![]() With access to the designed solution, the difference between it and previous iterates can be quantitatively evaluated to see whether this difference is significant with respect to a given CT imaging task. Convergent algorithms can also aid in determining at what iteration number to truncate an IIR algorithm. Achieving convergent algorithms is important, because they yield access to the designed solution of the optimization problem and allow for direct assessment of what factors to include in a particular optimization. Once the optimization problem is established, algorithms are developed to solve it. When designing IIR algorithms to account for various factors in the CT model, the actual designing occurs usually at the optimization problem and not the individual processing steps of the IIR algorithm. Iterative image reconstruction (IIR) algorithms in computed tomography (CT) are designed based on some form of optimization. The present paper demonstrates the methodology, and future work will illustrate its utility in actual CT application. The approach is amenable to recent methods for accelerating first-order algorithms which may be particularly useful for CT with limited angular-range scanning. The CP algorithms are seen in the empirical results to converge to the solution of their respective convex feasibility problems.Ĭonclusions: Formulation of convex feasibility problems can provide a useful alternative to unconstrained optimization when designing IIR algorithms for CT. Results: The accelerated CP algorithms are demonstrated on a simulation of circular fan-beam CT with a limited scanning arc of 144°. One of the proposed problems is seen to be equivalent to least-squares minimization, and two other problems provide alternatives to penalized, least-squares minimization. Methods: An accelerated version of the Chambolle−Pock (CP) algorithm is adapted to various convex feasibility problems of potential interest to IIR in CT. The convex feasibility approach can provide alternatives to unconstrained optimization approaches and at the same time allow for rapidly convergent algorithms for their solution-thereby facilitating the IIR algorithm design process. In this paper, we develop IIR algorithms which solve a certain type of optimization called convex feasibility. ![]() This issue is particularly acute for CT with a limited angular-range scan, which leads to poorly conditioned system matrices and difficult to solve optimization problems. Often times, however, it is impractical to achieve accurate solution to the optimization of interest, which complicates design of IIR algorithms. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the optimization problem on which it is based. All rights reserved.Purpose: Iterative image reconstruction (IIR) algorithms in computed tomography (CT) are based on algorithms for solving a particular optimization problem. The findings and insights gained in this work may be applied to other imaging modalities and other constrained optimization problems.īalance parameter Chambolle-Pock algorithm EPR imaging Optimization Total variation minimization.Ĭopyright © 2021 Elsevier Inc. 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. Experiments also show that underweighting the balance parameter leads to slow convergence, whereas overweighting the balance parameter leads to divergence. 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. 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. We hypothesize that this is due to the magnitude imbalance between the data fidelity term and the TV regularization term. However, when the DDcTV-CP algorithm is applied to 3D EPRI, it suffers from slow convergence rate or divergence. The data divergence constrained, TV minimization (DDcTV) model and its Chambolle-Pock (CP) solving algorithm have been proposed for CT. 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).
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |