In compressive imaging the measurement quantization and its impact on the overall system performance is an important problem. This work considers several challenges that derive from quantization of compressive measurements. We investigate the design of scalar quantizer (SQ), vector quantizer (VQ), and tree-structured vector quantizer (TSVQ) for information-optimal compressive imaging. The performance of these quantizer designs is quantified for a variety of compression rates and measurement signal-to-noise-ratio (SNR) using simulation studies. Our simulation results show that in the low SNR regime a low bit-depth (3 bit per measurement) SQ is sufficient to minimize the degradation due to measurement quantization. However, in mid-to-high SNR regime, quantizer design requires higher bit-depth to preserve the information in the measurements. Simulation results also confirm the superior performance of VQ over SQ. As expected, TSVQ provides a good tradeoff between complexity and performance, bounded by VQ and SQ designs on either side of performance/complexity limits. In compressive image the size of final measurement data (i.e. in bits) is also an important system design metric. In this work, we also optimize the compressive imaging system using this design metric, and investigate how to optimally allocate the number of measurement and bits per measurement, i.e. the rate allocation problem. This problem is solved using both an empirical data driven approach and a model-based approach. As a function of compression rate (bits per pixel), our simulation results show that compressive imaging can outperform traditional (non-compressive) imaging followed by image compression (JPEG 2000) in low-to-mid SNR regime. However, in high SNR regime traditional imaging (with image compression) offers a higher image fidelity compare to compressive imaging for a given data rate. Compressive imaging using blockwise measurements is partly limited due to its inability to perform global rate allocation. We also develop an optimal minimum mean-square error (MMSE) reconstruction algorithm for quantized compressed measurements. The algorithm employs Monte-Carlo Markov Chain (MCMC) sampling technique to estimate the posterior mean. Simulation results show significant improvement over approximate MMSE algorithms.

At the Gesellschaft für Schwerionenforschung in Darmstadt a therapy unit for heavy ion cancer treatment has been established in collaboration with the Deutsches Krebsforschungszentrum Heidelberg, the Radiologische Universitätsklinik Heidelberg and the Forschungszentrum Rossendorf. For quality assurance the dual-head positron camera BASTEI (Beta Activity meaSurements at the Therapy with Energetic Ions) has been integrated into this facility. It measures ß+-activity distributions generated via nuclear fragmentation reactions within the target volume. BASTEI has about 4 million coincidence channels. The emission data are acquired in a 3D regime and stored in a list mode data format. Typically counting statstics is two to three orders of magnitude lower than those of typical PET-scans in nuclear medicine. Two iterative 3D reconstruction algorithms based on ISRA (Image Space Reconstruction Algorithm) and MLEM (Maximum Likelihood Expectation Maximization), respectively, have been adapted to this imaging geometry. The major advantage of the developed approaches are run-time Monte-Carlo simulations which are used to calculate the transition matrix. The influences of detector sensitivity variations, randoms, activity from outside of the field of view and attenuation are corrected for the individual coincidence channels. Performance studies show, that the implementation based on MLEM is the algorithm of merit. Since 1997 it has been applied sucessfully to patient data. The localization of distal and lateral gradients of the ß+-activity distribution is guaranteed in the longitudinal sections. Out of the longitudinal sections the lateral gradients of the ß+-activity distribution should be interpreted using a priori knowledge.

