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

A 3-D iterative reconstruction algorithm which incorporates models of the geometric point response in the projector-backprojector is presented for parallel, fan, and cone beam geometries. It is shown that the geometric response function is shift-invariant for these three geometries if the distance from the collimator face is fixed. This property makes it possible to model the system point response function in the frequency domain. Compared with previous ray-driven models, the frequency domain implementation of the point response function correction significantly reduces the reconstruction time by about 50 times. Reconstructed images are compared with and without modeling the geometric response and attenuation. Improvements in image quality are shown when the geometric point response and attenuation are appropriately compensated. The modeling of the geometric response is shown to increase the image resolution; the attenuation compensation reduces the density nonuniformity artifacts.<>