This paper presents a fast algorithm to simulate inter-crystal scattering to increase the accurac... more This paper presents a fast algorithm to simulate inter-crystal scattering to increase the accuracy of Positron Emission Tomography (PET). Theoretically, inter-crystal scattering computation would require the solution of a particle transport problem, which is quite time consuming. However, most of this calculation can be ported to a pre-processing phase, taking advantage of the fact that the structure of the detector is fixed. Pre-computing the scattering probabilities inside the crystals, the final system response is the convolution of the geometric response obtained with the assumption that crystals are ideal absorbers and the crystal transport probability matrix. This convolution is four-dimensional which poses complexity problems as the complexity of the naive convolution evaluation grows exponentially with the dimension of the domain. We use Monte Carlo method to attack the curse of dimension. We demonstrate that these techniques have just negligible overhead.
This paper presents an efficient algorithm to sample free path in inhomogeneous participating med... more This paper presents an efficient algorithm to sample free path in inhomogeneous participating media. The method is based on the concept of mixing “virtual” particles to the medium, that complete the extinction coefficient to a piece-wise constant function. We use the sampling formulae developed for piece-wise homogeneous medium, but decide randomly whether a real or a virtual particle is hit.
Iterative positron emission tomography (PET) reconstruction computes projections between the voxe... more Iterative positron emission tomography (PET) reconstruction computes projections between the voxel space and the lines of response (LOR) space, which are mathematically equivalent to the evaluation of multi-dimensional integrals. The dimension of the integration domain can be very high if scattering needs to be compensated. Monte Carlo (MC) quadrature is a straightforward method to approximate high-dimensional integrals. As the numbers of voxels and LORs can be in the order of hundred millions and the projection also depends on the measured object, the quadratures cannot be precomputed, but Monte Carlo simulation should take place on-the-fly during the iterative reconstruction process. This paper presents modifications of the maximum likelihood, expectation maximization (ML-EM) iteration scheme to reduce the reconstruction error due to the on-the-fly MC approximations of forward and back projections. If the MC sample locations are the same in every iteration step of the ML-EM scheme, then the approximation error will lead to a modified reconstruction result. However, when random estimates are statistically independent in different iteration steps, then the iteration may either diverge or fluctuate around the solution. Our goal is to increase the accuracy and the stability of the iterative solution while keeping the number of random samples and therefore the reconstruction time low. We first analyze the error behavior of ML-EM iteration with on-the-fly MC projections, then propose two solutions: averaging iteration and Metropolis iteration. Averaging iteration averages forward projection estimates during the iteration sequence. Metropolis iteration rejects those forward projection estimates that would compromise the reconstruction and also guarantees the unbiasedness of the tracer density estimate. We demonstrate that these techniques allow a significant reduction of the required number of samples and thus the reconstruction time. The proposed methods are built into the Teratomo system. Index Terms-Graphics processing unit (GPU), positron emission tomography (PET), maximum likelihood, expectation maximization (ML-EM) reconstruction, Monte Carlo (MC) methods, scatter compensation. I. INTRODUCTION T OMOGRAPHY reconstruction is the inverse problem of particle transport in scattering and absorbing media, which requires the iteration of particle transport calculations Manuscript
virtuális részecskék hozzáaadásával teszi lehetové az új módszer. A valós és virtuális részecské... more virtuális részecskék hozzáaadásával teszi lehetové az új módszer. A valós és virtuális részecskék teljes kioltási tényezojét egy kisfelbontású, úgynevezett szuper-voxel rácson ırjuk le, melynek voxelei jóval nagyobbak lehetnek mint a szóró közeg definıciójánál ...
