טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentStanislav Cherkassky
SubjectList-Mode 3D Pet Reconstruction Using Bundle-Mirror
Optimization with Subsets
DepartmentDepartment of Electrical Engineering
Supervisor Dr. Zibulevsky Michael


Abstract

Positron emission tomography (PET) is a technique for measuring the concentrations of positron-emitting radioisotopes within the tissue of living subjects. It is widely used in cancer diagnostic, drug tracing, brain and cardiac studies, etc.


In this work the reconstruction is done from the list-mode format, which is produced directly from the list of detected photons, without building intermediate projections. Using this format leads to better resolution and significantly simplifies the computations for the 3D reconstruction problem.


Maximum likelihood 3D image reconstruction in PET requires solution of a very large-scale constrained optimization problem with millions of variables. Recently proposed by A. Nemirovsky Bundle-Mirror Descent (BM) is an efficient general-purpose optimization method for very large problems.


In this work we create a modification of the BM method tailored to the list-mode image reconstruction. The modified version of the algorithm processes data in subsets for faster convergence. The size of the subsets is dynamically updated in the reconstruction process, utilizing BM’s ability to provide bound on the optimal solution and statistical properties of list-mode data.


For better image quality, Total Variation (TV) based penalty is incorporated into optimization framework. The TV regularization allows for significant noise suppression, while preserving sharp edges in the reconstructed image.


Our simulations show that our modified BM method with subsets substantially outperforms the widely accepted Expectation Maximization algorithm, especially in the presence of TV penalty.


Keywords:

3D PET, list-mode, Maximum Likelihood, Expectation Maximization, Bundle Mirror Descent, Ordered Adaptive Subsets, Total Variation