Fast System Matrix Iterative Computation Algorithm for PET Image Reconstruction

In positron emission tomography (PET) studies, iterative method is usually used for iterative reconstruction of PET data, in which the system matrix reflects the mapping between image space and projection space, which is the key of iterative reconstruction algorithm. The previous orthogonal distance ray tracing algorithm is computationally complex and inefficient. To improve its computational speed and imaging quality, we propose a new algorithm. Firstly, incremental thinking was introduced on the basis of siddon algorithm to directly solve the neighborhood where the current voxel and the upper voxel do not repeat, and accelerate the calculation of voxel coordinate index. Secondly, the distance between the neighborhood voxel and LOR line was iteratively solved based on the distance between the voxel and LOR line, which further improved the calculation speed. Finally, the probability value of the voxel which is completely covered by the detector is set as a constant value, while the probability value of other voxels decreases with the distance from LOR line, which improves the imaging quality of the algorithm. A large number of evaluation experiments were performed on the resolution prosthesis model and the line-derived prosthesis model to verify the effectiveness of our method.