GPU Implementation of Multi-View Stereo Algorithms

Tohoku University青木孝

Portal-s: High-resolution real-time 3D video telepresence

The goal of telepresence is to allow a person to feel as if they are present in a location other than their true location; a common application of telepresence is video conferencing in which live video of a user is transmitted to a remote location for viewing. In conventional two-dimensional (2D) video conferencing, loss of correct eye gaze commonly occurs, due to a disparity between the capture and display optical axes. Newer systems are being developed which allow for three-dimensional (3D) video conferencing, circumventing issues with this disparity, but new challenges are arising in the capture, delivery, and redisplay of 3D contents across existing infrastructure. To address these challenges, a novel system is proposed which allows for 3D video conferencing across existing networks while delivering full resolution 3D video and establishing correct eye gaze. During the development of Portal-s, many innovations to the field of 3D scanning and its applications were made; specifically, this dissertation research has achieved the following innovations: a technique to realize 3D video processing entirely on a graphics processing unit (GPU), methods to compress 3D videos on a GPU, and combination of the aforementioned innovations with a special holographic display hardware system to enable the novel 3D telepresence system entitled Portal-s. The first challenge this dissertation addresses is the cost of real-time 3D scanning technology, both from a monetary and computing power perspective. New advancements in 3D scanning and computation technology are continuing to increase, simplifying the acquisition and display of 3D data. These advancements are allowing users new methods of interaction and analysis of the 3D world around them. Although the acquisition of static 3D geometry is becoming easy, the same cannot be said of dynamic geometry, since all aspects of the 3D processing pipeline, capture, processing, and display, must be realized in real-time simultaneously. Conventional approaches to solve these problems utilize workstation computers with powerful central processing units (CPUs) and GPUs to accomplish the large amounts of processing power required for a single 3D frame. A challenge arises when trying to realize real-time 3D scanning on commodity hardware such as a laptop computer. To address the cost of a real-time 3D scanning system, an entirely parallel 3D data processing pipeline that makes use of a multi-frequency phase-shifting technique is presented. This novel processing pipeline can achieve simultaneous 3D data capturing, processing, and display at 30 frames per second (fps) on a laptop computer. By implementing the pipeline within the OpenGL Shading Language (GLSL), nearly any modern computer with a dedicated graphics device can run the pipeline. Making use of multiple threads sharing GPU resources and direct memory access transfers, high frame rates on low compute power devices can be achieved. Although these advancements allow for low compute power devices such as a laptop to achieve real-time 3D scanning, this technique is not without challenges. The main challenge being selecting frequencies that allow for high quality phase, yet do not include phase jumps in equivalent frequencies. To address this issue, a new modified multi-frequency phase shifting technique was developed that allows phase jumps to be introduced in equivalent frequencies yet unwrapped in parallel, increasing phase quality and reducing reconstruction error. Utilizing these techniques, a real-time 3D scanner was developed that captures 3D geometry at 30 fps with a root mean square error (RMSE) of 0:00081 mm for a measurement area of 100 mm X 75 mm at a resolution of 800 X 600 on a laptop computer. With the above mentioned pipeline the CPU is nearly idle, freeing it to perform additional tasks such as image processing and analysis. The second challenge this dissertation addresses is associated with delivering huge amounts of 3D video data in real-time across existing network infrastructure. As the speed of 3D scanning continues to increase, and real-time scanning is achieved on low compute power devices, a way of compressing the massive amounts of 3D data being generated is needed. At a scan resolution of 800 X 600, streaming a 3D point cloud at 30 frames per second (FPS) would require a throughput of over 1.3 Gbps. This amount of throughput is large for a PCIe bus, and too much for most commodity network cards. Conventional approaches involve serializing the data into a compressible state such as a polygon file format (PLY) or Wavefront object (OBJ) file. While this technique works well for structured 3D geometry, such as that created with computer aided drafting (CAD) or 3D modeling software, this does not hold true for 3D scanned data as it is inherently unstructured. A challenge arises when trying to compress this unstructured 3D information in such a way that it can be easily utilized with existing infrastructure. To address the need for real-time 3D video compression, new techniques entitled Holoimage and Holovideo are presented, which have the ability to compress, respectively, 3D geometry and 3D video into 2D counterparts and apply both lossless and lossy encoding. Similar to the aforementioned 3D scanning pipeline, these techniques make use of a completely parallel pipeline for encoding and decoding; this affords high speed processing on the GPU, as well as compression before streaming the data over the PCIe bus. Once in the compressed 2D state, the information can be streamed and saved until the 3D information is needed, at which point 3D geometry can be reconstructed while maintaining a low amount of reconstruction error. Further enhancements of the technique have allowed additional information, such as texture information, to be encoded by reducing the bit rate of the data through image dithering. This allows both the 3D video and associated 2D texture information to be interlaced and compressed into 2D video, synchronizing the streams automatically. The third challenge this dissertation addresses is achieving correct eye gaze in video conferencing. In 2D video conferencing, loss of correct eye gaze commonly occurs, due to a disparity between the capture and display optical axes. Conventional approaches to mitigate this issue involve either reducing the angle of disparity between the axes by increasing the distance of the user to the system, or merging the axes through the use of beam splitters. Newer approaches to this issue make use of 3D capture and display technology, as the angle of disparity can be corrected through transforms of the 3D data. Challenges arise when trying to create such novel systems, as all aspects of the pipeline, capture, transmission, and redisplay must be simultaneously achieved in real-time with the massive amounts of 3D data. Finally, the Portal-s system is presented, which is an integration of all the aforementioned technologies into a holistic software and hardware system that enables real-time 3D video conferencing with correct mutual eye gaze. To overcome the loss of eye contact in conventional video conferencing, Portal-s makes use of dual structured-light scanners that capture through the same optical axis as the display. The real-time 3D video frames generated on the GPU are then compressed using the Holovideo technique. This allows the 3D video to be streamed across a conventional network or the Internet, and redisplayed at a remote node for another user on the Holographic display glass. Utilizing two connected Portal-s nodes, users of the systems can engage in 3D video conferencing with natural eye gaze established. In conclusion, this dissertation research substantially advances the field of real-time 3D scanning and its applications. Contributions of this research span into both academic and industrial practices, where the use of this information has allowed users new methods of interaction and analysis of the 3D world around them

