recfisz |
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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 |
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signal |
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1-d Noisy signal, length(signal)= 2^J |
policy |
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'MinMax' for minimax threshold; 'Universal' for universal threshold; |
type |
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'Hard' for hard thresholding; 'Soft' for soft thresholding |
lev |
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Coarsest resolution level |
h |
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Quadrature mirror filter for wavelet transform |
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OPTIONAL ARGUMENTS |
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h |
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Optional, Default = Symmlet 8 |
lev |
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Optional, Default= 4 |
type |
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Optional, Default= 'Hard' |
policy |
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Optional, Default= 'Universal' |
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VALUE |
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f |
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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