PET reconstruction

In statistical terms, filtered backprojection can be viewed as smoothed Least Squares (LS). In this paper, the authors report on improvement in LS resolution by: incorporating locally adaptive smoothers, imposing positivity and using statistical methods for optimal selection of the resolution parameter. The resulting algorithm has high computational efficiency relative to more elaborate Maximum Likelihood (ML) type techniques (i.e. EM with sieves). Practical aspects of the procedure are discussed in the context of PET and illustrations with computer simulated and real tomograph data are presented. The relative recovery coefficients for a 9mm sphere in a computer simulated hot-spot phantom range from .3 to .6 when the number of counts ranges from 10,000 to 640,000 respectively. The authors will also present results illustrating the relative efficacy of ML and LS reconstruction techniques