اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدStopping Rules for Algebraic Iterative Reconstruction Methods in Computed Tomography
78
0
0.0
(
0
)
نشر من قبل
Jakob Sauer J{\\o}rgensen
تاريخ النشر
2021
مجال البحث
الهندسة المعلوماتية
والبحث باللغة
English
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Algebraic models for the reconstruction problem in X-ray computed tomography (CT) provide a flexible framework that applies to many measurement geometries. For large-scale problems we need to use iterative solvers, and we need stopping rules for these methods that terminate the iterations when we have computed a satisfactory reconstruction that balances the reconstruction error and the influence of noise from the measurements. Many such stopping rules are developed in the inverse problems communities, but they have not attained much attention in the CT world. The goal of this paper is to describe and illustrate four stopping rules that are relevant for CT reconstructions.
قيم البحث
اقرأ أيضاً
Discrete variational methods have shown an excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative method for discrete variational methods appropriate for boundary value problems. More
concretely, we explore a parallelization strategy that leverages the power of multicore CPUs and GPUs (graphics cards). We study this parallel method for first-order and second-order Lagrangians and we illustrate its excellent behavior in some interesting applications, namely Zermelos navigation problem, a fuel-optimal navigation problem, and an interpolation problem.
We consider reconstructing multi-channel images from measurements performed by photon-counting and energy-discriminating detectors in the setting of multi-spectral X-ray computed tomography (CT). Our aim is to exploit the strong structural correlatio
n that is known to exist between the channels of multi-spectral CT images. To that end, we adopt the multi-channel Potts prior to jointly reconstruct all channels. This prior produces piecewise constant solutions with strongly correlated channels. In particular, edges are enforced to have the same spatial position across channels which is a benefit over TV-based methods. We consider the Potts prior in two frameworks: (a) in the context of a variational Potts model, and (b) in a Potts-superiorization approach that perturbs the iterates of a basic iterative least squares solver. We identify an alternating direction method of multipliers (ADMM) approach as well as a Potts-superiorized conjugate gradient method as particularly suitable. In numerical experiments, we compare the Potts prior based approaches to existing TV-type approaches on realistically simulated multi-spectral CT data and obtain improved reconstruction for compound solid bodies.
This paper gives a unified convergence analysis of additive Schwarz methods for general convex optimization problems. Resembling to the fact that additive Schwarz methods for linear problems are preconditioned Richardson methods, we prove that additi
ve Schwarz methods for general convex optimization are in fact gradient methods. Then an abstract framework for convergence analysis of additive Schwarz methods is proposed. The proposed framework applied to linear elliptic problems agrees with the classical theory. We present applications of the proposed framework to various interesting convex optimization problems such as nonlinear elliptic problems, nonsmooth problems, and nonsharp problems.
Often in applications ranging from medical imaging and sensor networks to error correction and data science (and beyond), one needs to solve large-scale linear systems in which a fraction of the measurements have been corrupted. We consider solving s
uch large-scale systems of linear equations $mathbf{A}mathbf{x}=mathbf{b}$ that are inconsistent due to corruptions in the measurement vector $mathbf{b}$. We develop several variants of iterative methods that converge to the solution of the uncorrupted system of equations, even in the presence of large corruptions. These methods make use of a quantile of the absolute values of the residual vector in determining the iterate update. We present both theoretical and empirical results that demonstrate the promise of these iterative approaches.
This survey concerns subspace recycling methods, a popular class of iterative methods that enable effective reuse of subspace information in order to speed up convergence and find good initial guesses over a sequence of linear systems with slowly cha
nging coefficient matrices, multiple right-hand sides, or both. The subspace information that is recycled is usually generated during the run of an iterative method (usually a Krylov subspace method) on one or more of the systems. Following introduction of definitions and notation, we examine the history of early augmentation schemes along with deflation preconditioning schemes and their influence on the development of recycling methods. We then discuss a general residual constraint framework through which many augmented Krylov and recycling methods can both be viewed. We review several augmented and recycling methods within this framework. We then discuss some known effective strategies for choosing subspaces to recycle before taking the reader through more recent developments that have generalized recycling for (sequences of) shifted linear systems, some of them with multiple right-hand sides in mind. We round out our survey with a brief review of application areas that have seen benefit from subspace recycling methods.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
