Inom nuklearmedicinsk diagnostik används radioaktiva läkemedel för att utvärdera olika organs metabolism och fysiologiska beteende. Genom att använda en scintillationskamera kan strålningen som erhålls när det administrerade läkemedlet sönderfaller i kroppen detekteras och en funktionell bild över aktivitetsfördelningen erhålls. En tredimensionell bildvolym kan erhållas om gammakameran får rotera runt patienten vilket kallas SPECT (Single Photon Emission Computed Tomography). Bildernas kvalitet är av stor betydelse för att kunna göra en noggrann bedömning av olika patologiska tillstånd. Kvaliteten begränsas av en mängd faktorer och en av dem är Comptonspridda fotoner. I denna studie optimerades bildkvaliteten för SPECT-undersökningar med 111In-Octreoscan för ett Infinia Hawkeye 4 (GE Healthcare, Wisconsin, USA) SPECT-system vid Norrlands universitetssjukhus (NUS). Optimeringen gjordes med avseende på detektion av små tumörer vid visuell inspektion av 111In-Octreoscan-bilder. Monte Carlo simuleringar användes för att utvärdera tre olika parallellhålskollimatorer med fyra olika fönsterinställningar. Rekonstruktion av bilder gjordes med den iterativa tekniken OSEM (Ordered Subset Expectation Maximization) med olika antal iterationer. Bilderna postfiltrerades med två olika filter med tre kritiska frekvenser vardera. Den lämpligaste inställningen för NUS visade sig vara MEGP-kollimatorn (Medium Energy General Purpose) tillsammans med en fönsterinställning med två huvudfönster centrerade kring 171 respektive 245 keV utan spridningskorrektion. Mest optimal rekonstruktion visade sig vara med två OSEM-iterationer (10 subsets) och postfiltrering med ett Butterworth-filter med kritisk frekvens 0.40 cm-1 och powerfaktor 8. I övrigt visade sig ELEGP-kollimatorn (Extended Low Energy General Purpose) vara den kollimator som optimerar bildkvaliteten mest med avseende på detektion av små tumörer, men den finns ännu inte på NUS. / Optimization of image quality for SPECT imaging with 111In-Octreoscan at the University Hospital of Umeå – a Monte Carlo study In nuclear medicine diagnostics, radiopharmaceuticals are used for evaluating metabolism and physiological behavior of various organs. By using a scintillation camera, radiation can be detected when the administered drug decays in the body, and the result is a functional image of the activity distribution within the patient. A three-dimensional image volume can be obtained by letting the gamma camera rotate around the patient. This method is called SPECT (Single Photon Emission Computed Tomography). Image quality is very important to make an accurate assessment of various pathological conditions. The quality is limited by many factors and one of them is the Compton scattered photons. In this study image quality of SPECT-examinations with 111In-Octreoscan were optimized for an Infinia Hawkeye 4 (GE Healthcare, Wisconsin, USA) SPECT-system at the University Hospital of Umeå (NUS). The optimization was made with respect to detecting small tumors for visual inspection of 111In-Octreoscan images. Monte Carlo simulations were used to evaluate three different parallel hole collimators with four different window settings. Reconstruction of images was performed with the iterative technique OSEM (Ordered Subset Expectation Maximization) with different numbers of iterations. The images were post-filtered with two different filters with three critical frequencies each. The most appropriate setting for the SPECT-system at NUS is the MEGP-collimator (Medium Energy General Purpose) with a window setting of two main windows centered around 171 and 245 keV, without scatter correction. The most optimal reconstruction is obtained by using two OSEM-iterations (10 subsets) and post-filtering with a Butterworth-filter with critical frequency 0.40 cm-1 and power factor 8. The ELEGP-collimator (Extended Low Energy General Purpose) proved however to be the most optimal collimator for detecting small tumors, but this collimator is currently not available at NUS.

