BPF Algorithms for Multiple Source-Translation Computed Tomography Reconstruction

Micro-computed tomography (micro-CT) is a widely used state-of-the-art instrument employed to study the morphological structures of objects in various fields. Object-rotation is a classical scanning mode in micro-CT allowing data acquisition from different angles; however, its field-of-view (FOV) is primarily constrained by the size of the detector when aiming for high spatial resolution imaging. Recently, we introduced a novel scanning mode called multiple source translation CT (mSTCT), which effectively enlarges the FOV of the micro-CT system. Furthermore, we developed a virtual projection-based filtered backprojection (V-FBP) algorithm to address truncated projection, albeit with a trade-off in acquisition efficiency (high resolution reconstruction typically requires thousands of source samplings). In this paper, we present a new algorithm for mSTCT reconstruction, backprojection-filtration (BPF), which enables reconstructions of high-resolution images with a low source sampling ratio. Additionally, we found that implementing derivatives in BPF along different directions (source and detector) yields two distinct BPF algorithms (S-BPF and D-BPF), each with its own reconstruction performance characteristics. Through simulated and real experiments conducted in this paper, we demonstrate that achieving same high-resolution reconstructions, D-BPF can reduce source sampling by 75% compared with V-FBP. S-BPF shares similar characteristics with V-FBP, where the spatial resolution is primarily influenced by the source sampling.Comment: 22 pages, 12 figure

Artefact Reduction Methods for Iterative Reconstruction in Full-fan Cone Beam CT Radiotherapy Applications

A cone beam CT (CBCT) system acquires two-dimensional projection images of an imaging object from multiple angles in one single rotation and reconstructs the object geometry in three dimensions for volumetric visualization. It is mounted on most modern linear accelerators and is routinely used in radiotherapy to verify patient positioning, monitor patient contour changes throughout the course of treatment, and enable adaptive radiotherapy planning. Iterative image reconstruction algorithms use mathematical methods to iteratively solve the reconstruction problem. Iterative algorithms have demonstrated improvement in image quality and / or reduction in imaging dose over traditional filtered back-projection (FBP) methods. However, despite the advancement in computer technology and growing availability of open-source iterative algorithms, clinical implementation of iterative CBCT has been limited. This thesis does not report development of codes for new iterative image reconstruction algorithms. It focuses on bridging the gap between the algorithm and its implementation by addressing artefacts that are the results of imperfections from the raw projections and from the imaging geometry. Such artefacts can severely degrade image quality and cannot be removed by iterative algorithms alone. Practical solutions to solving these artefacts will be presented and this in turn will better enable clinical implementation of iterative CBCT reconstruction

Mathematical Methods in Tomography

This is the seventh Oberwolfach conference on the mathematics of tomography, the first one taking place in 1980. Tomography is the most popular of a series of medical and scientific imaging techniques that have been developed since the mid seventies of the last century

Modeling and Development of Iterative Reconstruction Algorithms in Emerging X-ray Imaging Technologies