Evaluating perceptual maps of asymmetries for gait symmetry quantification and pathology detection

Le mouvement de la marche est un processus essentiel de l'activité humaine et aussi le résultat de nombreuses interactions collaboratives entre les systèmes neurologiques, articulaires et musculo-squelettiques fonctionnant ensemble efficacement. Ceci explique pourquoi une analyse de la marche est aujourd'hui de plus en plus utilisée pour le diagnostic (et aussi la prévention) de différents types de maladies (neurologiques, musculaires, orthopédique, etc.). Ce rapport présente une nouvelle méthode pour visualiser rapidement les différentes parties du corps humain liées à une possible asymétrie (temporellement invariante par translation) existant dans la démarche d'un patient pour une possible utilisation clinique quotidienne. L'objectif est de fournir une méthode à la fois facile et peu dispendieuse permettant la mesure et l'affichage visuel, d'une manière intuitive et perceptive, des différentes parties asymétriques d'une démarche. La méthode proposée repose sur l'utilisation d'un capteur de profondeur peu dispendieux (la Kinect) qui est très bien adaptée pour un diagnostique rapide effectué dans de petites salles médicales car ce capteur est d'une part facile à installer et ne nécessitant aucun marqueur. L'algorithme que nous allons présenter est basé sur le fait que la marche saine possède des propriétés de symétrie (relativement à une invariance temporelle) dans le plan coronal.The gait movement is an essential process of the human activity and also the result of coordinated effort between the neurological, articular and musculoskeletal systems. This motivates why gait analysis is important and also increasingly used nowadays for the (possible early) diagnosis of many different types (neurological, muscular, orthopedic, etc.) of diseases. This paper introduces a novel method to quickly visualize the different parts of the body related to an asymmetric movement in the human gait of a patient for daily clinical. The goal is to provide a cheap and easy-to-use method to measure the gait asymmetry and display results in a perceptually relevant manner. This method relies on an affordable consumer depth sensor, the Kinect. The Kinect was chosen because this device is amenable for use in small, confined area, like a living room. Also, since it is marker-less, it provides a fast non-invasive diagnostic. The algorithm we are going to introduce relies on the fact that a healthy walk has (temporally shift-invariant) symmetry properties in the coronal plane

Les algorithmes de haute résolution en tomographie d'émission par positrons : développement et accélération sur les cartes graphiques

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

Improving digital correlation algorithm for real time use.

