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General convergent expectation maximization (EM)-type algorithms for image reconstruction

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  • Obtaining high quality images is very important in many areas of applied sciences, such as medical imaging, optical microscopy, and astronomy. Image reconstruction can be considered as solving the ill-posed and inverse problem $y=Ax+n$, where $x$ is the image to be reconstructed and $n$ is the unknown noise. In this paper, we propose general robust expectation maximization (EM)-type algorithms for image reconstruction. Both Poisson noise and Gaussian noise types are considered. The EM-type algorithms are performed using iteratively EM (or SART for weighted Gaussian noise) and regularization in the image domain. The convergence of these algorithms is proved in several ways: EM with a priori information and alternating minimization methods. To show the efficiency of EM-type algorithms, the application in computerized tomography reconstruction is chosen.
    Mathematics Subject Classification: Primary: 90C30, 94A08; Secondary: 90C26, 92C55.


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