ABSTRACT In this paper, we present different approaches to the efficient handling of gamma intera... more ABSTRACT In this paper, we present different approaches to the efficient handling of gamma interaction within the detector crystal matrix for ML-EM-based 3D reconstruction algorithms for positron emission tomography (PET). Geometric calculations as well as approximation of inter-crystal scattering in the forward and in the back-projection are calculated on-the-fly by Monte Carlo techniques implemented on the GPU. Instead of an accu-rate treatment of scattering simulation, the main characteristics of the scattering effect are captured by approximate models or by performing most of the calculation as a pre-processing step based on prior Monte Carlo simulations. The discussed methods involve the modification of the detector radius in the geometric model; taking only the attenuation effect into account; applying 4D filtering on the lines-of-responses regarding the pre-calculated crystal-transport probability distributions; or replac-ing the simulated detector response function by an approximated one. Results of these different approaches are reported using phantom simulations as well as reconstructing real measurements performed on the NanoPET TM /CT small animal PET scanner.
As no civil infrastructure can escape aging and deterioration, health monitoring can prevent and ... more As no civil infrastructure can escape aging and deterioration, health monitoring can prevent and report serious structural damage. With the rapid evolution of computer vision algorithms, optical-based systems become an increasingly feasible option for automatic monitoring. This paper proposes a cheap and flexible standalone system based on marker tracking to report deflection of structural elements of civil infrastructure. A single marker is placed on tracked objects, which allows unambiguous identification of objects and accurate movement tracking. Accuracy of the system is discussed by presenting a theoretical analysis of the translation error. Additionally, as a proof of concept we extend our work with a low-cost laboratory test implementation.
2019 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC)
Dynamic positron emission tomography reconstructs the space-time dependence of radiotracer concen... more Dynamic positron emission tomography reconstructs the space-time dependence of radiotracer concentration in a human or animal body. The self-motion of the examined subject often cannot be avoided. Therefore, the motion should be measured and this information should be incorporated into the reconstruction process. The ML-EM reconstruction procedure [1] can be generalized to consider subject movement by concatenating a geometric transformation to the system matrix multiplication. However, a transformation is valid only for a single point in time, thus time frames should be short enough to allow the assumption that motion is constant within them. Fast movements, which occur in the study of neurological disorders, would require a very high number of frames, leading to unacceptable reconstruction times. To attack this problem, we re-formulate the ML-EM scheme to incorporate continuous motion during frames. Instead of a geometric transformation, we apply 3D motion blur. For efficient implementation, the paths of object-space voxels are approximated by polylines and antialiasing line drawing methods are adapted to calculate the blurred result. Having executed motion blur on the voxel array before forward projection and twice during back projection, all other components of the simulation can be reused from the dynamic reconstruction system developed without motion compensation.
2017 International Conference on 3D Immersion (IC3D), 2017
Our research is about the effects of non-photorealistic rendering in the perception of stereoscop... more Our research is about the effects of non-photorealistic rendering in the perception of stereoscopic cinema. We conducted a study with 27 participants, using eye-tracker to evaluate ocular behavior during the free viewing of a stereoscopic film. We obtained ocular fixation data that were correlated with visual entropy. Gaze data leads us to believe that facing a highly abstract non-photorealistic scene the gaze seems to react under the effect of a perceptive anxiety. This ocular response seems to spontaneously assign greater sensorimotor resources to the analysis of the character's behavior, transforming his face into the main key to analyse the information and sense of the global scene. This behavior appears to us as an adaptive response to a visual environment endowed with abstraction and cognitive uncertainty. Our results could be useful for conceiving new non-photorealistic rendering tools for 3D films and cinematic virtual reality.
Serious gaming has been proven to be an enjoyable tool to transfer particular knowledge or skills... more Serious gaming has been proven to be an enjoyable tool to transfer particular knowledge or skills to target players. In educational context, serious games offer a powerful and effective approach to teaching, learning and skill development for all ages. Realism is one of the considerable factors which motivates players to accomplish their goals in a serious game. In this paper we present the elements and the process of visual realism design for 3D serious gaming, extended with a case study in LISSA (LIfe Support Simulation Application), a serious game designed to teach and learn cardiopulmonary resuscitation (CPR). LISSA exploits video game technology to link computer-based case simulations with e-learning functionalities in a single framework. An evaluation of visual realism with regard to photorealism and camera viewpoint is presented.
