A Simple Calculation of System Matrix Base on 2-D Index

The system matrix plays an important role in the improvement of medical image reconstruction quality in iterative reconstruction. It consists of a certain sequence of projection coefficients. Projection coefficients indicate the radiological path through a tow-dimensional grid array which is constructed based on the reconstructed image. It is a common geometric problem of evaluating the radiological path through the grid array. This paper identifies the inefficient aspect of the traditionally precise evaluation of the radiological path. A new accurate and simple algorithm is presented, which considers that the projection coefficients can be shown in two-dimensional way. Experimental results based on GATE (Geant4 Application for Tomographic Emission) simulating PET (Positron Emission Tomography) imaging shows that the proposed algorithm is efficient to build up a system matrix, and the image can be reconstructed by the system matrix.