BMIE_TI |
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Bayesian Denoising Procedure
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DESCRIPTION
Implements a Bayesian method to estimate the intensity of a Poisson signal based on a Translation Invariant Multiscale Multiplicative Innovations Model.
USAGE
f = BMIE_TI(signal,lev)
REQUIRED ARGUMENTS |
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signal |
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1-d Noisy signal, length(signal)= 2^J |
lev |
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Coarsest resolution level |
VALUE |
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f |
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Estimated intensity function |
BACKGROUND
The Bayesian translation
invariant Multiscale Multiplicative Innovations Model estimator of the
intensity function uses a multiscale data analysis based on the unnormalized
Haar transform. The 'parent-child' relationship between the scaling
coefficients cj,k of the intensity function at different levels,
expressed by the canonical multiscale parameters Θj,k=cj+1,2k/cj,k,
leads to a factorization of the likelihood function and the posteriori
distribution that greatly facilitates analysis and modeling. The prior
distribution of the Θj,k's specified
by Timmermann & Nowak (1999) is a mixture of 3 beta distributions.
REFERENCES
Timmermann K. E. & Nowak R. D. (1999). Multiscale modeling and estimation of Poisson processes with applications to photon-limited imaging. IEEE Trans. Inf. Theor., 45, 846-862