Many new promising X-ray-based biomedical imaging technologies have emerged over the last two decades. Five different novel X-ray based imaging technologies are discussed in this dissertation: differential phase-contrast tomography (DPCT), grating-based phase-contrast tomography (GB-PCT), spectral-CT (K-edge imaging), cone-beam computed tomography (CBCT), and in-line X-ray phase contrast (XPC) tomosynthesis. For each imaging modality, one or more specific problems prevent them being effectively or efficiently employed in clinical applications have been discussed. Firstly, to mitigate the long data-acquisition times and large radiation doses associated with use of analytic reconstruction methods in DPCT, we analyze the numerical and statistical properties of two classes of discrete imaging models that form the basis for iterative image reconstruction. Secondly, to improve image quality in grating-based phase-contrast tomography, we incorporate 2nd order statistical properties of the object property sinograms, including correlations between them, into the formulation of an advanced multi-channel (MC) image reconstruction algorithm, which reconstructs three object properties simultaneously. We developed an advanced algorithm based on the proximal point algorithm and the augmented Lagrangian method to rapidly solve the MC reconstruction problem. Thirdly, to mitigate image artifacts that arise from reduced-view and/or noisy decomposed sinogram data in K-edge imaging, we exploited the inherent sparseness of typical K-edge objects and incorporated the statistical properties of the decomposed sinograms to formulate two penalized weighted least square problems with a total variation (TV) penalty and a weighted sum of a TV penalty and an l1-norm penalty with a wavelet sparsifying transform. We employed a fast iterative shrinkage/thresholding algorithm (FISTA) and splitting-based FISTA algorithm to solve these two PWLS problems. Fourthly, to enable advanced iterative algorithms to obtain better diagnostic images and accurate patient positioning information in image-guided radiation therapy for CBCT in a few minutes, two accelerated variants of the FISTA for PLS-based image reconstruction are proposed. The algorithm acceleration is obtained by replacing the original gradient-descent step by a sub-problem that is solved by use of the ordered subset concept (OS-SART). In addition, we also present efficient numerical implementations of the proposed algorithms that exploit the massive data parallelism of multiple graphics processing units (GPUs). Finally, we employed our developed accelerated version of FISTA for dealing with the incomplete (and often noisy) data inherent to in-line XPC tomosynthesis which combines the concepts of tomosynthesis and in-line XPC imaging to utilize the advantages of both for biological imaging applications. We also investigate the depth resolution properties of XPC tomosynthesis and demonstrate that the z-resolution properties of XPC tomosynthesis is superior to that of conventional absorption-based tomosynthesis. To investigate all these proposed novel strategies and new algorithms in these different imaging modalities, we conducted computer simulation studies and real experimental data studies. The proposed reconstruction methods will facilitate the clinical or preclinical translation of these emerging imaging methods

Latest developments in the improvement and quantification of high resolution X-ray tomography data