At the Gesellschaft für Schwerionenforschung in Darmstadt a therapy unit for heavy ion cancer treatment has been established in collaboration with the Deutsches Krebsforschungszentrum Heidelberg, the Radiologische Universitätsklinik Heidelberg and the Forschungszentrum Rossendorf. For quality assurance the dual-head positron camera BASTEI (Beta Activity meaSurements at the Therapy with Energetic Ions) has been integrated into this facility. It measures ß+-activity distributions generated via nuclear fragmentation reactions within the target volume. BASTEI has about 4 million coincidence channels. The emission data are acquired in a 3D regime and stored in a list mode data format. Typically counting statstics is two to three orders of magnitude lower than those of typical PET-scans in nuclear medicine. Two iterative 3D reconstruction algorithms based on ISRA (Image Space Reconstruction Algorithm) and MLEM (Maximum Likelihood Expectation Maximization), respectively, have been adapted to this imaging geometry. The major advantage of the developed approaches are run-time Monte-Carlo simulations which are used to calculate the transition matrix. The influences of detector sensitivity variations, randoms, activity from outside of the field of view and attenuation are corrected for the individual coincidence channels. Performance studies show, that the implementation based on MLEM is the algorithm of merit. Since 1997 it has been applied sucessfully to patient data. The localization of distal and lateral gradients of the ß+-activity distribution is guaranteed in the longitudinal sections. Out of the longitudinal sections the lateral gradients of the ß+-activity distribution should be interpreted using a priori knowledge.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21540号 / 理博第4447号 / 新制||理||1639(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 玉川 安騎男, 教授 向井 茂, 教授 望月 新一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

In laser wakefield acceleration, an ultra-short high-intensity laser pulse excites a plasma wave, which can sustain accelerating electric fields of several hundred GV/m. This scheme advances a novel concept for compact and less expensive electron accelerators, which can be hosted in a typical university size laboratory. Furthermore, laser wakefield accelerators (LWFA) feature unique electron bunch characteristics, namely micrometer size with duration ranging from several fs to tens of fs. Precise knowledge of the longitudinal profile of such ultra-short electron bunches is essential for the design of future table-top X-ray light-sources and remains a big challenge due to the resolution limit of existing diagnostic techniques. Spectral measurement of broadband coherent and incoherent transition radiation (TR) produced when electron bunches passing through a metal foil is a promising way to analyze longitudinal characteristics of these bunches. Due to the limited reproducibility of the electron source this measurement highly requires single-shot capability. An ultra-broadband spectrometer combines the TR spectrum in UV/NIR (200-1000 nm), NIR (0.9-1.7 µm) and mid-IR (1.6-12 µm). A high spectral sensitivity, dynamic bandwidth and spectral resolution are realized by three optimized dispersion and detection systems integrated into a single-shot spectrometer. A complete characterization and calibration of the spectrometer have been done concerning wavelengths, relative spectral sensitivities, and absolute photometric sensitivities, also taking into account for the light polarization. The TR spectrometer is able to characterize electron bunches with charges as low as 1pC and can resolve time-scales of 0.4 fs. Electron bunches up to 16 fs (rms width) can be reconstructed from their TR spectrum. In the presented work, the self-truncated ionization induced injection (STII) scheme has been explored to study the relevant beam parameters especially its longitudinal bunch profile and the resulting peak current.