A Positive Electron Tomography/Computed Tomography devise was installed in theX-ray section at US Linköping in May 2007. Positive Electron Tomography examinations with 18F-fluoro-deoxy-glucose are mainly used for tumor examinations. During 2007 occurred approximately 200 examinations and in 2008 600 are planned. Today there are two reconstruction methods commercially available, Filtered Back projection and Maximum Likelihood Expectation Maximiza tion, used in the faster version called Ordered Subsets Expectation Maximization. The image quality in Positive Electron Tomography depends on the choice of reconstruction method and the settings of its parameters. We have performed a physical phantom study with Positive Electron Tomography to determine optimal parameters for the iterative reconstruction algorithm Ordered Subsets Expectation Maximization. To find out whether or not the quality of the image can be improved, so that the patient received radiation dose and/or examination time can be lowered. The phantom used was a NEMA IEC Body PhantomTM, designed to mimic smallhot lesions typical in 18F, Fluorine-18 PET, and all calculations were done according to the NEMA NU2-2001 protocol. The main conclusion from this project is that a higher level of contrast can be reached, compared to the one clinically obtained today. Using more iterations then recommended from the manufacturer. / I maj 2007 installerades en Positiv Elektron Tomografi /DatoriseradTomografi-kamera, PET/CT, i Röntgenavdelningen Linköping US. PET med 18F-fluoro-deoxy-glucose används huvudsakligen för tumörundersökningar.2007 genomfördes ca 200 undersökningar, och för 2008 är ytterligare 600 planerade. Idag finns två olika bildrekonstruktionsmetoder kliniskt tillgängliga; Filtered Back projection och Maximum Likelihood Expectation Maximization, där den  vidareutvecklade versionen kallad Ordered Subsets Expectation Maximizationanvänds. Bildkvalitén från en Positive Electron Tomographykamera påverkas av valet av rekonstruktionsmetod och dess ingående parametrar. I detta projekt har en fantomstudie genomförts med syfte att bestämma de optimala parametrarna för den iterativa metoden Ordered Subsets Expectation Maximization. För att utreda huruvida stråldosen och/eller undersöknings tiden kan minskas. Det testfantom som användes var en NEMA IEC Body PhantomTM. Projektet följde metoden angiven i NEMA NU2-2001 protokollet. Det resultaten visar är att de rekommenderade inställningarna från tillverkaren inte är de optimala.

A Positive Electron Tomography/Computed Tomography devise was installed in the X-ray section at US Linköping in May 2007. Positive Electron Tomography examinations with 18F-fluoro-deoxyglucose are mainly used for tumor examinations. During 2007 occurred approximately 200 examinations and in 2008 600 are planned.Today there are two reconstruction methods commercially available, Filtered Back projection and Maximum Likelihood Expectation Maximiza tion, used in the faster version called Ordered Subsets Expectation Maximization. The image quality in Positive Electron Tomography depends on the choice of reconstruction method and the settings of its parameters. We have performed a physical phantom study with Positive Electron Tomography to determine optimal parameters for the iterativereconstruction algorithm Ordered Subsets Expectation Maximization. To find out whether or not the quality of the image can be improved, so that the patient received radiation dose and/or examination time can be lowered. The phantom used was a NEMA IEC Body PhantomTM, designed to mimic small hot lesions typicalin 18F, Fluorine-18 PET, and all calculations were done according to the NEMA NU2-2001 protocol. The main conclusion from this project is that a higher level of contrastcan be reached, compared to the one clinically obtained today. Using more iterations then recommended from the manufacturer.

