Computerized Medical Imaging andit (A. Motta).Fast 3D-EM reconstruction using Planograms for stationary planar positron emission mammography camera

At the University of Pisa we are building a PEM prototype, the YAP–PEM camera, consisting of two opposite 6!6!3 cm3 detector heads of 30!30 YAP:Ce finger crystals, 2!2!30 mm3 each. The camera will be equipped with breast compressors. The acquisition will be stationary. Compared with a whole body PET scanner, a planar Positron Emission Mammography (PEM) camera allows a better, easier and more flexible positioning around the breast in the vicinity of the tumor: this increases the sensitivity and solid angle coverage, and reduces cost. To avoid software rejection of data during the reconstruction, resulting in a reduced sensitivity, we adopted a 3D-EM reconstruction which uses all of the collected Lines Of Response (LORs). This skips the PSF distortion given by data rebinning procedures and/or Fourier methods. The traditional 3D-EM reconstruction requires several times the computation of the LOR-voxel correlation matrix, or probability matrix {pij}; therefore is highly time-consuming. We use the sparse and symmetry properties of the matrix {pij} to perform fast 3D-EM reconstruction. Geometrically, a 3D grid of cubic voxels (FOV) is crossed by several divergent 3D line sets (LORs). The symmetries occur when tracing different LORs produces the same pij value. Parallel LORs of different sets cross the FOV in the same way, and the repetition of pij values depends on the ratio between the tube and voxel sizes. By optimizing this ratio, the occurrence of symmetries is increased. We identify a nucleus of symmetry of LORs: for each set of symmetrical LORs we choose just one LOR to be put in the nucleus, while the others lie outside