2017 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC), 2017
This work adapts the concept of gradient-domain reconstruction to iterative positron emission tom... more This work adapts the concept of gradient-domain reconstruction to iterative positron emission tomography (PET). We apply separate iterative PET reconstructions to recover the partial derivatives, expressed as finite differences, of the objective radio-tracer density. The final reconstruction is then obtained by integrating the reconstructed partial derivatives using a Poisson solver. The motivation behind this method is that the sparsity of the individual partial derivatives often exceeds the sparsity in the image domain or in the field of gradient magnitudes, which may lead to improved quality compared to traditional methods and the total variation regularization. Additionally, working directly in the gradient domain, we believe it will be easier to integrate gradient domain approaches for particle simulation, image filtering, or regularization to the reconstruction loop. We demonstrate the gradient domain approach on a hypothetical 2D PET scanner and show that results are comparab...
2020 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC), 2020
Depth of Interaction (DOI) PET scanners extend the data stored about photon detection events by t... more Depth of Interaction (DOI) PET scanners extend the data stored about photon detection events by the depth of the gamma photon's absorption in the detector crystals. Popular DOI-based reconstruction methods disregard photon scattering in the detectors and simply modify the endpoints of the Lines of Responses (LORs). However, such simplification reduces the accuracy of the resulting image. This paper proposes the incorporation of the modeling of inter-crystal scattering into DOI-based PET reconstructions. The transfer probabilities caused by inter-crystal scattering are determined off-line with Monte Carlo simulation and are built into the system matrix as a factored component.
In visual communication, the proper style depends on the message we want to deliver to the obse... more In visual communication, the proper style depends on the message we want to deliver to the observers and the emotions we want to evoke in them. This may change from time to time and scene to scene in a game. In CGI, post production is far more efficient for changing and fine-tuning the style in terms of man-hours. Post production stylization tools should exist for video games. Providing multiple choices to players that give different game experience increases replayability. Rendering style definitely affects game experience, thus, a collection of styles may improve replay value. All in all: we need for easy to apply, easy to parameterize and reusable stylization effects that may be changed real-time NPR Effects for Games In video games, post-processing effects can serve these purposes, since they are very easy to apply to any games (including existing ones) and as they are computed in real-time, their parameters (and thus the rendering style) may change dynamically. Important requirements for the effects: online post-processing + image stream = real-time performance + temporal coherence In this work, we tried to give a proof of concept: Preliminary survey: gathered a collection of effects. State of the art and a few new ideas. Implementation in a widely used game engine: reusable effects in the Unity game engine, designed to be put after the realistic rendering pipeline. Application to existing games: Unity demos and our own development. Each application took only a few minutes.
International Journal of Creative Interfaces and Computer Graphics, 2015
Legends of Girona is a serious game which can be used to teach local history to students in the p... more Legends of Girona is a serious game which can be used to teach local history to students in the province of Girona in Spain. The game is a graphic adventure taking place in both present-day and medieval Girona. The authors describe in this paper the design of the game, including aspects related to artificial intelligence, advanced computer graphics, exergaming, mobile platforms and immersive devices. A collection of different devices is supported, including input devices such as head trackers and output devices such as cylindrical and spherical domes, immersapods, and 3D helmets. The authors provide an overview of all the stages required for the configuration of immersive devices (calibration procedure, adaptation and rendering). They also present some directions of future work.
In inverse problems like tomography reconstruction we need to solve an over-determined linear sys... more In inverse problems like tomography reconstruction we need to solve an over-determined linear system corrupted with noise. The ML-EM algorithm finds the solution for Poisson noise as the fixed point of iterating a forward projection and a non-linear back projection. In tomography we have several hundred million equations and unknowns. The elements of the huge matrix are high-dimensional integrals, which cannot be stored, but must be re-computed with Monte Carlo (MC) quadrature when needed. In this paper we address the problems of how the quadrature error affects the accuracy of the reconstruction, whether it is possible to modify the back projection to speed up convergence without compromising the accuracy, and whether we should always take the same MC estimate or modify it in every projection.