<p>A Positive Electron Tomography/Computed Tomography devise was installed in theX-ray section at US Linköping in May 2007. Positive Electron Tomography examinations with 18F-fluoro-deoxy-glucose are mainly used for tumor examinations. During 2007 occurred approximately 200 examinations and in 2008 600 are planned. Today there are two reconstruction methods commercially available, Filtered Back projection and Maximum Likelihood Expectation Maximiza tion, used in the faster version called Ordered Subsets Expectation Maximization. The image quality in Positive Electron Tomography depends on the choice of reconstruction method and the settings of its parameters. We have performed a physical phantom study with Positive Electron Tomography to determine optimal parameters for the iterative reconstruction algorithm Ordered Subsets Expectation Maximization. To find out whether or not the quality of the image can be improved, so that the patient received radiation dose and/or examination time can be lowered. The phantom used was a NEMA IEC Body PhantomTM, designed to mimic smallhot lesions typical in 18F, Fluorine-18 PET, and all calculations were done according to the NEMA NU2-2001 protocol.</p><p>The main conclusion from this project is that a higher level of contrast can be reached, compared to the one clinically obtained today. Using more iterations then recommended from the manufacturer.</p> / <p>I maj 2007 installerades en Positiv Elektron Tomografi /DatoriseradTomografi-kamera, PET/CT, i Röntgenavdelningen Linköping US. PET med 18F-fluoro-deoxy-glucose används huvudsakligen för tumörundersökningar.2007 genomfördes ca 200 undersökningar, och för 2008 är ytterligare 600 planerade. Idag finns två olika bildrekonstruktionsmetoder kliniskt tillgängliga; Filtered Back projection och Maximum Likelihood Expectation Maximization, där den  vidareutvecklade versionen kallad Ordered Subsets Expectation Maximizationanvänds. Bildkvalitén från en Positive Electron Tomographykamera påverkas av valet av rekonstruktionsmetod och dess ingående parametrar.</p><p>I detta projekt har en fantomstudie genomförts med syfte att bestämma de optimala parametrarna för den iterativa metoden Ordered Subsets Expectation Maximization. För att utreda huruvida stråldosen och/eller undersöknings tiden kan minskas. Det testfantom som användes var en NEMA IEC Body PhantomTM. Projektet följde metoden angiven i NEMA NU2-2001 protokollet. Det resultaten visar är att de rekommenderade inställningarna från tillverkaren inte är de optimala.</p>

<p>A Positive Electron Tomography/Computed Tomography devise was installed in the X-ray section at US Linköping in May 2007. Positive Electron Tomography examinations with 18F-fluoro-deoxyglucose are mainly used for tumor examinations. During 2007 occurred approximately 200 examinations and in 2008 600 are planned.Today there are two reconstruction methods commercially available, Filtered Back projection and Maximum Likelihood Expectation Maximiza tion, used in the faster version called Ordered Subsets Expectation Maximization. The image quality in Positive Electron Tomography depends on the choice of reconstruction method and the settings of its parameters. We have performed a physical phantom study with Positive Electron Tomography to determine optimal parameters for the iterativereconstruction algorithm Ordered Subsets Expectation Maximization. To find out whether or not the quality of the image can be improved, so that the patient received radiation dose and/or examination time can be lowered. The phantom used was a NEMA IEC Body PhantomTM, designed to mimic small hot lesions typicalin 18F, Fluorine-18 PET, and all calculations were done according to the NEMA NU2-2001 protocol.</p><p>The main conclusion from this project is that a higher level of contrastcan be reached, compared to the one clinically obtained today. Using more iterations then recommended from the manufacturer.</p>

