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.