rechaarTI

 

Translation Invariant Haar Thresholds Estimator

 

DESCRIPTION

Estimate the intensity function using the translation-invariant version Haar-based thresholds on the resulting wavelet coefficients. 

USAGE

f = rechaarTI(signal,lambda0,type,lev)

REQUIRED ARGUMENTS
 

signal

1-d Noisy signal, length(signal)= 2^J

lambda0

 

Background intensity level per bin (true value or an estimate)

type

'Hard' for hard thresholding; 'Soft' for soft thresholding

lev

Coarsest resolution level
OPTIONAL ARGUMENTS

lev

Optional, Default= 4

type

Optional, Default= 'Hard'
VALUE
 

f

  Estimated intensity function  

    

BACKGROUND

The procedure is based on a method due to Kolaczyk  (1999) to estimate burst-like intensity functions and it has been developed for the untransformed Poisson counts. In other words, the data are the results of a background homogeneous Poisson process  and an additional inhomogeneous Poisson process generating observations in bursts. Using the translation invariant version of Haar wavelets, he obtains level-dependent thresholds. Note that the user has to specify the level of the background intensity function lambda0 or an estimate.   

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.

Kolaczyk, E.D. (1997). Nonparametric estimation of Gamma-Ray burst intensities using Haar wavelets. Astrophys. J., 483, 340-349.

Kolaczyk, E.D. (1999). Wavelet shrinkage estimation of certain Poisson intensity signals using corrected thresholds. Statistica Sinica, 9, 119-135.

ACKNOWLEDGEMENT 

The rechaarTI function is based on a Matlab routine kindly provided by Eric Kolaczyk.