Total Variation Regularization In Medical Imaging

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Moosavi, Niloofar | 2016

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 48380 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Fotouhi Firouzabad, Morteza
Abstract:
In this thesis, we study image restoration problems, which can be modeled as inverse problems. Our main focus is on inverse problems with Poisson noise; which are useful in many problems like positron emission tomography, fluorescence microscopy, and astronomy imaging. As a popular method in the literature, we use statistic modeling of inverse problem with Poisson noise, in the MAP-estimation framework. Then we introduce a semi-implicit minimization method, FB-EM-TV, that involves two alternate steps, including an EM step and a weighted ROF problem. Then we study well-posedness, existence and stability of the solution. This method can be interpreted as a forward-backward splitting strategy, which is known in convex optimization. Finally we introduce a new method of image restoration in positron emission tomography, based on total variation regularization on both image and measurement space and give some numerical result for comparison
Keywords:
Image Reconstruction ; Bayesian Analysis ; Medical Imaging ; Regularization ; Total Variation