Σκοπός της παρούσας μελέτης είναι να εξετάσουμε πως οι παράμετροι σάρωσης και ανακατασκευής επηρεάζουν την ποιότητα της εικόνας. Καθόσον, ορισμένες από τις παραμέτρους, αυξάνουν την δόση στον εξεταζόμενο, μελετήσαμε σε ποιες περιπτώσεις θα πρέπει να τις τροποποιήσουμε, άλλοτε για λόγους ακτινοπροστασίας και άλλοτε για την βελτιστοποίηση της ποιότητα της εικόνας. Υλικό και μέθοδος : Το πείραμα μας έγινε σε ελικοειδή Υ .Τ (Philips 5000SR), χρησιμοποιώντας πρόγραμμα συμβατικής σάρωσης (τομής-τομής) και ελικοειδούς σάρωσης σε ομοίωμα που χρησιμοποιείται για τον ποιοτικό έλεγχο. Σαρώσαμε τα διαφορετικά τμήματα του ομοιώματος, εφαρμόζοντας όλους τους δυνατούς συνδυασμούς των παραμέτρων σάρωσης και ανακατασκευής. Μετρήσαμε σε όλες τις εικόνες τον θόρυβο, την χωρική διακριτική ικανότητα (Χ.Δ.Ι ) και την αντιθετική διακριτική ικανότητα. Αποτελέσματα: Η Χ.Δ.Ι μεταβάλλεται περισσότερο από το πάχος τομής και τον αλγόριθμο ανακατασκευής, ενώ οι παράμετροι έκθεσης την επηρεάζουν λιγότερο σε εξεταζομένους με φυσιολογικές διαπλάσεις. Ο θόρυβος της εικόνας είναι μεγαλύτερος στο κέντρο της εικόνας και αυξάνει περισσότερο όταν μειώνουμε τους παράγοντες έκθεσης. Η αντιθετική διακριτική ικανότητα βελτιώνεται με αύξηση των παραμέτρων έκθεσης και με εφαρμογή κατάλληλου αλγόριθμου ανακατασκευής. Συμπέρασμα: Η σωστή επιλογή των παραμέτρων σάρωσης και ανακατασκευής μπορεί να οδηγήσει στην βελτίωση της ποιότητας της εικόνας ή στην βέλτιστη εικόνα με την λιγότερη δυνατή δόση στον εξεταζόμενο. / The purpose of the present study is to examine how the scanning and reconstruction parameters effect the quality imaging. While, some of the parameters increase the dose to the patient, we studied in which cases we have to modify them either for the benefit of the radiation protection or for the optimization of the quality imaging. Material and method. Our experiment was put into practice in conventional spiral CT (Philips 5000SR), using conventional scanning software ( slice-slice) and helical scanning at a phantom situable for quality control. We scanned the different parts of the phantom, by appling all the various combinations of the scanning and reconstruction parameters. We measured in all the images the noise, the spacial resolution and the low contrast resolution. Results. The spacial resolution is mainly influenced by the slice thickness and the reconstuction algorithm, while is less affected by the exposure parameters as far as it concerns patients with normal body mass. The noise of the image is greater at the center of the image and increases mostly when the exposure parameters are reduced. The low contrast resolution is improved by the increase of the exposure parameters and by the application of the suitable reconstruction algorithm. Conclusion. The reasonable choice of the scanning and reconstruction parameters results in the optimization of the quality imaging or in the best image with the less possible dose for the patient.

We present an Embedded Boundary with Adaptive Mesh Refinement technique for solving the compressible Navier Stokes equations in arbitrary complex domains; followed by a numerical studies for the effect of circular cylinders on the transient dynamics of the Richtmyer-Meshkov Instability. A PDE multidimensional extrapolation approach is used to reconstruct the solution in the ghost-fluid regions and imposing boundary conditions on the fluid-solid interface, coupled with a multi-dimensional algebraic interpolation for freshly cleared cells. The Navier Stokes equations are numerically solved by the second order multidimensional upwind method. Block-structured AMR, implemented with the Chombo framework, is utilized to reduce the computational cost while keeping high resolution mesh around the Embedded Boundary and regions of high gradient solutions. The versatility of the method is demonstrated via several numerical examples, in both static and moving geometry, ranging from low Mach number nearly incompressible to supersonic flows. Our simulation results are extensively verified against other numerical results and validated against available experimental results where applicable. The effects on the transient dynamics of the Richtmyer-Meshkov instability due to small scale perturbations introduced on the shock-wave or the material interface by a single or set of solid circular cylinders were computationally investigated using the developed technique. First, we discuss the RMI initiated on a flat interface by a rippled shock-wave that is disturbed by a single circular cylinder. Then, we study the effect of introducing a number of circular cylinders on the interface. The arrangement of the cylinders set mimic (in a two dimensional domain) the presence of the solid supporting grid wires used in the formation of the material interface in the experimental setup. We analyzed their effects on the mixing layer growth and the mixedness level, and qualitatively demonstrate the cylinders' perturbation effects on the mixing layer structure. We modeled the cylinders' influence based on their diameters; and showed the model ability to predict the variation of the mixing layer growth for different flow parameters.

No description available.

