A rotating and squashing projector-backprojector pair for fan-beam and cone-beam iterative algorithms

The authors propose and implement a rotating-and-squashing projector-backprojector pair for fan-beam and cone-beam iterative algorithms. The motivation of their investigation is to significantly reduce both computation time and reconstruction artifacts when implementing attenuation, geometric and scatter correction models. At each projection angle, the authors´ projector/backprojector first rotates the image volume so that the front face of the volume is parallel to the detector, then squashes the image volume so that the fan-beam and cone-beam rays are converted into parallel rays. In the authors´ implementation, these two steps are combined and they only interpolate the voxel values once. The projection operation is achieved by a simple summation, and the backprojection operation is achieved by copying the projection array to the image volume. Another advantage of this projector/backprojector is that the system point response function can be deconvolved via the fast Fourier transform using the shift-invariant property of the point response function when the voxel-to-detector distance is constant. At each projection angle, the authors rotate and squash the image volume using interpolations. This causes smoothing of the image. However, this smoothing can be modeled as a point spread function and be deconvolved. The fan-beam and cone-beam rotating-and-squashing projector/backprojector have been implemented on a SPECT system for the EM-ML algorithm