Skip to main content

A Review: Relationship Between Response Properties of Visual Neurons and Advances in Nonlinear Approximation Theory

  • Conference paper
Advances in Neural Networks – ISNN 2005 (ISNN 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3496))

Included in the following conference series:

  • 981 Accesses

Abstract

In this review, we briefly introduce the ’sparse coding’ strategy employed in the sensory information processing system of mammals, and reveal the relationship between the strategy and some new advances in nonlinear approximation theory.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Olshausen, B.A., Field, D.J.: Sparse Coding of Sensory Inputs. Current Opinion in Neurobiology 14, 481–487 (2004)

    Article  Google Scholar 

  2. Olshausen, B.A., Field, D.J.: Sparse Coding With An Overcomplete Basis Set: a Strategy Employed By V1? Vision Res. 37, 3311–3325 (1997)

    Article  Google Scholar 

  3. Simoncelli, E.P., Olshausen, B.A.: Natural Image Statistics and Neural Representation. Annu. Rev. Neurosci 24, 1193–1216 (2001)

    Article  Google Scholar 

  4. DeVore, R.A.: Nonlinear Approximation. Acta Numerica. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  5. 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  Google Scholar 

  6. Van Hateren, J.H., Van Der Schaaf, A.: Independent Component Filters of Natural Images Compared with Simple Cells in Primary Visual Cortex. Proc. R. Soc. Lond. B Biol. Sci. 265, 359–366 (1998)

    Article  Google Scholar 

  7. Bell, A.J., Sejnowski, T.J.: The Independent Components. of Natural Scenes Are Edge Filters. Vision Res. 37, 3327–3338 (1997)

    Article  Google Scholar 

  8. Hyvarinen, A., Hoyer, P.O.: Emergence of Phase and Shift Invariant Features by Decomposition of Natural Images into Independent Feature Subspaces. Neural Comput 12, 1705–1720 (2000)

    Article  Google Scholar 

  9. Candès, E.J.: Harmonic Analysis of Neural Networks. Appl. Comput. Harmon. Anal. 6, 197–218 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  10. Donoho, D.L.: Orthonormal Ridgelet and Straight Singularities. SIAM J. Math. Anal. 31, 1062–1099 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  11. Candès, E.J.: On the Representation of Mutilated Sobolev Functions. SIAM J. Math. Anal. l, 2495–2509 (1999)

    Google Scholar 

  12. Shan, T., Jiao, L.C., Feng, X.C.: Ridgelet Frame. In: Campilho, A.C., Kamel, M.S. (eds.) ICIAR 2004. LNCS, vol. 3211, pp. 479–486. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  13. Tan, S., Zhang, X.R., Jiao, L.C.: Dual Ridgelet Frame Constructed Using Biorthonormal Wavelet Basis. In: IEEE International Conference on Acoustics, Speech, and Signal Processing (2005)

    Google Scholar 

  14. Candès, E.J., Donoho, D.L.: Curvelet-A Surprisingly Effective Nonadaptive Representation for Objects With Edges. In: Cohen, A., Rabut, C., Schumaker, L.L. (eds.) Curve and Surface Fitting: Saint-Malo, Nashville, Van-derbilt Univ. Press, TN (1999)

    Google Scholar 

  15. Do, M.N., Vetterli, M.: Contourlets. In: Stoeckler, J., Welland, G.V. (eds.) Beyond Wavelet, Academic Press, London (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Tan, S., Ma, X., Zhang, X., Jiao, L. (2005). A Review: Relationship Between Response Properties of Visual Neurons and Advances in Nonlinear Approximation Theory. In: Wang, J., Liao, X., Yi, Z. (eds) Advances in Neural Networks – ISNN 2005. ISNN 2005. Lecture Notes in Computer Science, vol 3496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427391_7

Download citation

  • DOI: https://doi.org/10.1007/11427391_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25912-1

  • Online ISBN: 978-3-540-32065-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics