An interior-point method for total variation regularized positron emission tomography image reconstruction

Bing Bai

doi:10.1117/12.910624

3 March 2012 An interior-point method for total variation regularized positron emission tomography image reconstruction

Bing Bai

Proceedings Volume 8313, Medical Imaging 2012: Physics of Medical Imaging; 83136B (2012) https://doi.org/10.1117/12.910624
Event: SPIE Medical Imaging, 2012, San Diego, California, United States

Abstract

There has been a lot of work on total variation (TV) regularized tomographic image reconstruction recently. Many of them use gradient-based optimization algorithms with a differentiable approximation of the TV functional. In this paper we apply TV regularization in Positron Emission Tomography (PET) image reconstruction. We reconstruct the PET image in a Bayesian framework, using Poisson noise model and TV prior functional. The original optimization problem is transformed to an equivalent problem with inequality constraints by adding auxiliary variables. Then we use an interior point method with logarithmic barrier functions to solve the constrained optimization problem. In this method, a series of points approaching the solution from inside the feasible region are found by solving a sequence of subproblems characterized by an increasing positive parameter. We use preconditioned conjugate gradient (PCG) algorithm to solve the subproblems directly. The nonnegativity constraint is enforced by bend line search. The exact expression of the TV functional is used in our calculations. Simulation results show that the algorithm converges fast and the convergence is insensitive to the values of the regularization and reconstruction parameters.

Citation Download Citation

Bing Bai "An interior-point method for total variation regularized positron emission tomography image reconstruction", Proc. SPIE 8313, Medical Imaging 2012: Physics of Medical Imaging, 83136B (3 March 2012); https://doi.org/10.1117/12.910624

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