V této práci je prezentována sada vylepšení algoritmu DIC. Výsledkem těchto vylepšení by měla větší uživatelská přívětivost algoritmu DIC a použitelnost pro běžného uživatele.První sada vylepšení se zaměřuje na implementaci algoritmu DIC pomocí programovacího jazyka OpenCL. To umožňuje spustit algoritmus na širokém spektru dostupného hardwaru, zejména na GPU. Jak ukazují testy, výpočet DIC na GPU vede k významnému zrychlení (až 30x oproti základní variantě a 10x v porovnání s paralelní variantou). Další vylepšení se zaměřují na optimalizaci velikosti dat s cílem snížit režii přenosu dat z RAM na GPU a studii o tom, jak implementace OpenCL funguje na integrovaných GPU a procesorech.Další vylepšení se snaží předzpracovat vstupní data tak, aby zlepšila strukturu vzorků, čímž aby se zlepšila kvalita výsledné korelace. Výsledky ukazují zlepšení kvality výsledků, jsou ale vykoupeny zvýšenou dobou výpočtu. Poslední vylepšení je návrh plně automatického algoritmu, který vybírá nejlepší velikost okna pro dosažení co nejlepšího výsledku. Algoritmus se pokusí nalézt optimální velikost okna pro vyvážení systematických a náhodných chyb sledováním funkční závislosti kvality korelace a velikosti okna.In this work, a set of improvements to DIC algorithm is presented. The result of these improvements should make the DIC algorithm more user friendly and better usable for common users.First set of improvements focuses on implementing the DIC algorithm using OpenCL programming language. This allows to run the algorithm on wide range of available hardware, most notably on GPUs. As tests show, running DIC on GPU leads to significant speedup (reaching 30x compared to basic variant and 10x compared to threaded variant). Further improvements focus on optimizing the data size in order to lower the overhead of RAM to GPU transfers and a study on how the OpenCL implementation performs on integrated GPUs and CPUs.Next improvement processes the input data in order to enhance the specimens texture to improve the quality of the correlations. The experiments show improvement of the quality of the results, but they are redeemed in increased computation time.Last improvement is a design of an fully automatic algorithm that selects the best subset size to get the best results possible. The algorithm tries to find the optimal subset size to balance the systematic and random errors by monitoring the function of correlation quality versus subset size

System Characterizations and Optimized Reconstruction Methods for Novel X-ray Imaging

In the past decade there have been many new emerging X-ray based imaging technologies developed for different diagnostic purposes or imaging tasks. However, there exist one or more specific problems that prevent them from being effectively or efficiently employed. In this dissertation, four different novel X-ray based imaging technologies are discussed, including propagation-based phase-contrast (PB-XPC) tomosynthesis, differential X-ray phase-contrast tomography (D-XPCT), projection-based dual-energy computed radiography (DECR), and tetrahedron beam computed tomography (TBCT). System characteristics are analyzed or optimized reconstruction methods are proposed for these imaging modalities. In the first part, we investigated the unique properties of propagation-based phase-contrast imaging technique when combined with the X-ray tomosynthesis. Fourier slice theorem implies that the high frequency components collected in the tomosynthesis data can be more reliably reconstructed. It is observed that the fringes or boundary enhancement introduced by the phase-contrast effects can serve as an accurate indicator of the true depth position in the tomosynthesis in-plane image. In the second part, we derived a sub-space framework to reconstruct images from few-view D-XPCT data set. By introducing a proper mask, the high frequency contents of the image can be theoretically preserved in a certain region of interest. A two-step reconstruction strategy is developed to mitigate the risk of subtle structures being oversmoothed when the commonly used total-variation regularization is employed in the conventional iterative framework. In the thirt part, we proposed a practical method to improve the quantitative accuracy of the projection-based dual-energy material decomposition. It is demonstrated that applying a total-projection-length constraint along with the dual-energy measurements can achieve a stabilized numerical solution of the decomposition problem, thus overcoming the disadvantages of the conventional approach that was extremely sensitive to noise corruption. In the final part, we described the modified filtered backprojection and iterative image reconstruction algorithms specifically developed for TBCT. Special parallelization strategies are designed to facilitate the use of GPU computing, showing demonstrated capability of producing high quality reconstructed volumetric images with a super fast computational speed. For all the investigations mentioned above, both simulation and experimental studies have been conducted to demonstrate the feasibility and effectiveness of the proposed methodologies

