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; 
'CV' for thresholding using the 'leave-out-half' cross-validation strategy

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 Wavelets47, 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

recanscombe, cv