Bladder artifacts during bone single photon emission computed tomography (SPECT) is a common source of errors. The extent and severity of bladder artifacts have been described for filtered back projection (FBP) reconstruction. OSEM may help to address this poor record of bladder artifacts, which render up to 20% of the images unreadable. Aims and objectives To evaluate the relationship of the bladder to acetabulum ratio in guiding the choice of the number of iterations and subsets used for OSEM reconstruction, for reducing bladder artifacts found on FBP reconstruction. Materials and Methods 105 patients with various indications for bone scans were selected and planar and SPECT images were acquired. The SPECT images were reconstructed with both filtered back projection and OSEM using four different combinations of iterations and subsets. The images were given to three well experienced Nuclear Physicians who were blinded to the diagnosis and type of reconstruction used. They then labelled images from the best to the worst after which the data was analysed. The bladder to acetabulum ratio for each image was determined which was then correlated with the different iterations and subsets used. Results The study demonstrated that reconstruction using OSEM led to better lesion detectability compared to filtered back projection in 87.62% of cases. It further demonstrated that the iterations and subsets used for reconstruction of an image correlates to the bladder to acetabulum ratio. Four iterations and 8 subsets yielded the best results in 48.5% of the images whilst two iterations and 8 subsets yielded the best results in 33.8%. The number of reconstructed images which yielded the best results with 2 iterations and 8 subsets were the same as or more than those with 4 iterations and 8 subsets when the bladder/acetabulum ratio was between 0.2-0.39. A ratio below 0.2 or above 0.39 supports the usage of 4 iterations and 8 subsets over 2 iterations and 8 subsets. Conclusion Bladder to acetabulum ratio can be used to select the optimum number of iterations and subsets for reconstruction of bone SPECT for accurate characterization of lesions. This study also confirms that reconstruction with OSEM (vs FBP) leads to better lesion detectability and characterisation. / Dissertation (MSc)--University of Pretoria, 2011. / Nuclear Medicine / unrestricted

<p>Simultaneous dual-isotope SPECT imaging has a number of applications, for exam- ple, cardiac, brain and cancer imaging. The major concern in simultaneous dual- isotope SPECT is the significant crosstalk contamination between the different isotopes used. The current study focuses on a method of crosstalk compensation between two isotopes in simultaneous dual isotope SPECT acquisition applied to cancer imaging using ^99mTc/¹¹¹In and breast SPECT using ^99mTc/¹²³I. Monte Carlo (MC), which is thought to offer the most realistic crosstalk and scatter compensation modelling, in typical implementations, has inherent long calculation times (often several hours or days) associated with it. This makes MC unsuitable for clinical applications. We have previously incorporated convolution based forced detection into SIMIND Monte Carlo (MC) program which have made MC feasible to use in clinical time frames. In order to evaluate the accuracy of our accelerated MC program a number of point source simulation results were compared to experimentally acquired data in terms of spatial resolution and detector sensitivity. We have developed an iterative MC based image reconstruction technique that simulates the photon down-scatter from one isotope into the acquisition window of a second isotope. The MC based estimation of scatter contamination contained in projection views is then used to compensate for the photon contamination during iterative reconstruction. We use a modified ordered subset expectation maximization (OSEM) alogrithm, named as simultaneous ordered subset-expectation maximization (Sim-OSEM), to perform this step. We have undertaken a number of simulation tests and phantom studies to verify this approach in case of both of the dual-isotope combinations (i.e. ^99mTc/¹¹¹In and ^99mTc/¹²³I). In breast SPECT studies three different breast sizes were simulated. For each of the breast sizes ten combinations of lesions with 3 lesions per combination, were selected randomly for acquisition and reconstruction of simulation data. The images reconstructed using Sim-OSEM showed crosstalk compensation when compared with images reconstructed using simultaneously (with crosstalk) acquired projection data using analytical attenuation based reconstruction. In case of Sim-OSEM the lesion to background ratios were much closer to actual values compared to images reconstructed for both separately (without crosstalk) and simultaneously (with crosstalk) acquired projection data using analytical attenuation based reconstruction. Activity estimation is also possible with Sim-OSEM and yielded accurate estimates of lesion