Fast tomographic inspection of cylindrical objects

This paper presents a method for improved analysis of objects with an axial symmetry using X-ray Computed Tomography (CT). Cylindrical coordinates about an axis fixed to the object form the most natural base to check certain characteristics of objects that contain such symmetry, as often occurs with industrial parts. The sampling grid corresponds with the object, allowing for down-sampling hence reducing the reconstruction time. This is necessary for in-line applications and fast quality inspection. With algebraic reconstruction it permits the use of a pre-computed initial volume perfectly suited to fit a series of scans where same-type objects can have different positions and orientations, as often encountered in an industrial setting. Weighted back-projection can also be included when some regions are more likely subject to change, to improve stability. Building on a Cartesian grid reconstruction code, the feasibility of reusing the existing ray-tracers is checked against other researches in the same field.Comment: 13 pages, 13 figures. submitted to Journal Of Nondestructive Evaluation (https://www.springer.com/journal/10921

Accurately approximating algebraic tomographic reconstruction by filtered backprojection

In computed tomography, algebraic reconstruction methods tend to produce reconstructions with higher quality than analytical methods when presented with limited and noisy projection data. The high computational requirements of algebraic methods, however, limit their usefulness in practice. In this paper, we propose a method to approximate the algebraic SIRT method by the computationally efficient filtered backprojection method. The method is based on an efficient way of computing a special angle-dependent convolution filter for filtered backprojection. Using this method, a reconstruction quality that is similar to SIRT can be achieved by existing efficient implementations of the filtered backprojection method. Results for a phantom image show that the method is indeed able to produce reconstructions with a quality similar to algebraic methods when presented with limited and noisy projection data

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

Modifications of iterative reconstruction algorithms for the reduction of artefacts in high resolution X-ray computed tomography

X-ray Computed Tomography is a non destructive technique which allows for the visualization of the internal structure of complex objects. Most commonly, algorithms based on filtered backprojection are used for reconstruction of the projection data obtained with CT. However, the reconstruction can also be done using iterative reconstructions methods. These algorithms have shown promising results regarding the improvement of the image quality. An additional advantage is that these flexible algorithms can be modified in order to incorporate prior knowledge about the sample during the reconstruction, which allows for the reduction of artefacts. In this paper some of these advantages will be discussed and illustrated: the incorporation of an initial solution, the reduction of metal artefacts and the reduction of beam hardening artefacts

Geometric reconstruction methods for electron tomography

Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is seriously affected by the problems of missing wedge artefacts and nonlinear projection intensities due to diffraction effects. The former refers to the fact that data cannot be acquired over the full $180^\circ$ tilt range; the latter implies that for some orientations, crystalline structures can show strong contrast changes. To overcome these problems we introduce and discuss several algorithms from the mathematical fields of geometric and discrete tomography. The algorithms incorporate geometric prior knowledge (mainly convexity and homogeneity), which also in principle considerably reduces the number of tilt angles required. Results are discussed for the reconstruction of an InAs nanowire

Four-dimensional tomographic reconstruction by time domain decomposition

Since the beginnings of tomography, the requirement that the sample does not change during the acquisition of one tomographic rotation is unchanged. We derived and successfully implemented a tomographic reconstruction method which relaxes this decades-old requirement of static samples. In the presented method, dynamic tomographic data sets are decomposed in the temporal domain using basis functions and deploying an L1 regularization technique where the penalty factor is taken for spatial and temporal derivatives. We implemented the iterative algorithm for solving the regularization problem on modern GPU systems to demonstrate its practical use