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Inverse Problems and Imaging (IPI)
 

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

Pages: 1007 - 1029, Volume 7, Issue 3, August 2013      doi:10.3934/ipi.2013.7.1007

 
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Ming Yan - Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095, United States (email)
Alex A. T. Bui - Department of Radiological Sciences, University of California, Los Angeles, Los Angeles, CA 90095, United States (email)
Jason Cong - Department of Computer Sciences, University of California, Los Angeles, Los Angeles, CA 90095, United States (email)
Luminita A. Vese - Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095-1555, United States (email)

Abstract: 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.

Keywords:  Expectation maximization (EM), Richardson-Lucy, simultaneous algebraic reconstruction technique (SART), image reconstruction, total variation (TV), computerized tomography.
Mathematics Subject Classification:  Primary: 90C30, 94A08; Secondary: 90C26, 92C55.

Received: July 2012;      Revised: May 2013;      Available Online: September 2013.

 References