activities with relatively small error compared to deposited activities. The proposed reconstruction technique also evaluated by reconstruction of experimentally acquired projection phantom data in case of ^99mTc/¹¹¹In. Reconstruction using Sim-OSEM showed very promising results in terms of crosstalk and small angle scatter compensation and uniformity of background compared to analytical attenuation based reconstruction after triple energy window (TEW) based scatter correction of projection data. In our case images obtained using Sim-OSEM showed more uniform background even when compared to the images reconstructed for separately acquired projection data using analytical attenuation based reconstruction may be due to better correction of photons scattered at small angle and got detected under photopeak.</p> / Master of Science (MSc)

Positron Emission Tomography (PET) is a widely used imaging modality for diagnosing patients with cancer. Recently, there have been three novel developments in PET imaging aiming to increase PET image quality and quantification. This thesis focuses on the optimization of PET image quality on these three developments. The first development is the fully 3D PET data acquisition and reconstruction. 3D Acquisitions are not constrained in collecting events in single 2D planes and can span across different planes. 3D acquisition provides better detection since it can accept more events. Also it can result in lower radiation dose to the patient and shorter imaging times. With the application of 3D acquisition, a fully 3D iterative reconstruction algorithm was also developed. The aim of the first project in this thesis is to evaluate the PET image and raw data quality when this fully 3D iterative reconstruction algorithm is applied. The second development in PET imaging is the time-of-flight (TOF) PET data acquisition and reconstruction. TOF imaging has the ability to measure the difference between the detection times, thus localize the event location more accurately to increase the image quality. The second project in this thesis focuses on optimizing the TOF reconstruction parameters on a newly developed TOF PET scanner. Then the improvement of TOF information on image quality is assessed using the derived optimal parameters. Finally the effect of scan duration is evaluated to determine whether similar image quality could be obtained between TOF and non-TOF while using less scan time for TOF. The third development is the interest in building PET / magnetic resonance (MR) multi-modality scanner. MR imaging has the ability to show high soft tissue contrast and can assess physiological processes, which cannot be achieved on PET images. One problem in developing PET/MR system is that it is not possible with current MR acquisition schemes to translate the MR image into an attenuation map to correct for PET attenuations. The third project in this thesis proposed and assessed an approach for the attenuation correction of PET data in potential PET/MR systems to improve PET image quality and quantification.

La tomographie d’émission par positrons (TEP) est une modalité d’imagerie moléculaire utilisant des radiotraceurs marqués par des isotopes émetteurs de positrons permettant de quantifier et de sonder des processus biologiques et physiologiques. Cette modalité est surtout utilisée actuellement en oncologie, mais elle est aussi utilisée de plus en plus en cardiologie, en neurologie et en pharmacologie. En fait, c’est une modalité qui est intrinsèquement capable d’offrir avec une meilleure sensibilité des informations fonctionnelles sur le métabolisme cellulaire. Les limites de cette modalité sont surtout la faible résolution spatiale et le manque d’exactitude de la quantification. Par ailleurs, afin de dépasser ces limites qui constituent un obstacle pour élargir le champ des applications cliniques de la TEP, les nouveaux systèmes d’acquisition sont équipés d’un grand nombre de petits détecteurs ayant des meilleures performances de détection. La reconstruction de l’image se fait en utilisant les algorithmes stochastiques itératifs mieux adaptés aux acquisitions à faibles statistiques. De ce fait, le temps de reconstruction est devenu trop long pour une utilisation en milieu clinique. Ainsi, pour réduire ce temps, on les données d’acquisition sont compressées et des versions accélérées d’algorithmes stochastiques itératifs qui sont généralement moins exactes sont utilisées. Les performances améliorées par l’augmentation de nombre des détecteurs sont donc limitées par les contraintes de temps de calcul. Afin de sortir de cette boucle et permettre l’utilisation des algorithmes de reconstruction robustes, de nombreux travaux ont été effectués pour accélérer ces algorithmes sur les dispositifs GPU (Graphics Processing Units) de calcul haute performance. Dans ce travail, nous avons rejoint cet effort de la communauté scientifique pour développer et introduire en clinique l’utilisation des algorithmes de reconstruction puissants qui améliorent la résolution spatiale et l’exactitude de la quantification en TEP. Nous avons d’abord travaillé sur le développement des stratégies pour accélérer sur les dispositifs GPU la reconstruction des images TEP à partir des données d’acquisition en mode liste. En fait, le mode liste offre de nombreux avantages par rapport à la reconstruction à partir des sinogrammes, entre autres : il permet d’implanter facilement et avec précision la correction du mouvement et le temps de vol (TOF : Time-Of Flight) pour améliorer l’exactitude de la quantification. Il permet aussi d’utiliser les fonctions de bases spatio-temporelles pour effectuer la reconstruction 4D afin d’estimer les paramètres cinétiques des métabolismes avec exactitude. Cependant, d’une part, l’utilisation de ce mode est très limitée en clinique, et d’autre part, il est surtout utilisé pour estimer la valeur normalisée de captation SUV qui est une grandeur semi-quantitative limitant le caractère fonctionnel de la TEP. Nos contributions sont les suivantes : - Le développement d’une nouvelle stratégie visant à accélérer sur les dispositifs GPU l’algorithme 3D LM-OSEM (List Mode Ordered-Subset Expectation-Maximization), y compris le calcul de la matrice de sensibilité intégrant les facteurs d’atténuation du patient et les coefficients de normalisation des détecteurs. Le temps de calcul obtenu est non seulement compatible avec une utilisation clinique des algorithmes 3D LM-OSEM, mais il permet également d’envisager des reconstructions rapides pour les applications TEP avancées telles que les études dynamiques en temps réel et des reconstructions d’images paramétriques à partir des données d’acquisitions directement. - Le développement et l’implantation sur GPU de l’approche Multigrilles/Multitrames pour accélérer l’algorithme LMEM (List-Mode Expectation-Maximization). L’objectif est de développer une nouvelle stratégie pour accélérer l’algorithme de référence LMEM qui est un algorithme convergent et puissant, mais qui a l’inconvénient de converger très lentement. Les résultats obtenus permettent d’entrevoir des reconstructions en temps quasi-réel que ce soit pour les examens utilisant un grand nombre de données d’acquisition aussi bien que pour les acquisitions dynamiques synchronisées. Par ailleurs, en clinique, la quantification est souvent faite à partir de données d’acquisition en sinogrammes généralement compressés. Mais des travaux antérieurs ont montré que cette approche pour accélérer la reconstruction diminue l’exactitude de la quantification et dégrade la résolution spatiale. Pour cette raison, nous avons parallélisé et implémenté sur GPU l’algorithme AW-LOR-OSEM (Attenuation-Weighted Line-of-Response-OSEM) ; une version de l’algorithme 3D OSEM qui effectue la reconstruction à partir de sinogrammes sans compression de données en intégrant les corrections de l’atténuation et de la normalisation dans les matrices de sensibilité. Nous avons comparé deux approches d’implantation : dans la première, la matrice système (MS) est calculée en temps réel au cours de la reconstruction, tandis que la seconde implantation utilise une MS pré- calculée avec une meilleure exactitude. Les résultats montrent que la première implantation offre une efficacité de calcul environ deux fois meilleure que celle obtenue dans la deuxième implantation. Les temps de reconstruction rapportés sont compatibles avec une utilisation clinique de ces deux stratégies. / Positron emission tomography (PET) is a molecular imaging modality that uses radiotracers labeled with positron emitting isotopes in order to quantify many biological processes. The clinical applications of this modality are largely in oncology, but it has a potential to be a reference exam for many diseases in cardiology, neurology and pharmacology. In fact, it is intrinsically able to offer the functional information of cellular metabolism with a good sensitivity. The