    Google Scholar 

  36. Box, G. E. P. & Tiao, G. C. Bayesian Inference in Statistical Analysis (Addison-Wesley, Reading, Massachusetts, 1973).

    Google Scholar 

  37. Mallat, S. G. A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989).

    Article  Google Scholar 

  38. Simoncelli, E. P. & Adelson, E. H. Noise removal via Bayesian wavelet coring in Proceedings of the 3rd IEEE International Conference on Image Processing Vol. 1, 379–382 (IEEE Signal Processing Society, Lausanne, 1996).

    Chapter  Google Scholar 

Download references

Acknowledgements

The author thanks C. Olson, B. Olshausen and L. Holt for discussions and feedback on the manuscript.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michael S. Lewicki.

Ethics declarations

Competing interests

The author declares no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lewicki, M. Efficient coding of natural sounds. Nat Neurosci 5, 356–363 (2002). https://doi.org/10.1038/nn831

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nn831

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing