Abstract
Total variation (TV) minimization algorithm is an effective algorithm capable of accurately reconstructing images from sparse projection data in a variety of imaging modalities including computed tomography (CT) and electron paramagnetic resonance imaging (EPRI). The data divergence constrained, TV minimization (DDcTV) model and its Chambolle-Pock (CP) solving algorithm have been proposed for CT. However, when the DDcTV-CP algorithm is applied to 3D EPRI, it suffers from slow convergence rate or divergence. We hypothesize that this is due to the magnitude imbalance between the data fidelity term and the TV regularization term. In this work, we propose a balanced TV (bTV) model incorporating a balance parameter and demonstrate its capability to avoid convergence issues for the 3D EPRI application. Simulation and real experiments show that the DDcTV-CP algorithm cannot guarantee convergence but the bTV-CP algorithm may guarantee convergence and achieve fast convergence by use of an appropriate balance parameter. Experiments also show that underweighting the balance parameter leads to slow convergence, whereas overweighting the balance parameter leads to divergence. The iteration-behavior change-law with the variation of the balance parameter is explained by use of the data tolerance ellipse and gradient descent principle. The findings and insights gained in this work may be applied to other imaging modalities and other constrained optimization problems.