principal limitations of this modality are the limited spatial resolution and the limited accuracy of the quantification. To overcome these limits, the recent PET systems use a huge number of small detectors with better performances. The image reconstruction is also done using accurate algorithms such as the iterative stochastic algorithms. But as a consequence, the time of reconstruction becomes too long for a clinical use. So the acquired data are compressed and the accelerated versions of iterative stochastic algorithms which generally are non convergent are used to perform the reconstruction. Consequently, the obtained performance is compromised. In order to be able to use the complex reconstruction algorithms in clinical applications for the new PET systems, many previous studies were aiming to accelerate these algorithms on GPU devices. Therefore, in this thesis, we joined the effort of researchers for developing and introducing for routine clinical use the accurate reconstruction algorithms that improve the spatial resolution and the accuracy of quantification for PET. Therefore, we first worked to develop the new strategies for accelerating on GPU devices the reconstruction from list mode acquisition. In fact, this mode offers many advantages over the histogram-mode, such as motion correction, the possibility of using time-of-flight (TOF) information to improve the quantification accuracy, the possibility of using temporal basis functions to perform 4D reconstruction and extract kinetic parameters with better accuracy directly from the acquired data. But, one of the main obstacles that limits the use of list-mode reconstruction approach for routine clinical use is the relatively long reconstruction time. To overcome this obstacle we : developed a new strategy to accelerate on GPU devices fully 3D list mode ordered-subset expectation-maximization (LM-OSEM) algorithm, including the calculation of the sensitivity matrix that accounts for the patient-specific attenuation and normalisation corrections. The reported reconstruction are not only compatible with a clinical use of 3D LM-OSEM algorithms, but also lets us envision fast reconstructions for advanced PET applications such as real time dynamic studies and parametric image reconstructions. developed and implemented on GPU a multigrid/multiframe approach of an expectation-maximization algorithm for list-mode acquisitions (MGMF-LMEM). The objective is to develop new strategies to accelerate the reconstruction of gold standard LMEM (list-mode expectation-maximization) algorithm which converges slowly. The GPU-based MGMF-LMEM algorithm processed data at a rate close to one million of events per second per iteration, and permits to perform near real-time reconstructions for large acquisitions or low-count acquisitions such as gated studies. Moreover, for clinical use, the quantification is often done from acquired data organized in sinograms. This data is generally compressed in order to accelerate reconstruction. But previous works have shown that this approach to accelerate the reconstruction decreases the accuracy of quantification and the spatial resolution. The ordered-subset expectation-maximization (OSEM) is the most used reconstruction algorithm from sinograms in clinic. Thus, we parallelized and implemented the attenuation-weighted line-of-response OSEM (AW-LOR-OSEM) algorithm which allows a PET image reconstruction from sinograms without any data compression and incorporates the attenuation and normalization corrections in the sensitivity matrices as weight factors. We compared two strategies of implementation: in the first, the system matrix (SM) is calculated on the fly during the reconstruction, while the second implementation uses a precalculated SM more accurately. The results show that the computational efficiency is about twice better for the implementation using calculated SM on-the-fly than the implementation using pre-calculated SM, but the reported reconstruction times are compatible with a clinical use for both strategies.

