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On signal reconstruction in white noise using dictionaries

  • Methods of Signal Processing
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Abstract

Assume that we observe a Gaussian vector Y = Xβ + σζ, where X is a known p × n matrix with p ≥ n, β ∈ ℝn is an unknown vector, and ζ ∈ ℝn is a standard Gaussian white noise. The problem is to reconstruct Xβ from observations Y, provided that β is a sparse vector.

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References

  1. Press, W.H. et al., Numerical Recipes: The Art of Scientific Computing, Cambridge: Cambridge Univ. Press, 2007, 3rd ed.

    MATH  Google Scholar 

  2. Tibshirani, R., Regression Shrinkage and Selection via the Lasso, J. Roy. Statist. Soc., 1996, vol. 58, no. 1, pp. 267–288.

    MATH  MathSciNet  Google Scholar 

  3. Candes, E. and Tao, T., The Dantzig Selector: Statistical Estimation when p Is Much Larger than n, Ann. Statist., 2007, vol. 35, no. 6, pp. 2313–2351.

    Article  MATH  MathSciNet  Google Scholar 

  4. Birgé, L. and Massart, P., Gaussian Model Selection, J. Eur. Math. Soc., 2001, vol. 3, no. 3, pp. 203–268.

    Article  MATH  MathSciNet  Google Scholar 

  5. Birgé, L. and Massart, P., Minimal Penalties for Gaussian Model Selection, Probab. Theory Related Fields, 2007, vol. 138, no. 1–2, pp. 33–73.

    Article  MATH  MathSciNet  Google Scholar 

  6. Abramovich, F., Benjamini, Y., Donoho, D.L., and Johstone, I.M., Adapting to Unknown Sparsity by Controlling False Discovery Rate, Ann. Statist., 2006, vol. 34, no. 2, pp. 584–653.

    Article  MATH  MathSciNet  Google Scholar 

  7. Abramovich, F., Grinshtein, V., and Pensky, M., On Optimality of Bayesian Testimation in the Normal Means Problem, Ann.’ Statist., 2007, vol. 35, no. 5, pp. 2261–2286.

    Article  MATH  MathSciNet  Google Scholar 

  8. Donoho, D.L. and Johnstone, I.M., Ideal Spatial Adaptation by Wavelet Shrinkage, Biometrika, 1994, vol. 81, no. 3, pp. 425–455.

    Article  MATH  MathSciNet  Google Scholar 

  9. Donoho, D.L., Johnstone, I.M., Kerkyacharian, G., and Picard, D., Wavelet Shrinkage: Asymptopia?, J. Roy. Statist. Soc., Ser. B, 1995, vol. 57, no. 2, pp. 301–369.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia

    G. K. Golubev

  2. University of Provence Aix-Marseille I, Marseille, France

    G. K. Golubev

Authors
  1. G. K. Golubev
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Correspondence to G. K. Golubev.

Additional information

Original Russian Text © G.K. Golubev, 2009, published in Problemy Peredachi Informatsii, 2009, Vol. 45, No. 4, pp. 91–106.

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Golubev, G.K. On signal reconstruction in white noise using dictionaries. Probl Inf Transm 45, 378–392 (2009). https://doi.org/10.1134/S0032946009040073

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  • DOI: https://doi.org/10.1134/S0032946009040073

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