Abstract
A number of authors have studied the problems associated with full three-dimensional reconstruction, especially in the case of positron tomography where three-dimensional reconstruction is likely to offer the greatest benefits. While most approaches follow that of filtered backprojection, the relationship between the various filters that have been proposed is far from evident. The authors clarify this relationship by analysing and generalising the different classes of published filters and establish the properties and characteristics of a general solution to the three-dimensional reconstruction problem. Some guidelines are suggested for the choice of an appropriate filter in a given situation.