Abstract: In emission tomography, iterative statistical methods are accepted as the reconstruction algorithms that achieve the best image quality. The accuracy of these methods relies partly on the quality of the system response matrix (SRM) that characterizes the scanner. The more physical phenomena included in the SRM, the higher the SRM quality, and therefore higher image quality is obtained from the reconstruction process. High-resolution small animal scanners contain as many as 10(3)-10(4) small crystal pairs, while the field of view (FOV) is divided into hundreds of thousands of small voxels. These two characteristics have a significant impact on the number of elements to be calculated in the SRM. Monte Carlo (MC) methods have gained popularity as a way of calculating the SRM, due to the increased accuracy achievable, at the cost of introducing some statistical noise and long simulation times. In the work presented here the SRM is calculated using MC methods exploiting the cylindrical symmetries of the scanner, significantly reducing the simulation time necessary to calculate a high statistical quality SRM and the storage space necessary. The use of cylindrical symmetries makes polar voxels a convenient basis function. Alternatively, spherically symmetric basis functions result in improved noise properties compared to cubic and polar basis functions. The quality of reconstructed images using polar voxels, spherically symmetric basis functions on a polar grid, cubic voxels and post-reconstruction filtered polar and cubic voxels is compared from a noise and spatial resolution perspective. This study demonstrates that polar voxels perform as well as cubic voxels, reducing the simulation time necessary to calculate the SRM and the disk space necessary to store it. Results showed that spherically symmetric functions outperform polar and cubic basis functions in terms of noise properties, at the cost of slightly degraded spatial resolution, larger SRM file size and longer reconstruction times. However, we demonstrate that post-reconstruction smoothing, usually applied in emission imaging to reduce the level of noise, can produce a spatial resolution degradation of similar to 50%, while spherically symmetric basis functions produce a degradation of only similar to 6%, compared to polar and cubic voxels, at the same noise level. Therefore, the image quality trade-off obtained with blobs is higher than that obtained with cubic or polar voxels.

Abstract: AC++/OpenCL software platform for emission image reconstruction of data from pinhole cameras has been developed. The software incorporates a new, accurate but computationally costly, probability distribution function for operating on list-mode data from detector stacks. The platform architecture is more general than previous works, supporting advanced models such as arbitrary probability distribution, collimation geometry and detector stack geometry. The software was implemented such that all performance-critical operations occur on OpenCL devices, generally GPUs. The performance of the software is tested on several commodity CPU and GPU devices.

Abstract: We present a deformation of the Minkowski space as embedded into the conformal space (in the formalism of twistors) based in the quantum versions of the corresponding kinematic groups. We compute explicitly the star product, whose Poisson bracket is quadratic. We show that the star product although defined on the polynomials can be extended differentiably. Finally we compute the Eucliden and Minkowskian real forms of the deformation.