Application Research On Expectation Maximization Algorithm In Medical Tomographic Imaging

Medical tomographic imaging is a kind of non-destructive technology, which can show the anatomical morphology of the human body clearly and reflect the physiological and biochemical process of pathological changes. So it has been one of the most important tools in medical diagnostic imaging field.The Medical tomographic imaging technology, such as X-CT and E-CT, makes use of a series of projection data of target from different observation angles to reconstruct tomographic images. The reconstruction algorithms in X-CT and E-CT have the same mathematical principle, and can be investigated under the identical mathematical model. The traditional reconstruction algorithms of Medical tomographic imaging include analytical methods and iterative methods. The iterative method has a slow reconstruction speed, but it can avoid some defects of analytical methods, specially in the case of sparse projection angles, and it has been one research hotspot.System matrix is the key factor which restricts the speed of iterative reconstruction methods. In the case of 2D fan-beam and 3D cone-beam scanning, a fast and real-time method of computing system matrix was implemented in our work. Based on a fast intersection and traverse algorithm of rays and voxels or pixels, it can improve the speed of iterative reconstruction.The radiation of photons in the actual imaging process meets the Poisson random process. According to this statistical property, EM algorithm is applied to reconstruct tomographic Images. It is based on the parameter estimation theory, and has a strong ability to suppress noise in certain iteration numbers. The images reconstructed by EM algorithm will be better, its value of pixels converge in a non-negative number. In the thesis, formula derivation and image reconstruction steps of EM algorithm in medical tomographic imaging is given, and the images reconstructed by EM,FBP or ART algorithms are compared and analyzed. At the same time, reconstructed images of MLEM and OSEM algorithms are also compared. In the case of sparse projection angles, EM algorithm will have a better reconstruction quality compared with FBP algorithm, but it still can not meet the requirements. Iterative image reconstruction using the combination of TV optimization and EM algorithm was implemented in the thesis (EM-TV algorithm). Compared with images reconstructed only by EM algorithm, the image reconstructed by EM-TV algorithm will be better.