Variable scale reprojection for iterative reconstruction: application to PET reconstruction with OSEM

Iterative reconstruction algorithms require the repetitive application of reprojection and backprojection operations. Reprojection of an image at angle θ can be decomposed into rotating the image by angle θ and summing it at angle 0. Here, the authors show that this “rotate and sum” (RS) technique can be reduced to applying one-dimensional translations of the image rows, followed by an interpolation-free summation of the image columns. This sequence actually yields the proper reprojection magnified by a factor that depends on the angle. By pre-processing the data to match this angular variation in scale, most iterative reconstructions can be performed with this variable scale reprojection scheme (VS). The main routine is a “translate and sum” function that accesses the memory row by row. The OSEM algorithm was implemented with the VS, the RS and the line-length model, and OSEM reconstructions were performed on real PET data. The VS scheme was demonstrated to be significantly faster than RS and twice as fast as LL, without compromising image quality, and even slightly improving it