recfisz

 

Fisz Transformation Estimator 

 

DESCRIPTION

 

Estimate the intensity function pre-processing the original data by the Fisz transformation and applying Gaussian-based global thresholds on the resulting wavelet coefficients.

 

USAGE

 

f = recfisz(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 Fisz (1955) transformation 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. & Johnstone, I.M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81, 425-455.

Fisz, M. (1955). The limiting distribution of a function of two independent   random variables and its statistical applications. Colloquium  Mathematicum, 3, 138-146.

Fryzlewicz, P. & Nason, G.P. (2004). A Haar-Fisz algorithm for Poisson intensity estimation. Journal of Computational and Graphical Statistics, 13, (to appear)

            
Nason, G.P. (1996). Wavelet shrinkage using cross-validation.  J. R. Statist. Soc. B, 58, 463-479.

 

SEE ALSO

 

recfiszTI, fisz, fiszinv, cv