Adam Alessio
Division of Nuclear Medicine, University of Washington
Date: May 9, 2005
Positron emission tomography (PET) scanners collect measurements of a
patient's in vivo radiotracer distribution. This work considers the
inverse problem of reconstructing an image from Fourier rebinned,
positron emission tomography (PET) measurements. I will briefly
discuss the rationale for the Fourier rebinning process. Then, I will
present some methods for including the structure of the noise
correlations in an accurate statistical reconstruction algorithm.
These methods are extendable to situations beyond the Fourier
rebinning application. The first order influence of the
correlations appears in the conditional mean and the second order
influence appears in the conditional covariance terms used in a
penalized weighted least squares objective function. The use of
complete covariance matrices in the weighting term can be simplified
by a) reducing the dimensionality of the correlations and b) adopting
a Markov random field assumption.