Bayesian Statistics Seminar
North Carolina State University
presents
Mr. John White
North Carolina State University
"A Bayesian Multi-Scale Model for Smoothing Images using the Chinese Restaurant Process"
ABSTRACT
Many multi-scale approaches to smoothing images with Poisson noise are currently available, including
various wavelet smoothing methods, Wedgelets, and Platelets. Another class of smoothing algorithms
utilizes Bayesian multi-scale models. In this presentation, a novel method for smoothing images with Poisson
data is introduced, and this new method uses a Bayesian multi-scale model with the Chinese Restaurant Process,
which is a sampling scheme closely related to the Dirichlet Process. More specifically, this new method
combines existing ideas of Bayesian multi-scale models for smoothing images with a different type of prior
that uses the Chinese restaurant process as well as a mixture of Dirichlet distributions providing independent
samples from the posterior distribution of the underlying intensity, or true object representation.
This new method still permits different levels of smoothing at the various scales of data.
In order to compare this new methodology to the current methods, a simulation example using a photon-limited
image source was conducted. Photon-limited images are common in astronomical imaging due to faint sources
or limited time of exposure. Applications to real astronomical images are given, and these images consist
of X-ray images from the Chandra X-ray observatory satellite. X-rays are an obvious candidate for images
with Poisson noise due to each pixel being represented as a count of photons. This presentation shows
this method outperforms many existing methods in its ability to estimate the true intensity image, as well
as having other favorable qualities that some methods lack, such as preserving photon flux and computation time.
Tuesday, November, 25, 2008
4:00 - 5:00 pm
208 Patterson Hall