2012 IEEE Nuclear Science Symposium and Medical Imaging Conference Record (NSS/MIC), 2012
This paper presents a fast GPU-based solution to compensate positron range effects in heterogeneo... more This paper presents a fast GPU-based solution to compensate positron range effects in heterogeneous media for iterative PET reconstruction. We assume a factorized approach, where projections are decomposed to phases according to the main physical effects. Positron range is the first effect in this chain, which causes a spatially varying blurring according to local material properties. In high-resolution small animal PET systems, the average free path length of positrons may be many times longer than the linear size of voxels. This means that positron range significantly compromises the reconstruction quality if it is not compensated, and also that the material dependent blurring should have a very large support so its voxel space calculation would take prohibitively long. Frequency domain filtering does not have such computational complexity problems, but its direct form is ruled out by the fact that we need a spatially variant filtering in heterogeneous media. To handle heterogeneous media, we execute Fast Fourier Transforms for each material type and for appropriately modulated tracer densities and merge these partial results into a density that describes the composed, heterogeneous medium. Fast Fourier Transform requires the filter kernels on the same resolution as the tracer density is defined, so we also present efficient methods for re-sampling the probability densities of positron range for different resolutions and basis functions. The algorithm is implemented on the GPU, built into the TeraTomo TM system, and requires just a few seconds on high resolution voxel arrays.
This paper describes a serious game intended to teach singing to children. The system shows the s... more This paper describes a serious game intended to teach singing to children. The system shows the students a virtual world they can explore, and the evolution of the world is based on their performance. Automatic content generation tecniques are used to present the player with different exercises, and their singing is evaluated using state of the art techniques. 2 The virtual world The developed music teaching game is designed primarily for children, thus we designed the virtual world, the game logic, the rendering and the interaction accordingly.
This paper presents a fast algorithm to simulate inter-crystal scattering to increase the accurac... more This paper presents a fast algorithm to simulate inter-crystal scattering to increase the accuracy of Positron Emission Tomography (PET). Theoretically, inter-crystal scattering computation would require the solution of a particle transport problem, which is quite time consuming. However, most of this calculation can be ported to a pre-processing phase, taking advantage of the fact that the structure of the detector is fixed. Pre-computing the scattering probabilities inside the crystals, the final system response is the convolution of the geometric response obtained with the assumption that crystals are ideal absorbers and the crystal transport probability matrix. This convolution is four-dimensional which poses complexity problems as the complexity of the naive convolution evaluation grows exponentially with the dimension of the domain. We use Monte Carlo method to attack the curse of dimension. We demonstrate that these techniques have just negligible overhead.
This paper presents an efficient algorithm to sample free path in inhomogeneous participating med... more This paper presents an efficient algorithm to sample free path in inhomogeneous participating media. The method is based on the concept of mixing “virtual” particles to the medium, that complete the extinction coefficient to a piece-wise constant function. We use the sampling formulae developed for piece-wise homogeneous medium, but decide randomly whether a real or a virtual particle is hit.
