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Bouhova-Thacker, E., Kostyukhin, V., Koffas, T., Liebig, W., Limper, M., Piacquadio, G. N., et al. (2010). Expected Performance of Vertex Reconstruction in the ATLAS Experiment at the LHC. IEEE Trans. Nucl. Sci., 57(2), 760–767.
Abstract: In the harsh environment of the Large Hadron Collider at CERN (design luminosity of 10(34) cm(-2) s(-1)) efficient reconstruction of vertices is crucial for many physics analyses. Described in this paper is the expected performance of the vertex reconstruction used in the ATLAS experiment. The algorithms for the reconstruction of primary and secondary vertices as well as for finding photon conversions and vertex reconstruction in jets are described. The implementation of vertex algorithms which follows a very modular design based on object-oriented C++ is presented. A user-friendly concept allows event reconstruction and physics analyses to compare and optimize their choice among different vertex reconstruction strategies. The performance of implemented algorithms has been studied on a variety of Monte Carlo samples and results are presented.
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Aguiar, P., Rafecas, M., Ortuño, J. E., Kontaxakis, G., Santos, A., Pavia, J., et al. (2010). Geometrical and Monte Carlo projectors in 3D PET reconstruction. Med. Phys., 37(11), 5691–5702.
Abstract: Purpose: In the present work, the authors compare geometrical and Monte Carlo projectors in detail. The geometrical projectors considered were the conventional geometrical Siddon ray-tracer (S-RT) and the orthogonal distance-based ray-tracer (OD-RT), based on computing the orthogonal distance from the center of image voxel to the line-of-response. A comparison of these geometrical projectors was performed using different point spread function (PSF) models. The Monte Carlo-based method under consideration involves an extensive model of the system response matrix based on Monte Carlo simulations and is computed off-line and stored on disk. Methods: Comparisons were performed using simulated and experimental data of the commercial small animal PET scanner rPET. Results: The results demonstrate that the orthogonal distance-based ray-tracer and Siddon ray-tracer using PSF image-space convolutions yield better images in terms of contrast and spatial resolution than those obtained after using the conventional method and the multiray-based S-RT. Furthermore, the Monte Carlo-based method yields slight improvements in terms of contrast and spatial resolution with respect to these geometrical projectors. Conclusions: The orthogonal distance-based ray-tracer and Siddon ray-tracer using PSF image-space convolutions represent satisfactory alternatives to factorizing the system matrix or to the conventional on-the-fly ray-tracing methods for list-mode reconstruction, where an extensive modeling based on Monte Carlo simulations is unfeasible.
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Blume, M., Martinez-Moller, A., Keil, A., Navab, N., & Rafecas, M. (2010). Joint Reconstruction of Image and Motion in Gated Positron Emission Tomography. IEEE Trans. Med. Imaging, 29(11), 1892–1906.
Abstract: We present a novel intrinsic method for joint reconstruction of both image and motion in positron emission tomography (PET). Intrinsic motion compensation methods exclusively work on the measured data, without any external motion measurements. Most of these methods separate image from motion estimation: They use deformable image registration/optical flow techniques in order to estimate the motion from individually reconstructed gates. Then, the image is estimated based on this motion information. With these methods, a main problem lies in the motion estimation step, which is based on the noisy gated frames. The more noise is present, the more inaccurate the image registration becomes. As we show both visually and quantitatively, joint reconstruction using a simple deformation field motion model can compete with state-of-the-art image registration methods which use robust multilevel B-spline motion models.
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Rodriguez-Alvarez, M. J., Sanchez, F., Soriano, A., & Iborra, A. (2010). Sparse Givens resolution of large system of linear equations: Applications to image reconstruction. Math. Comput. Model., 52(7-8), 1258–1264.
Abstract: In medicine, computed tomographic images are reconstructed from a large number of measurements of X-ray transmission through the patient (projection data). The mathematical model used to describe a computed tomography device is a large system of linear equations of the form AX = B. In this paper we propose the QR decomposition as a direct method to solve the linear system. QR decomposition can be a large computational procedure. However, once it has been calculated for a specific system, matrices Q and R are stored and used for any acquired projection on that system. Implementation of the QR decomposition in order to take more advantage of the sparsity of the system matrix is discussed.
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ANTARES Collaboration(Aguilar, J. A. et al), Bigongiari, C., Dornic, D., Emanuele, U., Gomez-Gonzalez, J. P., Hernandez-Rey, J. J., et al. (2011). A fast algorithm for muon track reconstruction and its application to the ANTARES neutrino telescope. Astropart Phys., 34(9), 652–662.
Abstract: An algorithm is presented, that provides a fast and robust reconstruction of neutrino induced upward-going muons and a discrimination of these events from downward-going atmospheric muon background in data collected by the ANTARES neutrino telescope. The algorithm consists of a hit merging and hit selection procedure followed by fitting steps for a track hypothesis and a point-like light source. It is particularly well-suited for real time applications such as online monitoring and fast triggering of optical follow-up observations for multi-messenger studies. The performance of the algorithm is evaluated with Monte Carlo simulations and various distributions are compared with that obtained in ANTARES data.
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