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The problem of reconstructing an image from a set of tomographic data is not new, nor is it lacking attention. However there is still a distinct gap between the mathematicians and the experimental scientists working in the computed tomography (CT) imaging community. One of the aims in this thesis is to bridge this gap with mathematical reconstruction algorithms and analysis approaches applied to practical CT problems. The thesis begins with an extensive analysis for assessing the suitability of reconstruction algorithms for a given problem. The paper presented examines the idea of extracting physical information from a reconstructed sample and comparing against the known sample characteristics to determine the accuracy of a reconstructed volume. Various test cases are studied, which are relevant to both mathematicians and experimental scientists. These include the variance in quality of reconstructed volume as the dose is reduced or the implementation of the level set evolution method, used as part of a simultaneous reconstruction and segmentation technique. The work shows that the assessment of physical attributes results in more accurate conclusions. Furthermore, this approach allows for further analysis into interesting questions in CT. This theme is continued throughout the thesis. Recent results in compressive sensing (CS) gained attention in the CT community as they indicate the possibility of obtaining an accurate reconstruction of a sparse image from severely limited or reduced amount of measured data. Literature produced so far has not shown that CS directly guarantees a successful recovery in X-ray CT, and it is still unclear under which conditions a successful sparsity regularized reconstruction can be achieved. The work presented in the thesis aims to answer this question in a practical setting, and seeks to establish a direct connection between the success of sparsity regularization methods and the sparsity level of the image, which is similar to CS. Using this connection, one can determine the sufficient amount of measurements to collect from just the sparsity of an image. A link was found in a previous study using simulated data, and the work is repeated here with experimental data, where the sparsity level of the scanned object varies. The preliminary work presented here verifies the results from simulated data, showing an "almost-linear" relationship between the sparsity of the image and the sufficient amount of data for a successful sparsity regularized reconstruction. Several unexplained artefacts are noted in the literature as the `partial volume', the 'exponential edge gradient' or the 'penumbra' effect, with no clear explanation for their cause, or established techniques to remove them. The work presented in this paper shows that these artefacts are due to a non-linearity in the measured data, which comes from either the set up of the system, the scattering of rays or the dependency of linear attenuation on wavelength in the polychromatic case. However, even in monochromatic CT systems, the non-linearity effect can be detected. The paper shows that in some cases, the non-linearity effect is too large to ignore, and the reconstruction problem should be adapted to solve a non-linear problem. We derive this non-linear problem and solve it using a numerical optimization technique for both simulatedand real, gamma-ray data. When compared to reconstructions obtained using the standard linear model, the non-linear reconstructed images show clear improvements in that the non-linear effect is largely eliminated. The thesis is finished with a highlight article in the special issue of Solid Earth, named "Pore-scale tomography & imaging - applications, techniques and recommended practice". The paper presents a major technical advancement in a dynamic 3D CT data acquisition, where the latest hardware and optimal data acquisition plan are applied and as a result, ultra fast 3D volume acquisition was made possible. The experiment comprised of fast, free-falling water-saline drops traveling through a pack of rock grains with varying porosities. The imaging work was enhanced by the use of iterative methods and physical quantification analysis performed. The data acquisition and imaging work is the first in the field to capture a free falling drop and the imaging work clearly shows the fluid interaction with speed, gravity and more importantly, the inter- and intra-grain fluid transfers.

This paper introduces 3D-DDnet, a cutting-edge 3D deep learning (DL) framework designed to improve the image quality of low-dose computed tomography (LDCT) scans. Although LDCT scans are advantageous for reducing radiation exposure, they inherently suffer from reduced image quality. Our novel 3D DL architecture addresses this issue by effectively enhancing LDCT images to achieve parity with the quality of standard-dose CT scans. By exploiting the inter-slice correlation present in volumetric CT data, 3D-DDnet surpasses existing denoising benchmarks. It incorporates distributed data parallel (DDP) and transfer learning techniques to significantly accelerate the training process. The DDP approach is particularly tailored for operation across multiple Nvidia A100 GPUs, facilitating the processing of large-scale volumetric data sets that were previously unmanageable due to size constraints. Comparative analyses demonstrate that 3D-DDnet reduces the mean square error (MSE) by 10% over its 2D counterpart, 2D-DDnet. Moreover, by applying transfer learning from pre-trained 2D models, 3D-DDnet effectively 'jump starts' the learning process, cutting training times by half without compromising on model accuracy.

