Transmission image reconstruction and redundant information in SPECT with asymmetric fanbeam collimation

Two novel approaches for the reconstruction of asymmetric fanbeam transmission computed tomography data are discussed. The first, called the hybrid approach, involves a Fourier-based rebinning of the fanbeam data into parallel-beam data, Reconstruction then proceeds by use of filtered backprojection (FBP). The second approach, called generalized fanbeam filtered backprojection (GFFBP), involves direct fanbeam FBP reconstruction of a modified fanbeam sinogram. In both cases, the data are multiplied by weight functions that seek to appropriately normalize redundant data while exploiting them for noise reduction. The GFFBP approach is found to have resolution-noise tradeoffs superior to those of the hybrid approach for low degrees of smoothing, although for the higher levels of smoothing likely to be of interest in practical situations, the difference between the approaches is negligible. However, GFFBP's distance-dependent fanbeam backprojection factor also produced a high-intensity peripheral artifact that impinged slightly upon the object of interest. Because it ultimately makes use of parallel-beam FBP for reconstruction, the hybrid approach avoids this artifact.