The aim of this Thesis is the development of stopping rule methods for the MLEM and OSEM algorithms used in image reconstruction positron emission tomography (PET). The development of the stopping rules is based on the study of the properties of both algorithms. Analyzing their mathematical expressions, it can be observed that the pixel updating coefficients (PUC) play a key role in the upgrading process of the reconstructed image from iteration k to k+1. For the analysis of the properties of the PUC, a PET scanner geometry was simulated using Monte Carlo methods. For image reconstruction using iterative techniques, the calculation of the transition matrix is essential. And it fully depends on the geometrical characteristics of the PET scanner. The MLEM and OSEM algorithms were used to reconstruct the projection data. In order to compare the reconstructed and true images, two figures of merit (FOM) were used; a) the Normalized Root Mean Square Deviation (NRMSD) and b) the chi-square χ2. The behaviour of the PUC C values for a zero and non-zero pixel in the phantom image was analyzed and it has been found different behavior for zero and non-zero pixels. Based on this assumption, the vector of all C values was analyzed for all non-zero pixels of the reconstructed image and it was found that the histograms of the values of the PUC have two components: one component around C(i)=1.0 and a tail component, for values C(i)<1.0. In this way, a vector variable has been defined, where I is the total number of pixels in the image and k is the iteration number. is the minimum value of the vector of the pixel updating coefficients among the non-zero pixels of the reconstructed image at iteration k. Further work was performed to find out the dependence of Cmin on the image characteristics, image topology and activity level. The analysis shows that the parameterization of Cmin is reliable and allows the establishment of a robust stopping rule for the MLEM algorithm. Furthermore, following a different approach, a new stopping rule using the log-likelihood properties of the MLEM algorithm has been developed. The two rules were evaluated using the independent Digimouse phantom. The study revealed that both stopping rules produce reconstructed images with similar properties. The same study was performed for the OSEM algorithm and a stopping rule for the OSEM algorithm dedicated to each number of subset was developed. / Σκοπός της διατριβής είναι η ανάπτυξη κριτηρίων παύσης για τους επαναληπτικούς αλγόριθμους (MLEM και OSEM) που χρησιμοποιούνται στην ανακατασκευή ιατρικής εικόνας στους τομογράφους εκπομπής ποζιτρονίου (PET). Η ανάπτυξη των κριτηρίων παύσης βασίστηκε στη μελέτη των ιδιοτήτων των αλγόριθμων MLEM & OSEM. Απο τη μαθηματική έκφραση των δύο αλγορίθμων προκύπτει ότι οι συντελεστές αναβάθμισης (ΣΑ) των pixels της εικόνας παίζουν σημαντικό ρόλο στην ανακατασκευή της απο επανάληψη σε επανάληψη. Για την ανάλυση ένας τομογράφος PET προσομοιώθηκε με τη χρήση των μεθόδων Μόντε Κάρλο.Για την ανακατασκευή της εικόνας με τη χρήση των αλγόριθμων MLEM και OSEM, υπολογίστηκε ο πίνακας μετάβασης. Ο πίνακας μετάβασης εξαρτάται απο τα γεωμετρικά χαρακτηριστικά του τομογράφου PET και για τον υπολογισμό του χρησιμοποιήθηκαν επίσης μέθοδοι Μόντε Κάρλο. Ως ψηφιακά ομοιώματα χρησιμοποιήθηκαν το ομοίωμα εγκεφάλου Hoffman και το 4D MOBY. Για κάθε ένα απο τα ομοιώματα δημιουργήθηκαν προβολικά δεδομένα σε διαφορετικές ενεργότητες. Για τη σύγκριση της ανακατασκευασμένης και της αρχικής εικόνας χρησιμοποιήθηκαν δύο ξεχωριστοί δείκτες ποίοτητας, το NRMSD και το chi square. Η ανάλυση έδειξε οτι οι ΣΑ για τα μη μηδενικά pixels της εικόνας τείνουν να λάβουν την τιμή 1.0 με την αύξηση των επαναλήψεων, ενώ για τα μηδενικά pixels αυτό δε συμβαίνει. Αναλύοντας περισσότερο το διάνυσμα των ΣΑ για τα μη μηδενικά pixels της ανακατασκευασμένης εικόνας διαπιστώθηκε ότι αυτό έχει δύο μέρη: α) Μια κορυφή για τιμές των ΣΑ = 1.0 και β) μια ουρά με τιμές των ΣΑ<1.0. Αυξάνοντας τις επαναλήψεις, ο αριθμός των pixels με ΣΑ=1.0 αυξάνονταν ενώ ταυτόχρονα η ελάχιστη τιμή του διανύσματος των ΣΑ μετακινούνταν προς το 1.0. Με αυτό τον τρόπο προσδιορίστηκε μια μεταβλητή της μορφής όπου N είναι ο αριθμός των pixels της εικόνας, k η επανάληψη και η ελάχιστη τιμή του διανύσματος των ΣΑ. Η ανάλυση που έγινε έδειξε ότι η μεταβλητή Cmin συσχετίζεται μόνο με την ενεργότητα της εικόνας και όχι με το είδος ή το μέγεθός της. Η παραμετροποίηση αυτής της σχέσης οδήγησε στην ανάπτυξη του κριτηρίου παύσης για τον MLEM αλγόριθμο. Μια άλλη προσέγγιση βασισμένη στις ιδιότητες πιθανοφάνειας του MLEM αλγόριθμου, οδήγησε στην ανάπτυξη ενός διαφορετικού κριτηρίου παύσης του MLEM. Τα δύο κριτήρια αποτιμήθηκαν με τη χρήση του ομοιώματος Digimouse και βρέθηκε να παράγουν παρόμοιες εικόνες. Η ίδια μελέτη έγινε και για τον OSEM αλγόριθμο και αναπτύχθηκε κριτήριο παύσης για διαφορετικό αριθμό subsets.