John M M Anderson | PubMed Health

PubMed2004

Improved Poisson intensity estimation: denoising application using Poisson data.

Recently, Timmermann and Nowak developed algorithms for estimating the means of independent Poisson random variables. The algorithms are based on a multiscale model where certain random variables are assumed to obey a beta-mixture density function. Timmermann and Nowak simplify the density estimation problem by assuming the beta parameters are known and only one mixture parameter is unknown. They use the observed data and the method of moments to estimate the unknown mixture parameter. Taking a different approach, we generate training data from the observed data and compute maximum likelihood estimates of all of the beta-mixture parameters. To assess the improved performance obtained by the proposed modification, we consider a denoising application using Poisson data.

Algorithms↗

PubMed2004

Regularized image reconstruction algorithms for positron emission tomography.

We develop algorithms for obtaining regularized estimates of emission means in positron emission tomography. The first algorithm iteratively minimizes a penalized maximum-likelihood (PML) objective function. It is based on standard de-coupled surrogate functions for the ML objective function and de-coupled surrogate functions for a certain class of penalty functions. As desired, the PML algorithm guarantees nonnegative estimates and monotonically decreases the PML objective function with increasing iterations. The second algorithm is based on an iteration dependent, de-coupled penalty function that introduces smoothing while preserving edges. For the purpose of making comparisons, the MLEM algorithm and a penalized weighted least-squares algorithm were implemented. In experiments using synthetic data and real phantom data, it was found that, for a fixed level of background noise, the contrast in the images produced by the proposed algorithms was the most accurate.

Algorithms↗