Astigmatic single photon emission computed tomography imaging with a displaced center of rotation

A filtered backprojection algorithm is developed for single photon emission computed tomography (SPECT) imaging with an astigmatic collimator having a displaced center of rotation. The astigmatic collimator has two perpendicular focal lines, one that is parallel to the axis of rotation of the gamma camera and one that is perpendicular to this axis. Using SPECT simulations of projection data from a hot rod phantom and point source arrays, it is found that a lack of incorporation of the mechanical shift in the reconstruction algorithm causes errors and artifacts in reconstructed SPECT images. The collimator and acquisition parameters in the astigmatic reconstruction formula, which include focal lengths, radius of rotation, and mechanical shifts, are often partly unknown and can be determined using the projections of a point source at various projection angles. The accurate determination of these parameters by a least squares fitting technique using projection data from numerically simulated SPECT acquisitions is studied. These studies show that the accuracy of parameter determination is improved as the distance between the point source and the axis of rotation of the gamma camera is increased. The focal length of the focal line perpendicular to the axis of rotation is determined more accurately than the focal length to the focal line parallel to this axis.