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; 
'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

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

recanscomeTI, cv