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.
Highlights
Obtaining high quality images is very important in many areas of applied science, such as medical imaging, optical microscopy, and astronomy
It is sensitive to noise and suffers from streak artifacts. An alternative to this analytical reconstruction is the use of the iterative reconstruction technique, which is quite different from filtered back projection (FBP)
The most common method used in commercial computed tomography (CT) is the filtered back projection (FBP), which can be implemented in a straight forward way and it can be computed rapidly
Summary
Obtaining high quality images is very important in many areas of applied science, such as medical imaging, optical microscopy, and astronomy For some applications such as positron-emission-tomography (PET) and computed tomography (CT), analytical methods for image reconstruction are available. It is sensitive to noise and suffers from streak artifacts (star artifacts) An alternative to this analytical reconstruction is the use of the iterative reconstruction technique, which is quite different from FBP. Y is the measured data (vector in RM in the discrete case). B is the background emission and n is the noise (both are vectors in RM in the discrete case). This is a conditional probability of having X = x given that y is the measured data.
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