X-ray Computed Tomography (CT) is a powerful tool to visualize the internal structure of objects. Although X-ray CT is often used for medical purposes, it has many applications in the academic and industrial world. X-ray CT is a non destructive tool which provides the possibility to obtain a three dimensional (3D) representation of the investigated object. The currently available high resolution systems can achieve resolutions of less than one micrometer which makes it a valuable technique for various scientific and industrial applications. At the Centre for X-ray Tomography of the Ghent University (UGCT) research is performed on the improvement and application of high resolution X-ray CT (µCT). Important aspects of this research are the development of state of the art high resolution CT scanners and the development of software for controlling the scanners, reconstruction software and analysis software. UGCT works closely together with researchers from various research fields and each of them have their specific requirements. To obtain the best possible results in any particular case, the scanners are developed in a modular way, which allows for optimizations, modifications and improvements during use. Another way of improving the image quality lies in optimization of the reconstruction software, which is why the software package Octopus was developed in house. Once a scanned volume is reconstructed, an important challenge lies in the interpretation of the obtained data. For this interpretation visualization alone is often insufficient and quantitative information is needed. As researchers from different fields have different needs with respect to quantification of their data, UGCT developed the 3D software analysis package Morpho+ for analysing all kinds of samples. The research presented in this work focuses on improving the accuracy and extending the amount of the quantitative information which can be extracted from µCT data. Even if a perfect analysis algorithm would exist, it would be impossible to accurately quantify data of which the image quality is insufficient. As image quality can significantly be improved with the aid of adequate reconstruction techniques, the research presented in this work focuses on analysis as well as reconstruction software. As the datasets obtained with µCT at UGCT are of substantial size, the possibility to process large datasets in a limited amount of time is crucial in the development of new algorithms. The contributions of the author can be subdivided in three major aspects of the processing of CT data: The modification of iterative reconstruction algorithms, the extension and optimization of 3D analysis algorithms and the development of a new algorithm for discrete tomography. These topics are discussed in more detail below. A main aspect in the improvement of image quality is the reduction of artefacts which often occur in µCT such as noise-, cone beam- and beam hardening artefacts. Cone beam artefacts are a result of the cone beam geometry which is often used in laboratory based µCT and beam hardening is a consequence of the polychromaticity of the beam. Although analytical reconstruction algorithms based on filtered back projection are still most commonly used for the reconstruction of µCT datasets, there is another approach which is becoming a valuable alternative: iterative reconstruction algorithms. Iterative algorithms are inherently better at coping with the previously mentioned artefacts. Additionally iterative algorithms can improve image quality in case the number of available projections or the angular range is limited. In chapter 3 the possibility to modify these algorithms to further improve image quality is investigated. It is illustrated that streak artefacts which can occur when metals are present in a sample can be significantly reduced by modifying the reconstruction algorithm. Additionally, it is demonstrated that the incorporation of an initial solution (if available) allows reducing the required number of projections for a second slightly modified sample. To reduce beam hardening artefacts, the physics of the process is modelled and incorporated in the iterative reconstruction algorithm, which results in an easy to use and efficient algorithm for the reduction of beam hardening artefacts and requires no prior knowledge about the sample. In chapter 4 the 3D analysis process is described. In the scope of this work, algorithms of the 3D-analysis software package Morpho+ were optimized and new methods were added to the program, focusing on quantifying connectivity and shape of the phases and elements in the sample, as well as obtaining accurate segmentation, which is essential step in the analysis process is the segmentation of the reconstructed sample. Evidently, the different phases in the sample need to be separated from one another. However, often a second segmentation step is needed in order to separate the different elements present in a volume, such as pores in a pore network, or to separate elements which are physically separated but appear to be connected on the reconstructed images to limited resolution and/or limited contrast of the scan. The latter effect often occurs in the process of identifying different grains in a geological sample. Algorithms which are available for this second segmentation step often result in over-segmentation, i.e. elements are not only separated from one another but also separations inside a single element occur. To overcome this effect an algorithm is presented to semi-automically rejoin the separated parts of a single element. Additionally, Morpho+ was extended with tools to extract information about the connectivity of a sample, which is difficult to quantify but important for samples from various research fields. The connectivity can be described with the aid of the calculation of the Euler Number and tortuosity. Moreover, the number of neighbouring objects of each object can be determined and the connections between objects can be quantified. It is now also possible to extract a skeleton, which describes the basic structure of the volume. A calculation of several shape parameters was added to the program as well, resulting in the possibility to visualize the different objects on a disc-rod diagram. The many possibilities to characterize reconstructed samples with the aid of Morpho+ are illustrated on several applications. As mentioned in the previous section, an important aspect for correctly quantifying µCT data is the correct segmentation of the different phases present in the sample. Often it is the case that a sample consists of only one or a limited number of materials (and surrounding air). In this case this prior knowledge about the sample can be incorporated in the reconstruction algorithm. These kind of algorithms are referred to as discrete reconstruction algorithms, which are used when only a limited number of projections is available. Chapter 5 deals with discrete reconstruction algorithms. One of these algorithms is the Discrete Algebraic Reconstruction Technique, which combines iterative with discrete reconstruction and has shown excellent results. DART requires knowledge about the attenuation coefficient(s) and segmentation threshold(s) of the material(s). For µCT applications (resulting in large datasets) reconstruction times can significantly increase when DART is used in comparison with standard iterative reconstruction, as DART requires more iterations. This complicates the practical applicability of DART for routine applications at UGCT. Therefore a modified algorithm (based on the DART algorithm) for reconstruction of samples consisting out of only one material and surrounding air was developed in the scope of this work, which is referred to as the Experimental Discrete Algebraic Reconstruction Technique (EDART). The goal of this algorithm is to obtain better reconstruction results in comparison with standard iterative reconstruction algorithms, without significantly increasing reconstruction time. Moreover, a fast and intuitive technique to estimate the attenuation coefficient and threshold was developed as a part of the EDART algorithm. In chapter 5 it is illustrated that EDART provides improved image quality for both phantom and real data, in comparison with standard iterative reconstruction algorithms, when only a limited number of projections is available. The algorithms presented in this work can be subsequently applied but can also be combined with one another. It is for example illustrated in chapter 5 that the beam hardening correction method can also be incorporated in the EDART algorithm. The combination of the introduced methods allows for an improvement in the process of extracting accurate quantitative information from µCT data