recanscombe |
|
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 Gaussian-based global thresholds on the resulting empirical wavelet coefficients.
USAGE
f = recanscombe(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
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