reccorrectedTI |
|
Translation Invariant Corrected Thresholds Estimator |
DESCRIPTION
Estimate the intensity function using the translation-invariant version of orthonormal wavelets and corrected thresholds on the resulting wavelet coefficients.
USAGE
f = reccorrectedTI(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
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. (1999). Wavelet shrinkage estimation of certain Poisson intensity signals using corrected thresholds. "Statistica Sinica", 9, 119-135.
ACKNOWLEDGEMENT
The reccorrectedTI function is based on a Matlab routine kindly provided by Eric Kolaczyk.
SEE ALSO