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Original Articles

Variance Estimation in Heteroscedastic Models by Undecimated Haar Transform

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Pages 1532-1544 | Received 19 Dec 2012, Accepted 26 Jun 2013, Published online: 10 Dec 2014

References

  • Antoniadis, A., Lavergne, C. (1994). Variance function estimation in regression by wavelet methods. In: Wavelets and Statistics, Lecture Notes in Statistics. Vol. 44. Eds., A. Antoniadis and G. Oppenheim. New York: Springer-Verlag, pp. 31–42.
  • Bioucas-Dias, J., Figueiredo, M., Oliveira, J. (2006). Total-variation image deconvolution: A majorization-minimization approach. In: Proceedings of International Conference on Acoustics, Speech and Signal Processing (ICASSP) on Acoustics, Speech and Signal Processing (ICASSP), Vol. II, pp. 861–864. Toulouse, France.
  • Brown, L.D., Levine, M. (2007). Variance estimation in nonparametric regression via the difference sequence method. Annals of Statistics 35:2219–2232.
  • Cai, T., Wang, L. (2004). Adaptive variance function estimation in heteroscedastic nonparametric regression. Annals of Statistics 35:2025–2054.
  • Coifman, R.R., Donoho, D.L. (1995). Translation invariant de-noising. In: Wavelets and Statistics. Springer Lecture Notes in Statistics. Vol. 44. Eds., A. Antoniadis and G. Oppenheim. New York: Springer-Verlag, pp. 125–150.
  • Davidian, M., Carroll, R.J. (1987). Variance Function Estimation. Journal of the American Statistical Association 82(400):1079–1091.
  • Donoho, D.L., Johnstone, I.M. (1994). Ideal spatial adaptation via wavelet shrinkage. Biometrka 81: 425–455.
  • Donoho, D.L., Johnstone, I.M. (1998). Minimax estimation via wavelet shrinkage. Annals of Statistics 26:879–921.
  • Dragotti, P.L., Vetterli, M. (2000). Shift-n-variant Gibb’s free denoising algorithm based on wavelet transform footprints. In: Proceedings of SPIE’2000, Wavelet Application in Signal and Image Processing VIII, SPIE-INT. SOC. OPTICAL ENGINEERING, pp. 821–830. San Diego.
  • Durand, S., Froment, J. (2003). Reconstruction of wavelet coefficients using total variation minimization. SIAM Journal on Scientific Computing 24(5):1754–1767.
  • Elad, M., Milanfar, P., Rubinstein, R. (2007). Analysis versus synthesis in signal priors. Inverse Problems 23: 947–968.
  • Figueiredo, M., Bioucas-Dias, J., Oliveira, J.P., Nowak, R.D. (2006). On total-variation denoising: A new majorization-minimization algorithm and an experimental comparison with wavelet denoising. In: Proceedings of the IEEE International Conference on Image Processing, pp. 2633–2636. Atlanta, Georgia, USA.
  • Hall, P., Carroll, R.J. (1989). Variance function estimation in regression: The effect of estimating the mean. Journal of the Royal Statistical Society, Series B 51:3–14.
  • Hall, P., Kay, P. J.W., Titterington, D.M. (1990). Asymptotically optimal difference-based estimation of variance in nonparametric regression. Biometrika 77:521–528.
  • Hao, B.-B., Li, M., Feng, X.-C. (2008). Wavelet iterative regularization for image restoration with varying scale parameter. Signal Processing: Image Communication 23(6):433–441.
  • Müller, H.G., Stadtmüller, U. (1987). Estimation of heteroscedasticity in regression analysis. Annals of Statistics 15:610–625.
  • Nason, G.P., Silverman, B.W. (1995). The Stationary Wavelet Transform and Some Statistical Applications, Wavelets and Statistics (Lecture Notes in Statistics). New York: Springer-Verlag.
  • Osher, S., Burger, M., Goldfarb, D., Xu, J., Yin, W. (2005). An iterative regularization method for total variation based image restoration. Multiscale Modeling and Simulation 4:460–489.
  • Palanisamy, T., Ravichandran, J. (2014). Estimation of variance function in heteroscedastic regression models by generalized coiflets. Communications in Statistics - Simulation and Computation 43(10): 2213–2224.
  • Rudin, L., Osher, S., Fatemi, E. (1992). Nonlinear total variation based noise removal algorithms. Physica D 60: 259–268.
  • Selesnick, I.W., Figueiredo, M. A.T. (2009). Signal restoration with overcomplete wavelet transforms: Comparison of Analysis and synthesis priors. Proceedings of SPIE 7446, 0D–15D.
  • Shen, S., Mei, C. (2009). Estimation of the variance function in heteroscedastic linear regression models. Communications in Statistics - Theory and Methods 38(7): 1098–1112.
  • Starck, J.L., Fadili, J., Murtagh, F. (2004). The undecimated wavelet decomposition and its reconstruction. Applied and Computational Harmonic Analysis 14: 257–275.
  • Steidl, G., Weickert, J., Brox, T., Mrzek, P., Welk, M. (2003). On the Equivalence of Soft Wavelet Shrinkage, Total Variation Diffusion, Total Variation Regularization, and Sides, Technical Report 26, Germany: Department of Mathematics, University of Bremen.

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