A multi-level preconditioned Krylov method for the efficient solution of algebraic tomographic reconstruction problems

Classical iterative methods for tomographic reconstruction include the class of Algebraic Reconstruction Techniques (ART). Convergence of these stationary linear iterative methods is however notably slow. In this paper we propose the use of Krylov solvers for tomographic linear inversion problems. These advanced iterative methods feature fast convergence at the expense of a higher computational cost per iteration, causing them to be generally uncompetitive without the inclusion of a suitable preconditioner. Combining elements from standard multigrid (MG) solvers and the theory of wavelets, a novel wavelet-based multi-level (WMG) preconditioner is introduced, which is shown to significantly speed-up Krylov convergence. The performance of the WMG-preconditioned Krylov method is analyzed through a spectral analysis, and the approach is compared to existing methods like the classical Simultaneous Iterative Reconstruction Technique (SIRT) and unpreconditioned Krylov methods on a 2D tomographic benchmark problem. Numerical experiments are promising, showing the method to be competitive with the classical Algebraic Reconstruction Techniques in terms of convergence speed and overall performance (CPU time) as well as precision of the reconstruction.Comment: Journal of Computational and Applied Mathematics (2014), 26 pages, 13 figures, 3 table

The Impact of Fiscal Rules on Public Finances: Theory and Empirical Evidence for the Euro Area

This paper presents a review of the most significant fiscal rules policymakers can choose from. The insights from this review are then applied to the current budgetary situation of the European Union. In the European Union, the supranational Stability and Growth Pact (SGP) should provide the necessary guidance in limiting governmental borrowing by member states. In addition to the SGP, European countries are implementing various other fiscal rules that bind central, regional and local governments. We provide empirical estimates of the effect of fiscal rules on fiscal balance, government spending and government revenues, using a Fiscal Rule Index. We find that fiscal rules have some effect on fiscal balances.euro area, fiscal policy, policy rules, fiscal sustainability

Super-Resolution for Computed Tomography Based on Discrete Tomography

In computed tomography (CT), partial volume effects impede accurate segmentation of structures that are small with respect to the pixel size. In this paper, it is shown that for objects consisting of a small number of homogen

Easy implementation of advanced tomography algorithms using the ASTRA toolbox with Spot operators

Mathematical scripting languages are commonly used to develop new tomographic reconstruction algorithms. For large experimental datasets, high performance parallel (GPU) implementations are essential, requiring a re-implementation of the algorithm using a language that is closer to the computing hardware. In this paper, we introduce a new Matlab interface to the ASTRA toolbox, a high performance toolbox for building tomographic reconstruction algorithms. By exposing the ASTRA linear tomography operators through a standard Matlab matrix syntax, existing and new reconstruction algorithms implemented in Matlab can now be applied directly to large experimental datasets. This is achieved by using the Spot toolbox, which wraps external code for linear operations into Matlab objects that can be used as matrices. We provide a series of examples that demonstrate how this Spot operator can be used in combination with existing algorithms implemented in Matlab and how it can be used for rapid development of new algorithms, resulting in direct applicability to large-scale experimental datasets

The ASTRA Toolbox: A platform for advanced algorithm development in electron tomography

We present the ASTRA Toolbox as an open platform for 3D image reconstruction in tomography. Most of the software tools that are currently used in electron tomography offer limited flexibility with respect to the geometrical parameters of the acquisition model and the algorithms used for reconstruction. The ASTRA Toolbox provides an extensive set of fast and flexible building blocks that can be used to develop advanced reconstruction algorithms, effectively removing these limitations. We demonstrate this flexibility, the resulting reconstruction quality, and the computational efficiency of this toolbox by a series of experiments, based on experimental dual-axis tilt series