Frequency domain implementation of the three-dimensional geometric point response correction in SPECT imaging

Analytical expressions exist for the geometric point response functions for parallel, fan, and cone beam collimators. The geometric point response functions are shown to be shift-invariant for these three collimators if the distance between the point source and the detection plane is constant. For single photon emission computed tomography (SPECT), this property is used in the projector/backprojector to correct for geometric distortion using the iterative EM reconstruction algorithm. In the implementation, the system geometric response, the crystal intrinsic response and the attenuation were compensated. The attenuation compensation was accomplished in the spatial domain. The point response corrections were accomplished using frequency domain filtering, taking advantage of the shift-invariance of the system point response function at a fixed depth. The frequency domain implementation significantly speeded up the algorithm. Phantom studies showed the increase of resolution and the reduction of density nonuniformity artifacts which were due to the spatially varying system response function and the attenuation effect