Iterative positron emission tomography (PET) reconstruction computes projections between the voxe... more Iterative positron emission tomography (PET) reconstruction computes projections between the voxel space and the lines of response (LOR) space, which are mathematically equivalent to the evaluation of multi-dimensional integrals. The dimension of the integration domain can be very high if scattering needs to be compensated. Monte Carlo (MC) quadrature is a straightforward method to approximate high-dimensional integrals. As the numbers of voxels and LORs can be in the order of hundred millions and the projection also depends on the measured object, the quadratures cannot be precomputed, but Monte Carlo simulation should take place on-the-fly during the iterative reconstruction process. This paper presents modifications of the maximum likelihood, expectation maximization (ML-EM) iteration scheme to reduce the reconstruction error due to the on-the-fly MC approximations of forward and back projections. If the MC sample locations are the same in every iteration step of the ML-EM scheme, then the approximation error will lead to a modified reconstruction result. However, when random estimates are statistically independent in different iteration steps, then the iteration may either diverge or fluctuate around the solution. Our goal is to increase the accuracy and the stability of the iterative solution while keeping the number of random samples and therefore the reconstruction time low. We first analyze the error behavior of ML-EM iteration with on-the-fly MC projections, then propose two solutions: averaging iteration and Metropolis iteration. Averaging iteration averages forward projection estimates during the iteration sequence. Metropolis iteration rejects those forward projection estimates that would compromise the reconstruction and also guarantees the unbiasedness of the tracer density estimate. We demonstrate that these techniques allow a significant reduction of the required number of samples and thus the reconstruction time. The proposed methods are built into the Teratomo system. Index Terms-Graphics processing unit (GPU), positron emission tomography (PET), maximum likelihood, expectation maximization (ML-EM) reconstruction, Monte Carlo (MC) methods, scatter compensation. I. INTRODUCTION T OMOGRAPHY reconstruction is the inverse problem of particle transport in scattering and absorbing media, which requires the iteration of particle transport calculations Manuscript
virtuális részecskék hozzáaadásával teszi lehetové az új módszer. A valós és virtuális részecské... more virtuális részecskék hozzáaadásával teszi lehetové az új módszer. A valós és virtuális részecskék teljes kioltási tényezojét egy kisfelbontású, úgynevezett szuper-voxel rácson ırjuk le, melynek voxelei jóval nagyobbak lehetnek mint a szóró közeg definıciójánál ...
ABSTRACT In this paper, we present different approaches to the efficient handling of gamma intera... more ABSTRACT In this paper, we present different approaches to the efficient handling of gamma interaction within the detector crystal matrix for ML-EM-based 3D reconstruction algorithms for positron emission tomography (PET). Geometric calculations as well as approximation of inter-crystal scattering in the forward and in the back-projection are calculated on-the-fly by Monte Carlo techniques implemented on the GPU. Instead of an accu-rate treatment of scattering simulation, the main characteristics of the scattering effect are captured by approximate models or by performing most of the calculation as a pre-processing step based on prior Monte Carlo simulations. The discussed methods involve the modification of the detector radius in the geometric model; taking only the attenuation effect into account; applying 4D filtering on the lines-of-responses regarding the pre-calculated crystal-transport probability distributions; or replac-ing the simulated detector response function by an approximated one. Results of these different approaches are reported using phantom simulations as well as reconstructing real measurements performed on the NanoPET TM /CT small animal PET scanner.
As no civil infrastructure can escape aging and deterioration, health monitoring can prevent and ... more As no civil infrastructure can escape aging and deterioration, health monitoring can prevent and report serious structural damage. With the rapid evolution of computer vision algorithms, optical-based systems become an increasingly feasible option for automatic monitoring. This paper proposes a cheap and flexible standalone system based on marker tracking to report deflection of structural elements of civil infrastructure. A single marker is placed on tracked objects, which allows unambiguous identification of objects and accurate movement tracking. Accuracy of the system is discussed by presenting a theoretical analysis of the translation error. Additionally, as a proof of concept we extend our work with a low-cost laboratory test implementation.
2019 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC)
Dynamic positron emission tomography reconstructs the space-time dependence of radiotracer concen... more Dynamic positron emission tomography reconstructs the space-time dependence of radiotracer concentration in a human or animal body. The self-motion of the examined subject often cannot be avoided. Therefore, the motion should be measured and this information should be incorporated into the reconstruction process. The ML-EM reconstruction procedure [1] can be generalized to consider subject movement by concatenating a geometric transformation to the system matrix multiplication. However, a transformation is valid only for a single point in time, thus time frames should be short enough to allow the assumption that motion is constant within them. Fast movements, which occur in the study of neurological disorders, would require a very high number of frames, leading to unacceptable reconstruction times. To attack this problem, we re-formulate the ML-EM scheme to incorporate continuous motion during frames. Instead of a geometric transformation, we apply 3D motion blur. For efficient implementation, the paths of object-space voxels are approximated by polylines and antialiasing line drawing methods are adapted to calculate the blurred result. Having executed motion blur on the voxel array before forward projection and twice during back projection, all other components of the simulation can be reused from the dynamic reconstruction system developed without motion compensation.