Studying the Properties of Cellular Materials with GPU Acceleration

There has always been a great interest in cellular behaviour. From the molecular level, studying the chemistry of the reactions that occur in cell, and the physical interactions between those molecules, to the scale of the cell itself and its behaviour in response to various phenomena. Suffice it to say, that cellular behaviour is highly complex and, therefore, it is difficult to predict how cells will behave or to even describe their behaviour in detail. Traditionally cell biology has been done solely in the laboratory. That has always yielded interesting results and science. There are some aspects of phenomena that, due to cost, time, or other factors, need to be studied computationally. Especially if these stimuli occur on very short or long time scales. Therefore, a number of models have been proposed in order to study cell behaviour. Unfortunately, these methods can only be used in certain situations and circumstances. These methods can, and do, produce interesting and valid results. Yet there is not really any model available that can be used to model more than one or two kinds of cell behaviour. For example, methods that can show cell sorting do not necessarily show packing. Furthermore, many of the models in the literature represent cells as collections of points, or polygons, so cellular interactions at interfaces cannot be studied efficiently. The goal of the work presented here was to develop a three dimensional model of cells using Molecular Dynamics. Cells are represented as spherical meshes of mass points. And these mass points are placed in a force field that emulates cellular interactions such as adhesion, repulsion, and friction. The results of this work indicates that the model developed can reproduce qualitatively valid cellular behaviour. And the model can be extended to include other effects. It must also be recognized that \gls{md} is very expensive computationally. Especially in the case of this model as many mass points are needed in the cellular mesh to ensure adequate spatial resolution. Higher performance is always needed either to study larger systems or to iterate on smaller systems more quickly. The most obvious way to alleviate this problem is too use high performance hardware. It will be shown that this performance is most accessible, after some effort, with \gls{gpu} acceleration. The model developed in this work will be implemented with \gls{gpu} acceleration. The code generated in this way is quite fast

Amélioration qualitative et quantitative de reconstruction TEP sur plate-forme graphique

In positron emission tomography, reconstructed images suffer from a high noise level and a low resolution. Iterative reconstruction processes require an estimation of the system response (scanner and patient) and the quality of the images depends on the accuracy of this estimate. Accurate and fast to compute models already exists for the attenuation, scattering, random coincidences and dead times. Thus, this thesis focuses on modeling the system components associated with the detector response and the positron range. A new multi-GPU parallelization of the reconstruction based on a cutting of the volume is also proposed to speed up the reconstruction exploiting the computing power of such architectures. The proposed detector response model is based on a multi-ray approach that includes all the detector effects as the geometry and the scattering in the crystals. An evaluation study based on data obtained through Mote Carlo simulation (MCS) showed this model provides reconstructed images with a better contrast to noise ratio and resolution compared with those of the methods from the state of the art. The proposed positron range model is based on a simplified MCS, integrated into the forward projector during the reconstruction. A GPU implementation of this method allows running MCS three order of magnitude faster than the same simulation on GATE, while providing similar results. An evaluation study shows this model integrated in the reconstruction gives images with better contrast recovery and resolution while avoiding artifacts.En tomographie par émission de positon, les images souffrent d'un bruit élevé et d'une résolution faible. Leur reconstruction à l'aide d'un processus itératif nécessite d'estimer la réponse du système (scanner et patient) et leur qualité dépend directement de la précision de cette estimation. Des méthodes fidèles et rapides d'exécution existent pour estimer les composantes d'atténuation, de diffusion, les coïncidences fortuites ainsi que les temps morts. Cette thèse propose des méthodes de modélisation précises des composantes du système associées au détecteur du scanner et au parcours du positon. Une nouvelle méthode de parallélisation de la reconstruction sur plateforme multi-GPU basée sur une découpe du volume reconstruit est aussi proposée, afin d'exploiter la puissance de calcul d'une telle architecture pour accélérer la reconstruction. Le modèle de la réponse du détecteur proposé exploite une approche multiligne et intègre les effets associés à la géométrie du détecteur et à la diffusion intercristaux. Une étude d'évaluation basée sur des données obtenues par simulation Monte-Carlo (SMC) montre, par rapport à l'état de l'art, une amélioration du rapport contraste sur bruit et de la résolution des images reconstruites. Le modèle du parcours du positon proposé repose sur une SMC simplifiée, intégrée à l'opération de projection dans la reconstruction. Cette simulation implémentée sur GPU fournit des résultats proches de ceux obtenus avec la plateforme GATE pour des temps d'exécution de trois ordres de grandeur plus courts. Une étude d'évaluation montre que cette méthode permet une amélioration importante du contraste et de la résolution, sans introduire d'artefacts