The EM Imaging Iterative Algorithm On The Discrete Reconstruction Points

Computed tomography is the issue of image reconstruction from projections theoretically,which is divided into analytical reconstruction algorithm and algebraic iterative reconstructionalgorithm. Analytical reconstruction algorithm is based on the continuous model and thetheory of Fourier center section theorem, which has faster speed and better image quality, butit is more sensitive to noise and requires complete projection data. Iterative algorithm is builton the discrete model, transforms the reconstruction problem into solving linear equations. Inthe condition of high noise and incomplete data, algebraic iterative reconstruction algorithm isalso available, but the large amount of calculation and slow reconstruction speed constraint itspractical application.This thesis based on parallel beam scan model studies the image reconstruction iterativealgorithm. First it describes the history and fundamentals of computer tomography, thendiscusses the image discrete model under parallel beam scan mode. For the shortcomings oftraditional discrete model, the thesis introduces a new discrete reconstruction points modelwith smaller reconstruction error. According to the characteristics of the new discrete model,this thesis fully utilizes the basis function to depict the ideal area of reconstruction points. Inthe discrete reconstruction point model, photon radiation obeys Poisson probability model, onwhich the thesis derives and establishes the new model’ EM iteration based.The paper gives a general description of subset balance theorem based on the discretereconstruction points. Based on the Poisson probability model, this paper proposes a methodto divide subsets according to steps and finds two iteration method of OSEM. The subsetsdivided by steps satisfy the subset balance, which can be used to optimize the iterativesequence and improve the speed of reconstruction.This thesis validates the algorithm and analyzes the experimental results. Numerical resultsshow that the discrete reconstruction points model can reduces the error compared with the traditional model. The EM algorithm under this new model improves the imaging accuracy ina certain degree, and its OSEM algorithm will also accelerate the convergence rate under theconditions of subset balance.