Spectral x-ray computed tomography (CT) is an important nascent imaging modality with several exciting potential applications. The research presented in this thesis separates into two primary areas with the common underlying theme of spectral CT; the first area is Compton scatter estimation and the second is interior tomography. First, the research is framed and outputs are identified. Background on the concepts used in the thesis is offered, including x-ray imaging and computed tomography, CT scanner architecture, spectral imaging, interior tomography and x-ray scatter. The mathematical background of techniques for image reconstruction from x-ray transmission measurements are presented. Many of the tools used to perform the research, both hardware and software, are described. An algorithm is developed for estimating the intensity of Compton scattered photons within a spectral CT scan, and a major approximation used by the algorithm is analysed. One proposed interior reconstruction algorithm is briefly evaluated; while this is not directly linked to spectral CT, it is related to the work on a novel hybrid spectral interior micro-CT architecture. Conclusions are summarised and suggestions for future work are offered. Scatter is known to cause artefacts in CT reconstructions, and several methods exist to correct data that has been corrupted by scatter. Compton scatter affects the energy of photons, therefore spectral CT measurements offer the potential to correct for this phenomenon more accurately than conventional measurements. A Compton scatter algorithm is developed and is found to match very well to Monte Carlo validation simulations, with the constraints that the object be at the micro-CT scale and that electron-binding effects are omitted. Development of the algorithm uses an approximation of the post-scatter attenuation to simplify the estimation problem and enable implementation. The consequences of this approximation are analysed, and the error introduced is found to be less than 5% in most biomedical micro-CT situations. Interior tomography refers to the incomplete data situation caused by the truncation of some or all CT projections, and is an active research area. A recently proposed interior reconstruction algorithm is evaluated with regard to its sensitivity to input error, and is found to have mediocre performance in this respect. Published results are not found to be reproducible, suggesting some omission from the published algorithm. A novel hybrid spectral interior architecture is described, along with an iterative reconstruction algorithm for hybrid data sets. The system combines a full field of view conventional imaging chain and an interior field of view spectral imaging chain to enable spectral measurement of a region of interest, and addresses some important limitations of spectral x-ray detectors; promising results are shown. Spectral reconstructions from interior data are shown to have sufficient information to distinguish two k-edge contrast agents (iodine and gadolinium) not only within the interior field of view but also beyond it. The architecture is further explored in the context of radiation exposure reduction, including testing of an analytical hybrid reconstruction algorithm.

The goal in medical x-ray imaging is to obtain the image quality requiredfor a given detection task, while ensuring that the patient dose is kept as lowas reasonably achievable. The two most common strategies for dose reductionare: optimizing incident x-ray beams and utilizing energy informationof transmitted beams with new detector techniques (spectral imaging). Inthis thesis, dose optimization schemes were investigated in two x-ray imagingsystems: digital mammography and computed tomography (CT). In digital mammography, the usefulness of anti-scatter grids was investigatedas a function of breast thickness with varying geometries and experimentalconditions. The general conclusion is that keeping the grid is optimalfor breasts thicker than 5 cm, whereas the dose can be reduced without a gridfor thinner breasts. A photon-counting silicon-strip detector developed for spectral mammographywas characterized using synchrotron radiation. Energy resolution, ΔE/Ein, was measured to vary between 0.11-0.23 in the energy range 15-40 keV, which is better than the energy resolution of 0.12-0.35 measured inthe state-of-the-art photon-counting mammography system. Pulse pileup hasshown little effect on energy resolution. In CT, the performance of a segmented silicon-strip detector developedfor spectral CT was evaluated and a theoretical comparison was made withthe state-of-the-art CT detector for some clinically relevant imaging tasks.The results indicate that the proposed photon-counting silicon CT detector issuperior to the state-of-the-art CT detector, especially for high-contrast andhigh-resolution imaging tasks. The beam quality was optimized for the proposed photon-counting spectralCT detector in two head imaging cases: non-enhanced imaging and Kedgeimaging. For non-enhanced imaging, a 120-kVp spectrum filtered by 2half value layer (HVL) copper (Z = 29) provides the best performance. Wheniodine is used in K-edge imaging, the optimal filter is 2 HVL iodine (Z = 53)and the optimal kVps are 60-75 kVp. In the case of gadolinium imaging, theradiation dose can be minimized at 120 kVp filtered by 2 HVL thulium (Z =69). / <p>QC 20160401</p>