2017 International Conference on 3D Immersion (IC3D), 2017
Our research is about the effects of non-photorealistic rendering in the perception of stereoscop... more Our research is about the effects of non-photorealistic rendering in the perception of stereoscopic cinema. We conducted a study with 27 participants, using eye-tracker to evaluate ocular behavior during the free viewing of a stereoscopic film. We obtained ocular fixation data that were correlated with visual entropy. Gaze data leads us to believe that facing a highly abstract non-photorealistic scene the gaze seems to react under the effect of a perceptive anxiety. This ocular response seems to spontaneously assign greater sensorimotor resources to the analysis of the character's behavior, transforming his face into the main key to analyse the information and sense of the global scene. This behavior appears to us as an adaptive response to a visual environment endowed with abstraction and cognitive uncertainty. Our results could be useful for conceiving new non-photorealistic rendering tools for 3D films and cinematic virtual reality.
Serious gaming has been proven to be an enjoyable tool to transfer particular knowledge or skills... more Serious gaming has been proven to be an enjoyable tool to transfer particular knowledge or skills to target players. In educational context, serious games offer a powerful and effective approach to teaching, learning and skill development for all ages. Realism is one of the considerable factors which motivates players to accomplish their goals in a serious game. In this paper we present the elements and the process of visual realism design for 3D serious gaming, extended with a case study in LISSA (LIfe Support Simulation Application), a serious game designed to teach and learn cardiopulmonary resuscitation (CPR). LISSA exploits video game technology to link computer-based case simulations with e-learning functionalities in a single framework. An evaluation of visual realism with regard to photorealism and camera viewpoint is presented.
2017 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC), 2017
This work adapts the concept of gradient-domain reconstruction to iterative positron emission tom... more This work adapts the concept of gradient-domain reconstruction to iterative positron emission tomography (PET). We apply separate iterative PET reconstructions to recover the partial derivatives, expressed as finite differences, of the objective radio-tracer density. The final reconstruction is then obtained by integrating the reconstructed partial derivatives using a Poisson solver. The motivation behind this method is that the sparsity of the individual partial derivatives often exceeds the sparsity in the image domain or in the field of gradient magnitudes, which may lead to improved quality compared to traditional methods and the total variation regularization. Additionally, working directly in the gradient domain, we believe it will be easier to integrate gradient domain approaches for particle simulation, image filtering, or regularization to the reconstruction loop. We demonstrate the gradient domain approach on a hypothetical 2D PET scanner and show that results are comparab...
2020 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC), 2020
Depth of Interaction (DOI) PET scanners extend the data stored about photon detection events by t... more Depth of Interaction (DOI) PET scanners extend the data stored about photon detection events by the depth of the gamma photon's absorption in the detector crystals. Popular DOI-based reconstruction methods disregard photon scattering in the detectors and simply modify the endpoints of the Lines of Responses (LORs). However, such simplification reduces the accuracy of the resulting image. This paper proposes the incorporation of the modeling of inter-crystal scattering into DOI-based PET reconstructions. The transfer probabilities caused by inter-crystal scattering are determined off-line with Monte Carlo simulation and are built into the system matrix as a factored component.
