A rotating and warping projector/backprojector for fan-beam and cone-beam iterative algorithm

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Abstract
A rotating-and-warping projector/backprojector is proposed for iterative algorithms used to reconstruct fan-beam and cone-beam single photon emission computed tomography (SPECT) data. The development of a new projector/backprojector for implementing attenuation, geometric point response, and scatter models is motivated by the need to reduce the computation time yet to preserve the fidelity of the corrected reconstruction. At each projection angle, the projector/backprojector first rotates the image volume so that the pixelized cube remains parallel to the detector, and then warps 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 so that the interpolation of voxel values are performed only once. The projection operation is achieved by a simple weighted summation, and the backprojection operation is achieved by copying weighted projection array values to the image volume. An 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 when the voxel-to-detector distance is constant. The fan-beam and cone-beam rotating-and-warping projector/backprojector is applied to SPECT data showing improved resolution.