recanscombeTI |
|
Anscombe Transformation Denoising Procedure |
DESCRIPTION
Estimate the intensity function of a Poisson signal by first preprocessing the original data by the Anscombe transformation and then applying translation invariant Gaussian-based global thresholds on the resulting empirical wavelet coefficients.
USAGE
f = recanscombeTI(signal,policy,type,lev,h)
REQUIRED ARGUMENTS | ||
signal |
1-d Noisy signal, length(signal)= 2^J | |
policy |
'MinMax' for minimax threshold; 'Universal' for universal threshold; |
|
type |
'Hard' for hard thresholding; 'Soft' for soft thresholding | |
lev |
Coarsest resolution level | |
h |
Quadrature mirror filter for wavelet transform | |
OPTIONAL ARGUMENTS | ||
h |
Optional, Default = Symmlet 8 | |
lev |
Optional, Default= 4 | |
type |
Optional, Default= 'Hard' | |
policy |
Optional, Default= 'Universal' | |
VALUE | ||
f |
Estimated intensity function |
BACKGROUND
The procedure is based on the normalising and variance-stabilising Anscombe (1948) transformation ( zi=2*sqrt(yi+3/8), i=1,...,n) making possible the application of the usual wavelet methodology on the transformed data vector. The inverse transformation leads to an estimate of the underlying intensity function.
REFERENCES
Coifman, R.R. & Donoho, D.L. (1995). Translation-invariant de-noising. In Wavelets and Statistics, Antoniadis, A. & Oppenheim, G. (Eds.), Lect. Notes Statist., 103, pp. 125-150, New York: Springer-Verlag
Donoho, D.L. (1993). Non-linear wavelet methods for recovery of signals, densities and spectra from indirect and noisy data. In Proceedings of Symposia in Applied Mathematics: Different Perspectives on Wavelets, 47, Ed. I. Daubechies, pp. 173-205. San Antonio: American Mathematical Society
Donoho, D.L. & Johnstone, I.M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81, 425-455
Nason, G.P. (1996). Wavelet shrinkage using cross-validation. J. R. Statist. Soc. B, 58, 463-479.
SEE ALSO