China
Africa
Explore chapters and articles related to this topic
Charged Particle Radiography and Tomographic Imaging
Published in Paul R. Bolton, Katia Parodi, Jörg Schreiber, Applications of Laser-Driven Particle Acceleration, 2018
The next steps in the development of preclinical pCT scanning were the further development of the most likely path (MLP) concept using the particle tracking information [Schulte 2008], and the development of iterative reconstruction techniques enhanced with the superiorization methodology for reconstruction of proton CT images with about 1-mm lateral spatial resolution [Penfold 2010].
Strong convergence of over-relaxed multi-parameter proximal scaled gradient algorithm and superiorization
Published in Optimization, 2021
To apply the superiorization method, we define another objective function and expect the function to get a smaller value. To do this, some suitable iterative direction is selected (the negative gradient direction, for example). In addition, a I steering steps is applied aimed at reducing the values of φ at the iterative points. The function φ is considered an optimization criterion. The superiorization method provides us not only the algorithm for solving problem (1) but also one for solving a problem of finding smaller value of φ on H. For more details about the superiorization method, please see [19,33]. Suppose that we also obtain a summable sequence of positive real numbers, then we have
Bounded perturbation resilience and superiorization techniques for a modified proximal gradient method
Published in Optimization, 2020
On the other hand, we know that the errors often are produced in the process of calculation. It is an important property of algorithms which guarantees the convergence of the iterate under summable errors. Hence bounded perturbation resilience and superiorization of iterative methods are studied in many references such as [7–13]. The problem has received much attention due to its applications in convex feasibility problems [14], image reconstruction [15] and inverse problems of radiation therapy [16], and so on. The superiorization is finding a solution that is feasible and superior, but not necessarily optimal, which respect to the given objective function. see the reference [8].
XCT image reconstruction by a modified superiorized iteration and theoretical analysis
Published in Optimization Methods and Software, 2020
Shousheng Luo, Yanchun Zhang, Tie Zhou, Jinping Song, Yanfei Wang
The aim of superiorization algorithm is to seek a superior point rather than the optimal point with respect to the objective function of the constrained optimization problem. Although one cannot get the optimal point of the constrained problem by the superiorized iteration, the reconstruction image is usually acceptable and superior because the optimal point is probably not the solution which we want for practical problems [1,7]. For example, the optimal solution often suffers from staircase if the objective function is the total variation (TV) [11,28,32].