General Convergent Expectation Maximization (em)-type Algorithms for Image Reconstruction

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.