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.