Lung cancer is a common type of cancer that causes death if not detectedearly enough. Doctors use computed tomography (CT) images to diagnoselung cancer. The accuracy of the diagnosis relies highly on the doctor'sexpertise. Recently, clinical decision support systems based on deep learningvaluable recommendations to doctors in their diagnoses. In this paper, wepresent several deep learning models to detect non-small cell lung cancer inCT images and differentiate its main subtypes namely adenocarcinoma,large cell carcinoma, and squamous cell carcinoma. We adopted standardconvolutional neural networks (CNN), visual geometry group-16 (VGG16),and VGG19. Besides, we introduce a variant of the CNN that is augmentedwith convolutional block attention modules (CBAM). CBAM aims to extractinformative features by combining cross-channel and spatial information.We also propose variants of VGG16 and VGG19 that utilize a supportvector machine (SVM) at the classification layer instead of SoftMax. Wevalidated all models in this study through extensive experiments on a CTlung cancer dataset. Experimental results show that supplementing CNNwith CBAM leads to consistent improvements over vanilla CNN. Resultsalso show that the VGG variants that use the SVM classifier outperform theoriginal VGGs by a significant margin.

Sandwich structural elements consist of two metallic or non-metallic laminated skins separated by a lightweight thicker core layer, maximizing in this manner weight efficiency and structural performance. From the available core configurations, phenolic resin impregnated Nomex® paper honeycomb cores are highly preferred in aerospace industry because of their lower density, excellent thermal resistance, and curved shape adaptability. Despite the inherent benefits of Nomex® paper sandwich structures, their impact response is still questionable. Towards this direction, a series of simulated hail ice impact tests was performed on flat carbon fiber sandwich panels via gas gun test apparatus to assess Nomex® paper core damage. Impact test results revealed significant core crushing in the form of cell collapse without any externally visible signs of damage on the impacted skin surface.Since high-velocity impact tests on sandwich panels are by nature highly complex, the out-of-plane response of over-expanded Nomex® cores was phenomenologically characterized through quasi-static flatwise compression tests on stabilized sandwich core coupons. Localized detachment and crushing of the phenolic resin accumulation regions between adjacent cell walls, were the main damage modes that triggered honeycomb collapse.X-ray Computed Tomography (CT) scans were also employed to assess damage modes on the interior cells of tested sandwich core coupons. Given several sets of X-ray CT scan 3D data, an automated B-spline image-based reconstruction scheme was developed to numerically capture scanned honeycomb core geometries. Different applications of the proposed reconstruction scheme are going to be presented. Finally, the contribution of the phenolic resin accumulation regions on the out-of-plane response was investigated through numerical modeling of the reconstructed B-spline geometry. To this end, constituent material properties were determined through uniaxial tensile testing on in-situ phenolic resin impregnated paper coupons as well as bare aramid paper coupons. Numerical simulations on sandwich cores without the phenolic resin accumulations yielded significant reduction of the collapse limit, validating in this way the experimental observations.

This thesis concerns the simulation of locomotion in vertebrates. The state-of-the-art uses genetic algorithms together with solid body kinematics to generate possible solutions for stable gaits. In recent work, this methodology led to a hopping gait in a dinosaur and the researchers wondered if this was realistic. The purpose of the research carried out in this thesis was to examine whether quick and simple finite-element analyses could be added to the simulator, to evaluate a simple ―break or―not break failure criterion. A break would rule out gaits that might damage theowner‘s skeleton. Linear elastic analysis was considered as a possible approach as it would add little overhead to the simulations. The author used X-ray computed tomography and the finite element method to examine the axial loading of a barnacle goose femur. The study considered four levels of detail for a linear elastic simulation, finding that all the analyses carried out overestimated the strength of the bone, when considering safety factors. The conclusion is that to incorporate stress-strain analysis into the gait simulation requires more realistic models of bone behaviour that incorporate the nonlinear response of bone to applied loading. A new study focusing on the use of novel techniques such as model order reduction is recommended for future work. The outputs of this research include chapters written up as journal papers covering a 4D tomography experiment; a level of detail study; an analysis of a purported tendon avulsion injury in Tyrannosaurus rex and a review of the elastic properties of bone.

