reccorrected

 

 Corrected Thresholds Estimator 

 

DESCRIPTION

Estimate the intensity function using the orthonormal wavelets and corrected thresholds on the resulting wavelet coefficients.

USAGE

f = reccorrected(signal,lambda0,ordind,type,lev,h)

REQUIRED ARGUMENTS
 

signal

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

lambda0

 

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

ordind

Order indicator dictating whether skewness alone (i.e. 3) is corrected for, or both skewness and kurtosis (i.e.  4) are corrected for

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'

ordind

Optional, Default= 4
VALUE
 

f

  Estimated intensity function  

 

NOTES

It is suggested to use lev>=4 (there is a warning in TholdSolve.m  called by reccorrected.m), but the code works also for lev<4. Moreover if lambda0 < 5.5 Kolaczyk suggests to use the Haar-based wavelet shrinkage methodology.

BACKGROUND

The procedure is based on a method due to Kolaczyk  (1999) to obtain Poisson counts estimates using arbitrary wavelet bases. In this case he derives implicit level-dependent thresholds depending on lambda0. These thresholds are called "corrected thresholds" due to the fact that they are, essentially, corrected versions of the usual Gaussian-based thresholds.

REFERENCES

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

ACKNOWLEDGEMENT

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

SEE ALSO

reccorrectedTI