A general method for three-dimensional filter computation (positron emission tomography application)

Abstract

Application of the Fourier space deconvolution algorithm to three-dimensional (3D) reconstruction problems necessitates the computation of a frequency space filter; which requires taking the 3D Fourier transform of the system response function. In this paper, it is shown that for system response functions of the specific form d( theta , phi )/r², with d( theta , phi ) an angular function describing the imaging system, the filter computation can always be reduced to single integration which, in many cases, may be performed analytically. Complete expressions are derived for the general 3D filter, and two examples are given to illustrate the use of such expressions.