Positron Emission Topography Tomography (PET) is a nuclear medicine image technique. The scanning machine of PET can be characterized by a (sparse) matrix A. The result of scanning is stored in an image vector g. The image reconstruction of PET is not different from solving a linear equation system A f = g. The main purpose of this thesis is to develop and compare different implementations of Maximum Likelihood Expectation Maximization (MLEM) algorithm, which can be used to solve the linear equation system Af = g. The target platform of all implementations are heterogeneous systems with NVIDIA GPUs that enable CUDA. The host program is written in C/C++, while the GPU kernel functions are written in CUDA. The MLEM algorithm can be further divided into four steps, among which two are equivalent to (sparse) matrix-vector (SpMV) multiplication, respectively using the original matrix A and its transposition AT. The main focus is then on the implementing and comparing of SpMV algorithms. In this thesis, two different SpMV algorithms are applied, namely the merge-based SpMV and the csr-vector SpMV. Apart from that, a novel parallel algorithm for matrix transposition is also covered in this thesis. The case when it is not possible to use transposed matrix is considered as well. Moreover the NCCL (NVIDIA Collective Communication Library) operations are also used as more than one GPUs may be applied to run the program. In the last chapters, the performances of different SpMV and SpMV-T algorithms are investigated and compared. Their accuracy as well as the influence of number of GPUs are discussed in dedicated sections respectively. Lastly, the limitations of current implementation and some possible improvements are analyzed.     «

Positron Emission Topography Tomography (PET) is a nuclear medicine image technique. The scanning machine of PET can be characterized by a (sparse) matrix A. The result of scanning is stored in an image vector g. The image reconstruction of PET is not different from solving a linear equation system A f = g. The main purpose of this thesis is to develop and compare different implementations of Maximum Likelihood Expectation Maximization (MLEM) algorithm, which can be used to solve the linear equ...     »