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Image Representation in Visual Cortex and High Nonlinear Approximation

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Book cover Advances in Neural Networks – ISNN 2005 (ISNN 2005)

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

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Abstract

We briefly review the “sparse coding” principle employed in the sensory information processing system of mammals and focus on the phenomenon that such principle is realized through over-complete representation strategy in primary sensory cortical areas (V1). Considering the lack of quantitative analysis of how many gains in sparsenality the over-complete representation strategy brings in neuroscience, in this paper, we give a quantitative analysis from the viewpoint of nonlinear approximation. The result shows that the over-complete strategy can provide sparser representation than the complete strategy.

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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. Willshaw, D.J., Buneman, O.P., Longuet-Higgins, H.C.: Nonholographic Associative Memory. Nature 222, 960–962 (1969)

    Article  Google Scholar 

  3. Barlow, H.B.: Possible Principles Underlying the Transformation of Sensory Messages. In: Rosenblith, W.A. (ed.) Sensory Communication, pp. 217–234. MIT Press, Cambridge (1961)

    Google Scholar 

  4. Attwell, D., Laughlin, S.B.: An Energy Budget for Signaling in The Grey Matter of The Brain. J. Cereb. Blood Flow Metab. 21, 1133–1145 (2001)

    Article  Google Scholar 

  5. Lennie, P.: The Cost of Cortical Computation. Curr. Biol. 13, 493–497 (2003)

    Article  Google Scholar 

  6. Olshausen, B.A.: Principles of Image Representation in Visual Cortex. In: Chalupa, L.M., Werner, J.S., Boston, M.A. (eds.) The Visual Neurosciences, pp. 1603–1615. MIT Press, Cambridge (2003)

    Google Scholar 

  7. Lee, K.S., Pedersen, D., Mumford: The Nonlinear Statistics of High-contrast Patches in Natural Images. Int. J. Comput. Vis. 54, 83–103 (2003)

    Article  MATH  Google Scholar 

  8. Roweis, S.T., Saul, L.L.: Nonlinear Dimensionality Reduction By Locally Linear Embedding. Science 290, 2323–2326 (2000)

    Article  Google Scholar 

  9. Wiskott, L., Sejnowski, L.: Slow Feature Analysis: Unsupervised Learning of Invariances. Neural Comput. 14, 715–770 (2002)

    Article  MATH  Google Scholar 

  10. 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 

  11. Lewicki, M.S., Sejnowski, T.J.: Learning Overcomplete Representations. Neural Comput. 12, 337–365 (2000)

    Article  Google Scholar 

  12. De Vore, R.A.: Nonlinear Approximation. Acta Numerica. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  13. Donoho, D.L., Elad, M.: Optimally Sparse Representation in General (Non-orthogonal) Dictionaries Via Minimization. Proc. Nat. Aca. Sci. 100, 2197–2202 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  14. Feuer, N.A.: On Sparse Representations in Pairs of Bases. IEEE Trans. Inform. Theory 49, 1579–1581 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  15. Starck, J.L., Elad, M., Donoho, D.L.: Image Decomposition Via the Compination of Sparse Representations And A Variational Approach. Submitted to IEEE. IP (2004)

    Google Scholar 

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© 2005 Springer-Verlag Berlin Heidelberg

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Tan, S., Zhang, X., Wang, S., Jiao, L. (2005). Image Representation in Visual Cortex and High Nonlinear Approximation. 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_8

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  • DOI: https://doi.org/10.1007/11427391_8

  • 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)

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