Lung cancer is responsible for the majority of cancer related deaths in the United States. One way to improve the chance of survival is early detection of Lung Nodules. Lung nodules are small, spherical, potentially cancerous growths within the lung. Several Computer Aided Detection (CAD) systems have been developed to aid in the detection of lung nodules both in computed tomography (CT) and chest radiograph scans. To increase performance and reduce the number of false positives, or misclassifications, in the detection, a feature selection technique is often applied to CAD systems. Feature selection is a method of selecting an optimal subset of features from all features calculated. In this case, a feature is defined as a quantitative characteristic calculated for a potential lung nodule directly from the input scan. Examples of simple features calculated for CAD systems include size, brightness, and shape of potential lung nodules. Common algorithms for feature selection include genetic algorithms and sequential forward selection. This paper proposes a genetic algorithm approach to feature selection for lung nodule CAD systems. Using existing CAD systems with our new feature selection technique, performance is evaluated on both CT scans using the LIDC-IDRI dataset as well as Chest Radiograph scans using the JRST dataset. A total number of 503 features are evaluated for the CT CAD system and 117 features for chest radiographs. Both classification systems utilize the Fisher Linear Discriminant (FLD) classifier. A composite GA fitness function is implemented capable of minimizing the number of false positives in addition to the size of the subset selected. Experimental results indicate that for CAD systems employing a high number of features, a genetic algorithm approach is superior compared to sequential forward selection in both Computed Tomography and Chest Radiography CAD systems.

Medical image reconstruction by total variation minimization is a newly developed area in computed tomography (CT). In compressed sensing literature, it hasbeen shown that signals with sparse representations in an orthonormal basis may be reconstructed via l1-minimization. Furthermore, if an image can be approximately modeled to be piecewise constant, then its gradient is sparse. The application of l1-minimization to a sparse gradient, known as total variation minimization, may then be used to recover the image. In this paper, the steepest descent method is employed to update the approximation of the image. We propose a way to estimate an optimal step size so that the total variation is minimized. A new minimization problem is also proposed. Numerical tests are included to illustrate the improvement.

Computed tomography (CT) is image reconstruction of objects using computer processed transmission or reflection data, usually referred to as projection data, from x-ray scanning. This projection data is often modeled using line integrals, but x-rays are of finite width in reality, so the accuracy of the projection data can be improved if an area based approach is used instead. In addition emitter beam shapes affect the reconstruction effectiveness and data collection efficiency, with the two main types of beam choice for 2-D scanning being fan beam and parallel beam. Fan beam scanning offers some advantages over parallel beam, such as faster data collection. This paper presents an area based fan beam projection model for CT and discusses its effectiveness based on numerical image reconstruction experiments using the proposed model, and several different reconstruction algorithms.

Computed Tomography (CT) is the standard in medical imaging field. In this study, we look at the curvelet transform in an attempt to use it as a basis for representing a function. In doing so, we seek a way to reconstruct a function from the Radon data that may produce clearer results. Using curvelet decomposition, any known function can be represented as a sum of curvelets with corresponding coefficients. It can be shown that these corresponding coefficients can be found using the Radon data, even if the function is unknown. The use of curvelets has the potential to solve partial or truncated Radon data problems. As a result, using a curvelet representation to invert radon data allows the chance of higher quality images to be produced. This paper examines this method of reconstruction for computed tomography (CT). A brief history of CT, an introduction to the theory behind the method, and implementation details will be provided.

X-ray Computed Tomography (CT) is a process that produces three-dimensional x-ray images, allowing for better diagnosis and analysis of complex internal medical conditions. New advances in the optical techniques used in this process promise to produce better results while reducing patient risk. One of these developments calls for precise optical gratings that can be expensive and difficult to manufacture. This paper presents a simple process developed specifically for the production of these gratings using cost effective techniques. The process uses well understood semiconductor fabrication steps including oxidation, deep reactive ion etching and electroplating. While not entirely successful, the process presented within provides a proof of concept for development of the gratings and discusses improvements that could be made to allow for success.