Wim van Aarle

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.

Fast and flexible X-ray tomography using the ASTRA toolbox

Object reconstruction from a series of projection images, such as in computed tomography (CT), is a popular tool in many different application fields. Existing commercial software typically provides sufficiently accurate and convenient-to-use reconstruction tools to the end-user. However, in applications where a non-standard acquisition protocol is used, or where advanced reconstruction methods are required, the standard software tools often are incapable of computing accurate reconstruction images. This article introduces the ASTRA Toolbox. Aimed at researchers across multiple tomographic application fields, the ASTRA Toolbox provides a highly efficient and highly flexible open source set of tools for tomographic projection and reconstruction. The main features of the ASTRA Toolbox are discussed and several use cases are presented.

Optimal Threshold Selection for Segmentation of Dense Homogeneous Objects in Tomographic Reconstructions

In this paper, we present a novel approach to segment dense, homogeneous objects in a tomographic reconstruction (or tomogram). A popular method to extract such objects from a tomogram is global thresholding, in which the threshold value is determined from the image histogram. However, accurate threshold selection is not straightforward, since, due to noise or artefacts in the reconstruction, the histogram does not always contain a clear, separate peak for the dense object. We propose a new threshold estimation approach, segmentation inconsistency minimization, that exploits the available projection data to determine the optimal global threshold. The proposed algorithm was tested on simulation data and on experimental μCT data. The results show that this method results in more accurate segmentations, compared to alternative threshold selection methods.

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 homogeneous materials, the reconstruction resolution can be substantially increased without altering the acquisition process. A super-resolution reconstruction approach is introduced that is based on discrete tomography, in which prior knowledge about the materials in the object is assumed. Discrete tomography has already been used to create reconstructions from a low number of projection angles, but in this paper, it is demonstrated that it can also be applied to increase the reconstruction resolution. Experiments on simulated and real μCT data of bone and foam structures show that the proposed method indeed leads to significantly improved structure segmentation and quantification compared with what can be achieved from conventional reconstructions.

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.

A discrete tomography approach for superresolution micro-CT images: application to bone

In micro-CT imaging, the effective spatial resolution of the reconstructed images is generally limited by X-ray dose restrictions, the detector configuration or the scanning geometry. In this paper, we show that, using prior information on the grey values of the scanned objects, the spatial resolution of the reconstructed images can dramatically be improved. The proposed method is based on an upsampling of the reconstruction grid, combined with the DART algorithm (discrete algebraic reconstruction technique [1]), in which the scanned object is assumed to be composed of homogeneous materials. Experiments were run on simulated data as well as real X-ray CT data of the rat trabecular bone. Results show that the proposed method generates reconstructions with significantly more detail compared to conventional reconstruction algorithms.

An accurate projection model for diffraction image formation and inversion using a polychromatic cone beam

Recently, the concept of X-ray diffraction contrast tomography (DCT) has been extended to the case of more widely available laboratory source CT systems. Using well known concepts from geometrical ray optics, an exact formulation is derived for the forward and backward projection geometry encountered under polychromatic cone beam illumination, and it is shown how this projection model can be efficiently implemented in practice. The new projection model is subsequently used for iterative tomographic reconstruction of the three-dimensional shape of a grain from a set of experimentally observed cone beam projections and shows a clear improvement compared to the simplified projection model used previously.

Threshold Selection for Segmentation of Dense Objects in Tomograms

Tomographic reconstructions are often segmented to extract valuable quantitative information. In this paper, we consider the problem of segmenting a dense object of constant density within a continuous tomogram, by means of global thresholding. Selecting the proper threshold is a nontrivial problem, for which hardly any automatic procedures exists. We propose a new method that exploits the available projection data to accurately determine the optimal global threshold. Results from simulation experiments show that our algorithm is capable of finding a threshold that is close to the optimal threshold value.

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.

Discrete algebraic reconstruction technique : a new approach for superresolution reconstruction of license plates

Abstract. A new superresolution algorithm is proposed to reconstruct a high-resolution license plate image from a set of low-resolution camera images. The reconstruction methodology is based on the discrete algebraic reconstruction technique (DART), a recently developed reconstruction method. While DART has already been successfully applied in tomographic imaging, it has not yet been transferred to the field of camera imaging. DART is introduced for camera imaging through a demonstration of how prior knowledge of the colors of the license plate can be directly exploited during the reconstruction of a high-resolution image from a set of low-resolution images. Simulation experiments show that DART can reconstruct images with superior quality compared to conventional reconstruction methods.