We present new reconstruction results and methods for limited data problems in photoelastic tomography. We begin with a survey of the current state of x-ray tomography. Discussing the Radon transform and its inversion we also consider some stability results for reconstruction in Sobolev spaces. We describe certain limited data problems and ways to tackle these, in particular the Two Step Hilbert reconstruction method. We then move on to photoelastic tomography, where we make use of techniques from scalar tomography to develop new methods for photoelastic tomographic reconstruction. We present the main mathematical model used in photoelasticity, the Truncated Transverse Ray Transform (TTRT). After some initial numerical studies, we extend a recently presented reconstruction algorithm for the TTRT from the Schwartz class to certain Sobolev spaces. We also give some stability results for inversion in these spaces. Moving on from general reconstruction to focus on inversion of some special cases of tensors we consider solenoidal and potential tensor fields. We discuss existing reconstruction methods and present several novel reconstructions and discuss their advantages over using more general machinery. We also extend our new algorithms, as well as existing ones, to certain cases of data truncation. Finally, we present numerical studies of the general reconstruction method. We give the first published results of TTRT reconstruction and go into some detail describing the implementation before presenting our results.

This dissertation discusses a certain aspect of opitcal data processing--namely the concept of performing a convolution operation of an incoherent optical light field with a specified processing kernel. The theory that shows that an incoherent imaging system performs a convolution by the very process of imaging is reviewed. The constraints on the form of processing kernel are discussed. The most severe constraint is the restriction of positive real kernels. Methods for extending the versatility of incoherent systems to include bipolar and even complex kernels are described. The most promising methods are those that encode the bipolar or complex information on either a spatial or temporal carrier frequency. The dissertation includes a presentation of two systems that are applicable to the demodulation of the signals generated by a temporal carrier approach. One of the systems introduces the concept of bipolar detection, which may have a strong influence on the performance of incoherent optical processing systems in the future. The other system is a synergism of optical and digital components that produces a hybrid system capable of high performance. The main motivation of this investigation was an outgrowth of our interest in developing a computed tomography system based on film recording of the projection data. The theory of computed tomography is reviewed in this text and an optical processing system based in part on the hybrid approach to the filtering operation is presented. This system represents a very concrete example of the capabilities of an incoherent optical processor.

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The removal of scattered radiation is recognised as one of the major goals to be achieved in SPECT. In this work three scatter removal techniques were investigated. These were dual window scatter subtraction, deconvolution using a Wiener filter and energy weighted acquisition (EWA) using a weighted acquisition module (WAM). In addition to this, the effects of simple background subtraction on SPECT images was also investigated. The techniques were investigated in both a semi-quantitative manner, in terms of the effects of each technique on the cold lesion contrast and image mottle, and qualitatively, in terms of the ability of observers to perform a detection task. This was done using Relative Operating Characteristic (ROC) experiments. Each technique is investigated individually to discover the parameters needed to optimise performance. The results showed that the optimum parameters for each scatter reduction technique was dependent on the measure of image quality used for optimisation and showed that all of the techniques investigated produced better results than those produced using the standard 20&'37 photopeak acquisition approach, however, in general no significant difference could be found between the techniques. The image noise produced by each technique was also evaluated by calculating the noise power spectra (NPS) produced by each technique. The calculated NPS showed the spatial content of the noise produced by each technique was different for each scatter reduction technique. The results in this work showed that empirically defined measures of image quality are poor predictors of observer performance.

The backprojection method for electrical impedance image reconstruction has been adapted for the opposing current drive configuration implemented in the second generation of Aberdeen impedance imaging systems. The logarithmic conformal transformation is used to solve the Forward problem for a two-dimensional homogeneous medium of circular cross-section. Pixel weights of backprojection are calculated from the normalised distances of the pixel centres from the boundary side of backprojection. An experimental solution to the Forward problem is a homogeneous medium of irregular cross-section and three-dimensional boundary is proposed and implemented. A thorax phantom was built for this purpose using radiotherapy moulding techniques. The potential distribution in this phantom was measured using a tetrapolar inpedance measuring device and the equipotential lines falling on the electrodes were plotted. A reconstruction matrix capable of reconstructing dynamic impedance images of the thorax was formulated. Images representing resistivity change distributions between maximum inspiration and maximum expiration have been reconstructed. These thorax cross-section images show the most faithful representation of the expected resistivity changes due to respiration.

Convergent plate boundaries evolve through the dynamic interaction between subducting oceanic lithosphere, overriding lithosphere, and adjacent flow of the convective mantle. These lithospheric plates contain remarkable heterogeneity in thickness, strength, and observable seismic character. I investigate the role of variable thickness of continental lithosphere with respect to mantle flow dynamics and develop a relationship of this subduction configuration with the construction of the Andes Mountains. By inclusion of this geodynamic model into the Andean Orogeny, numerous irreconcilable observations in the Eocene and Oligocene can be related with a comprehensive tectonic model. Lithospheric heterogeneity can be imaged with the inversion of seismic travel time data. I develop an analysis of a potential source of non-unique modeling of seismic velocity structure and then develop a case study of a currently subducting oceanic lithosphere using an iterative ray tracing approach. First, I consider the impact of the assumption of isotropic wave propagation implicit in a common methodology of data inversion. First-order structure is shown to be well resolved, but higher-order structure can be significantly different in regions of observed high-amplitude or null SKS splitting observations. The southern edge of the Juan de Fuca plate is imaged by traditional methods and an iterative ray tracing approach. The inclusion of ray tracing allows modeling of a more realistic velocity model by minimizing the error in source to receiver sensitivity. Compared to the standard imaging procedure, the resolved structure with this updated method contains smaller, more confined anomalies that represent the subducted oceanic lithosphere. Velocity perturbation amplitudes generally are decreased for slow structure and increase for fast structures. These changes in velocity structure provide an explanation for the decreased root mean square residual of the data that remain after inversion. I find that the high amplitude fast velocity of the Juan de Fuca is a robust feature and the currently subducting slab does not penetrate the mantle transition zone. I attribute the locus of very fast Juan de Fuca sub-continental lithosphere to be related to deformation of the plate prior to and during subduction. This dissertation includes previously published co-authored material.

Current methods for assessing the health of insects and their colonies are carried out by researchers making dissections on individual insects (which inevitably kills them) or making visual inspections of colonies and then documenting their observations. For colonies, researchers look for behavioural signs which indicate healthy individuals where foragers are regularly bringing in resources or in weak colonies, where there are fewer foragers working with a more lethargic and less purposeful manner. These methods are prone to large errors and they kill many insects in the process. The research detailed in this thesis addresses the subjective and destructive nature of these methods. This thesis also describes new methods using x-ray CT to develop and adopt protocols to accurately study insects non-invasively. Chapter one covers the current literature on tomography and some background on the different CT methods. Chapter two gives a thorough description of the new methods being developed to study insects non-invasively and details techniques that can be adopted by researchers who require non-invasive approaches to their work. Chapter three describes in detail three examples of research that has been conducted on locusts, ladybirds and butterflies to non-invasively study aspects of their morphology. The methods described maintain the integrity of the specimens for future use if so required. Chapter four covers a specific example of a fine detail study on plasticity of the honeybee brain using X-ray MicroCT and discusses the potential for live scanning to observe brain plasticity in insects. Chapter five extends the work from chapter two to show the usefulness of CT for studying insect behaviour by documenting and describing previously unreported honeybee storage behaviour. Chapter six draws conclusions from the other chapters and discusses future research.