In positron emission tomography (PET) the current trend is to use the fully 3D capabilities of the scanner to increase sensitivity, hence improve the quality of data or reduce the scanning time. However, some difficulties have to be resolved. In 3D PET, the largest contributor to image degradation is Compton scatter since the scattered photons may comprise more than 50% out of all coincidences in the whole body studies. Much progress has been achieved the last few years by the use of scatter correction algorithms, such as the single scatter simulation (SSS). In this work, a model-based scatter simulation (MBSS) algorithm has been implemented in a software library called STIR (i.e. Software for Tomographic Image Reconstruction) initially based on SSS. The aim of the current work is to validate the MBSS implementation; investigate the influence of several parameters; and, if possible extend the existing algorithm. The results are compared with both SimSET Monte Carlo simulation package and measured data. The comparison shows that SSS is in excellent agreement with the single scatter distribution produced by SimSET and in several cases can also approximate accurately the total scatter. However, SSS is just an attempt to estimate the total Compton scatter effect, as it is possible that both photons may scatter, and potentially more than once. As shown, the single scatter distribution may have different shape from the total scatter distribution. How accurate this approximation is, it depends on how many detected photons are scattered multiple times. Multiple scatter is more likely to happen if the attenuation medium has large volume, hence it is more severe in 3D studies of the torso than the brain. In this work, the methodology used for the single scatter simulation algorithm is extended to handle twice-scattered events. Detailed description on how to implement the double scatter simulation (DSS) together with a preliminary evaluation is included. The results are promising even if the required computational time for DSS is much higher than for SSS, though not being prohibited. Finally, at the end of the thesis, an efficient recursive formula is proposed to estimate the rest multiple scatter distribution. / Κατά την τομογραφική απεικόνιση εκπομπόμενων ποζιτρονίων είναι αρκετά διαδεδομένη η χρήση της τρισδιάστατης ανίχνευσης, ώστε να βελτιωθεί η ευαισθησία και η ποιότητα των δεδομένων, αλλά και να μειωθεί ο συνολικός χρόνος εξέτασης. Για να είναι αυτά εφικτά πρέπει πρωτίστως να αντιμετωπιστούν αποτελεσματικά κάποιες δυσκολίες. Συγκεκριμένα, ένας από τους σημαντικότερους παράγοντες που υποβαθμίζουν την ποιότητα της εικόνας είναι η σκέδαση Compton, διότι, εξαιτίας αυτής, τα σκεδαζόμενα φωτόνιων που ανιχνεύονται μπορούν να ξεπεράσουν το 50% των συνολικών ανιχνεύσεων σε αρκετές μελέτες του ανθρώπινου κορμού. Σημαντική πρόοδος έχει επιτευχθεί τα τελευταία χρόνια με τη χρήση αλγόριθμων διόρθωσης σκέδασης και, κυρίως, με τη χρήση του αλγόριθμου προσομοίωσης μίας και μόνο σκέδασης (ΠΜΣ). Στην παρούσα μελέτη, ένας αλγόριθμος βασισμένος σε αυτό το μοντέλο δημιουργήθηκε σε μια βιβλιοθήκη λογισμικού για ανακατασκευή τομογραφικής εικόνας. Ο στόχος αυτής της εργασίας είναι να πιστοποιήσει τη σωστή λειτουργία του αλγόριθμου, να μελετήσει την επίδραση διαφόρων παραμέτρων και, εάν είναι εφικτό, να τη βελτιώσει. Η σύγκριση των αποτελεσμάτων έδειξε πως ο ΠΜΣ επιβεβαιώνεται με Μόντε Κάρλο προσομοιώσεις. Ωστόσο, ο αλγόριθμος ΠΜΣ είναι μια προσέγγιση του συνολικού ποσοστού φωτονίων σκέδασης Compton. Υπάρχει πάντα πιθανότητα και τα δύο φωτόνια να σκεδαστούν μία ή και περισσότερες φορές. Όπως αποδεικνύεται στην παρούσα μελέτη, η κατανομή μίας και μόνο σκέδασης έχει διαφορετική μορφή σε σύγκριση με τη συνολική κατανομή της. Πόσο ακριβής είναι αυτή η προσέγγιση εξαρτάται από τον αριθμό των πολλαπλά σκεδαζόμενων φωτονίων που έχουν ανιχνευτεί. Το φαινόμενο πολλαπλής σκέδασης είναι πιθανότερο εάν το μέσον απορρόφησης ακτινοβολίας καταλαμβάνει μεγάλον όγκο και συνεπώς κατά τις τρισδιάστατες μελέτες του κορμού, παρά του εγκεφάλου. Στην παρούσα εργασία η μεθοδολογία που χρησιμοποιήθηκε για τον αλγόριθμο προσομοίωσης μίας και μόνο σκέδασης επεκτάθηκε, ώστε να συμπεριλάβει και γεγονότα διπλής σκέδασης. Μια αναλυτική περιγραφή παρουσιάζεται για το πώς μπορεί να υλοποιηθεί η προσομοίωση διπλής σκέδασης (ΠΔΣ), που ακολουθείται από μία προκαταρκτική αξιολόγηση. Τα αποτελέσματα είναι αρκετά ενθαρρυντικά ακόμη και αν ο απαιτούμενος υπολογιστικός χρόνος για την ΠΔΣ είναι αρκετά μεγαλύτερος από την ΠΜΣ, χωρίς να την καθιστά απαγορευτική. Στο τέλος της διπλωματικής εργασίας προτείνεται ένας ολοκληρωμένος αναδρομικός αλγόριθμος για τον αποδοτικό υπολογισμό του συνολικού ποσοστού σκεδάσεων.