Although the potential benefits of maximum likelihood reconstruction h
ave been recognised for many years, the technique has only recently fo
und widespread popularity in clinical practice, Factors which have con
tributed to the wider acceptance include improved models for the emiss
ion process, better understanding of the properties of the algorithm a
nd, not least, the practicality of application with the development of
acceleration schemes and the improved speed of computers, The objecti
ve in this article is to present a framework for applying maximum like
lihood reconstruction for a wide range of clinically based problems, T
he article draws particularly on the experience of the three authors i
n applying an acceleration scheme involving use of ordered subsets to
a range of applications, The potential advantages of statistical recon
struction techniques include: (a) the ability to better model the emis
sion and detection process, in order to make the reconstruction conver
ge to a quantitative image, (b) the inclusion of a statistical noise m
odel which results in better noise characteristics, and (c) the possib
ility to incorporate prior knowledge about the distribution being imag
ed, The great flexibility in adapting the reconstruction for a specifi
c model results in these techniques having wide applicability to probl
ems in clinical nuclear medicine.