Computing System Matrix for OSEM and MLEM Iterative Image Reconstruction Algorithms

This documentation describes a MATLAB-based program for computing system matrices used in iterative image reconstruction algorithms. The core function Generate_SystemMatrix calculates the system matrix required by both OSEM and MLEM algorithms, which are widely used in medical imaging reconstruction. The function accepts the parameter 'pixel' representing the image dimension (commonly 64×64, 128×128, or 256×256 pixels). The computational complexity increases with larger pixel values due to the expanded matrix dimensions. The included diedai-test file provides a straightforward implementation of the MLEM reconstruction algorithm. This test script requires loading the system matrix generated by Generate_SystemMatrix(128), which must be precomputed and saved as "SystemMatrix.mat" for proper execution. The algorithm works by iteratively updating image estimates using expectation-maximization principles to maximize likelihood function. Additionally, the testsino file contains sample sinogram data representing projection measurements - essentially the input data for MLEM reconstruction that simulates Radon transform projections. These files collectively demonstrate complete workflow from system matrix generation to image reconstruction, providing practical examples for understanding MATLAB implementation details and operational procedures for iterative reconstruction algorithms. The system matrix generation typically involves modeling geometric relationships between image pixels and detector responses, while the reconstruction algorithms implement statistical optimization methods for noise reduction and image quality improvement.