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 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