An analytical reconstruction algorithm for multifocal converging-beam SPECT

Multifocal converging-beam collimation has been suggested for cardiac SPECT imaging to increase sensitivity over the heart without truncation of the activity distribution in the chest. In this study, an analytical reconstruction algorithm is derived for multifocal fan-beam and multifocal cone-beam tomography. In the algorithm, the projection data are differently weighted and filtered, depending on the distance from the detector. For a given image point, the set of filtered data corresponding to the distance between this point and detector is backprojected to determine the pixel value of the point. Thus, the backprojection is done only once at each projection view. To evaluate the algorithm, simulation studies are performed using a 3D Defrise slab phantom without considering photon attenuation and scatter, detector response, and statistical noise. Reconstructed images demonstrate that reasonable quality can be achieved with a modest focal-length variation rate and with a small radius of rotation. A collimator with a focal length increasing quickly near its centre provides better quality in the image region distant from the central plane of the cone geometry, but produces more severe artifacts at the centre of the reconstructed image, compared to a collimator with an initially slowly varying focal length.