Polar pixels for high resolution small animal PET

In this work, we introduce polar-pixel basis functions for iterative reconstruction of small animal PET data. Our aim was to accelerate the reconstruction when using a system matrix stored on-disk, as well as the Monte-Carlo simulations related to the calculation of the matrix. The study was restricted to 2D. A common approach to reduce the number of the system matrix elements to be calculated and stored is using symmetries. While the conventional Cartesian discretization usually constraints the symmetries to three planes, a polar-pixel discretization of the FOV allows all the symmetries of a PET scanner to be used. We have simulated a two-head small animal PET scanner (4-steps rotation). The symmetries of the scanner allowed the FOV to be subdivided into 16 sectors. For comparison purposes, a Cartesian discretization of the image in pixels of size 0.5 times 0.5 mm² was also used. Three polar-pixel schemes were tested: (a) Polar pixels of constant area (equal to the area of the Cartesian pixels) and constant radial length; (b) square-like polar pixels, whose radial length was equal to the length of the Cartesian pixels, and (c) square-like polar pixels as in (b), excepting the pixels at the center of FOV, which were substituted by a circular pixel. The system matrix and various phantoms were calculated using Monte-Carlo simulations, and the algorithm MLEM was implemented. The results show that polar-pixel schemes (b) and (c) yield images very similar to the Cartesian ones, and only negligible degradation effects on image quality were observed.