BMIE_TI

Bayesian Denoising Procedure

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
signal	1-d Noisy signal, length(signal)= 2^J
lev	Coarsest resolution level
VALUE
f	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 c_j,k of the intensity function at different levels, expressed by the canonical multiscale parameters Θ_j,k=c_j+1,2k/c_j,k, leads to a factorization of the likelihood function and the posteriori distribution that greatly facilitates analysis and modeling. The prior distribution of the Θ_j,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