BMSMShrink

 

Bayesian Denoising Procedure 

 

DESCRIPTION

 

Implements a Bayesian method for the intensity of a Poisson signal based on a Translation Invariant Multiscale Model.

 

USAGE

 

[f,ppp,qqq] = BMSMShrink(signal,pqind)

 

REQUIRED ARGUMENTS

 

 

 

signal

 

1-d Noisy signal, length(signal)= 2^J

pqind

 

Indicator for default values of parameters p and q (i.e. 1) or estimation through method of marginal maximum likelihood (i.e. 2)

 

 

 

VALUE

 

 

 

f

 

Estimated intensity function

ppp

 

(Uncorrected) vector of mixing probabilities

qqq

 

(Uncorrected) vector of beta shape parameters

     

BACKGROUND

 

The translation invariant Multiscale 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 Kolaczyk (1999) is a mixture of a point mass at 1/2 and a symmetric beta distribution.

 

REFERENCES

 

Kolaczyk, E.D. (1999). Bayesian multiscale models for Poisson processes. J. Amer. Statist. Ass., 94, 920-933.

ACKNOWLEDGEMENT 

The BMSMShrink function is based on a Matlab routine kindly provided by  Eric Kolaczyk.