Electronic Portal Image Devices (EPID) são dispositivos eletrônicos que foram criados originalmente para aquisição de imagens portais. Atualmente eles também têm sido estudados para reconstrução de dose no plano do eixo central (paralelo ao EPID) na modalidade transit (modalidade que considera um material atenuador entre a fonte e o EPID). Neste trabalho foi determinado um algoritmo de reconstrução de dose para relacionar mapas bidimensionais de dose localizados dentro de geometrias que simularam uma situação clínica em radioterapia de forma simplificada. Para tal foram feitas simulações Monte Carlo utilizando o pacote de simulação PENELOPE de maneira que um cubo composto de água representou o corpo do paciente e um paralelepípedo retângulo composto de água representou o EPID. Definiu-se primeiramente a geometria controle e os parâmetros de irradiação controle e então foram feitas simulações para determinar a equação de reconstrução de dose referencial. Uma vez determinada essa equação, foram feitas novas simulações variando o tamanho de campo, espessura do objeto simulador do corpo, distância entre a fonte e a superfície de entrada do objeto simulador do corpo (DFS) e distância entre a superfície de saída do objeto simulador do corpo e o centro do objeto simulador do EPID (DSDE). Os arquivos de saída dessas simulações alimentaram o programa contendo o algoritmo de reconstrução de dose, feito em MATLAB®. Após a aplicação do programa, comparou-se a matriz que representa o mapa bidimensional localizado dentro do objeto simulador do corpo com a matriz localizada no mesmo local, reconstruída a partir da matriz que representa o objeto simulador do EPID. Os resultados encontrados neste trabalho mostram que a equação de reconstrução de dose e o algoritmo de reconstrução de dose propostos são válidos com desvios padrão menor que 1,6%. / Electronic Portal Image Devices (EPID) were originally created to acquire portal images, but they have also been studied for dose reconstruction in the central axis plane (parallel to the EPID) in transit mode (mode which considers an attenuator material between the source and the EPID). In this work we determined a dose reconstruction algorithm that relate two-dimensional dose maps located within geometries that simulated a clinical situation in simplified form. For this, simulations were performed using the simulation package PENELOPE so that a cube composed of water represented the patients body and a rectangle parallelepiped composed of water represented the EPID. We defined a control geometry and control irradiation parameters first, then simulations were performed to determine the referential dose reconstruction equation. Once determined this equation, new simulations were performed varying the field size, the body phantom thickness, the distance between the source and the body phantom entrance surface (DFS) and the distance between the body phantom exit surface and the EPID phantom center. The output files of these simulations fed the program containing the dose reconstruction algorithm, wrote in MATLAB®. After the program application, we compared the matrix that represents the two-dimensional map located within the body phantom with the matrix located at the same site, reconstructed from the matrix that represents the EPID phantom. The results in this work show that the dose reconstruction equation and the dose reconstruction algorithm proposed are valid with less than 1,6% standard deviation.

Cartesian grids offer a valuable option to simulate aerodynamic flows around complex geometries such as multi-element airfoils, aircrafts, and rockets. Therefore, an adaptively-refined Cartesian grid generator and Euler solver are developed. For the mesh generation part of the algorithm, dynamic data structures are used to determine connectivity information between cells and uniform mesh is created in the domain. Marching squares and cubes algorithms are used to form interfaces of cut and split cells. Geometry-based cell adaptation is applied in the mesh generation. After obtaining appropriate mesh around input geometry, the solution is obtained using either flux vector splitting method or Roe&rsquo / s approximate Riemann solver with cell-centered approach. Least squares reconstruction of flow variables within the cell is used to determine high gradient regions of flow. Solution based adaptation method is then applied to current mesh in order to refine these regions and also coarsened regions where unnecessary small cells exist. Multistage time stepping is used with local time steps to increase the convergence rate. Also FAS multigrid technique is used in order to increase the convergence rate. It is obvious that implementation of geometry and solution based adaptations are easier for Cartesian meshes than other types of meshes. Besides, presented numerical results show the accuracy and efficiency of the algorithm by especially using geometry and solution based adaptation. Finally, Euler solutions of Cartesian grids around airfoils, projectiles and wings are compared with the experimental and numerical data available in the literature and accuracy and efficiency of the solver are verified.