Constructing Algorithm Iterative Image Reconstruction System Matrix Method

Positron emission tomography (PET) is one of the most advanced technologies of the nuclear medicine diagnosis and research, and it has become an important mean of the function imaging of living tissues and organs. Analytic and iterative techniques are common algorithms for the image reconstruction of the nuclear medicine. Due to the principle and characteristics of PET, Maximum Likelihood Expectation Maximization (MLEM) and Ordered Sub-sets Expectation Maximization (OSEM) are applied to reconstruct images.The system matrix plays an important role in the improvement of image reconstruction quality in MLEM and OSEM iterative image reconstruction. It determines whether an image could be reconstructed well. Prior to the iteration, the accurate system matrix guarantees the iterative reconstruction smoothly.There are mainly two algorithms to calculate the system matrix:the strip area weighted and the line weighted. This paper proposes an improved line weighted algorithm based on the traditional line weighted algorithm, especially, the grid indexes retrieval method, from the one-dimensional method into two-dimensional retrieval method. It improves the retrieval efficiency, also reduces the complexity of the algorithm. And expanded the proposed algorithm, while the image can be reconstructed well, the system matrix merges with some filters, and the reconstructed image quality will be improved greatly.In this paper, the proposed algorithm is validated by two kinds of data, one is ideally original projection data that is without any interference in the process of data collection, such as noise interference, in general, the data can obtain by the radon transform; another is the simulation data which is close to realistic circumstance, and it obtains by PET simulation platform, that the Geant4Simulation Application for Tomographic Emission (GATE) open source software package structures.The proposed algorithm is achieved and analyzed by Matlab software. The image can be reconstructed by the original projection data, and its quality will be evaluated to further verify the validity of the proposed algorithm in this paper. The experimental results show that while the reconstruction image quality guarantees, the proposed algorithm can quickly and accurately calculate the system matrix. After the expansion of the proposed algorithm, calculation of the system matrix has a certain filter function, so the quality of the reconstructed image is improved significantly.