In visual communication, the proper style depends on the message we want to deliver to the obse... more In visual communication, the proper style depends on the message we want to deliver to the observers and the emotions we want to evoke in them. This may change from time to time and scene to scene in a game. In CGI, post production is far more efficient for changing and fine-tuning the style in terms of man-hours. Post production stylization tools should exist for video games. Providing multiple choices to players that give different game experience increases replayability. Rendering style definitely affects game experience, thus, a collection of styles may improve replay value. All in all: we need for easy to apply, easy to parameterize and reusable stylization effects that may be changed real-time NPR Effects for Games In video games, post-processing effects can serve these purposes, since they are very easy to apply to any games (including existing ones) and as they are computed in real-time, their parameters (and thus the rendering style) may change dynamically. Important requirements for the effects: online post-processing + image stream = real-time performance + temporal coherence In this work, we tried to give a proof of concept: Preliminary survey: gathered a collection of effects. State of the art and a few new ideas. Implementation in a widely used game engine: reusable effects in the Unity game engine, designed to be put after the realistic rendering pipeline. Application to existing games: Unity demos and our own development. Each application took only a few minutes.
International Journal of Creative Interfaces and Computer Graphics, 2015
Legends of Girona is a serious game which can be used to teach local history to students in the p... more Legends of Girona is a serious game which can be used to teach local history to students in the province of Girona in Spain. The game is a graphic adventure taking place in both present-day and medieval Girona. The authors describe in this paper the design of the game, including aspects related to artificial intelligence, advanced computer graphics, exergaming, mobile platforms and immersive devices. A collection of different devices is supported, including input devices such as head trackers and output devices such as cylindrical and spherical domes, immersapods, and 3D helmets. The authors provide an overview of all the stages required for the configuration of immersive devices (calibration procedure, adaptation and rendering). They also present some directions of future work.
In inverse problems like tomography reconstruction we need to solve an over-determined linear sys... more In inverse problems like tomography reconstruction we need to solve an over-determined linear system corrupted with noise. The ML-EM algorithm finds the solution for Poisson noise as the fixed point of iterating a forward projection and a non-linear back projection. In tomography we have several hundred million equations and unknowns. The elements of the huge matrix are high-dimensional integrals, which cannot be stored, but must be re-computed with Monte Carlo (MC) quadrature when needed. In this paper we address the problems of how the quadrature error affects the accuracy of the reconstruction, whether it is possible to modify the back projection to speed up convergence without compromising the accuracy, and whether we should always take the same MC estimate or modify it in every projection.
2012 IEEE Nuclear Science Symposium and Medical Imaging Conference Record (NSS/MIC), 2012
This paper presents a fast GPU-based solution to compensate positron range effects in heterogeneo... more This paper presents a fast GPU-based solution to compensate positron range effects in heterogeneous media for iterative PET reconstruction. We assume a factorized approach, where projections are decomposed to phases according to the main physical effects. Positron range is the first effect in this chain, which causes a spatially varying blurring according to local material properties. In high-resolution small animal PET systems, the average free path length of positrons may be many times longer than the linear size of voxels. This means that positron range significantly compromises the reconstruction quality if it is not compensated, and also that the material dependent blurring should have a very large support so its voxel space calculation would take prohibitively long. Frequency domain filtering does not have such computational complexity problems, but its direct form is ruled out by the fact that we need a spatially variant filtering in heterogeneous media. To handle heterogeneous media, we execute Fast Fourier Transforms for each material type and for appropriately modulated tracer densities and merge these partial results into a density that describes the composed, heterogeneous medium. Fast Fourier Transform requires the filter kernels on the same resolution as the tracer density is defined, so we also present efficient methods for re-sampling the probability densities of positron range for different resolutions and basis functions. The algorithm is implemented on the GPU, built into the TeraTomo TM system, and requires just a few seconds on high resolution voxel arrays.
This paper describes a serious game intended to teach singing to children. The system shows the s... more This paper describes a serious game intended to teach singing to children. The system shows the students a virtual world they can explore, and the evolution of the world is based on their performance. Automatic content generation tecniques are used to present the player with different exercises, and their singing is evaluated using state of the art techniques. 2 The virtual world The developed music teaching game is designed primarily for children, thus we designed the virtual world, the game logic, the rendering and the interaction accordingly.
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Papers by Milan Magdics