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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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Freitas, E. D. C., Monteiro, C. M. B., Ball, M., Gomez-Cadenas, J. J., Lopes, J. A. M., Lux, T., et al. (2010). Secondary scintillation yield in high-pressure xenon gas for neutrinoless double beta decay (0 nu beta beta) search. Phys. Lett. B, 684(4-5), 205–210.
Abstract: The search for neutrinoless double beta decay (0 nu beta beta) is an important topic in contemporary physics with many active experiments. New projects are planning to use high-pressure xenon gas as both source and detection medium. The secondary scintillation processes available in noble gases permit large amplification with negligible statistical fluctuations, offering the prospect of energy resolution approaching the Fano factor limit. This Letter reports results for xenon secondary scintillation yield, at room temperature, as a function of electric field in the gas scintillation gap for pressures ranging from 2 to 10 bar. A Large Area Avalanche Photodiode (LAAPD) collected the VUV secondary scintillation produced in the gas. X-rays directly absorbed in the LAAPD are used as a reference for determining the number of charge carriers produced by the scintillation pulse and, hence, the number of photons impinging the LAAPD. The number of photons produced per drifting electron and per kilovolt, the so-called scintillation amplification parameter, displays a small increase with pressure, ranging from 141 +/- 6 at 2 bar to 170 +/- 10 at 8 bar. In our setup, this Parameter does not increase above 8 bar due to nonnegligible electron attachment. The results are in good agreement with those presented in the literature in the 1 to 3 bar range. The increase of the scintillation amplification parameter with pressure for high gas densities has been also observed in former work at cryogenic temperatures.
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Rodriguez-Alvarez, M. J., Sanchez, F., Soriano, A., Iborra, A., & Mora, C. (2011). Exploiting symmetries for weight matrix design in CT imaging. Math. Comput. Model., 54(7-8), 1655–1664.
Abstract: In this paper we propose several methods of constructing the system matrix (SM) of a Computed Tomography (CT) scanner with two objectives: (1) to construct SMs in the shortest possible time and store them in an ordinary PC without losing quality, (2) to analyze the possible applications of the proposed method to 3D, taking into account SMs' sizes, computing time and reconstructed image quality. In order to build the SM, we propose two new field of view (FOV) pixellation schemes, based on a polar coordinate system (polar grid) by taking advantage of the polar rotation symmetries of CT devices. Comparisons between the SMs proposed are performed using two phantom and a real CT-simulator images. Global error, contrast, noise and homogeneity of the reconstructed images are discussed.
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Nieves, J., Sanchez, F., Ruiz Simo, I., & Vicente Vacas, M. J. (2012). Neutrino energy reconstruction and the shape of the charged current quasielastic-like total cross section. Phys. Rev. D, 85(11), 113008–9pp.
Abstract: We show that because of the multinucleon mechanism effects, the algorithm used to reconstruct the neutrino energy is not adequate when dealing with quasielastic-like events, and a distortion of the total flux-unfolded cross-section shape is produced. This amounts to a redistribution of strength from high to low energies, which gives rise to a sizable excess (deficit) of low (high) energy neutrinos. This distortion of the shape leads to a good description of the MiniBooNE unfolded charged current quasielastic-like cross sections published by A. A. Aguilar-Arevalo et al. [(MiniBooNE Collaboration), Phys. Rev. D 81, 092005 (2010)]. However, these changes in the shape are artifacts of the unfolding process that ignores multinucleon mechanisms.
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Carles, M., Lerche, C. W., Sanchez, F., Mora, F., & Benlloch, J. M. (2011). Position correction with depth of interaction information for a small animal PET system. Nucl. Instrum. Methods Phys. Res. A, 648, S176–S180.
Abstract: In this work we study the effects on the spatial resolution when depth of interaction (001) information is included in the parameterization of the line of response (LOR) for a small animal positron emission tomography (PET) system. One of the most important degrading factors for PET is the parallax error introduced in systems that do not provide DOI information of the recorded gamma-rays. Our group has designed a simple and inexpensive method for DOI determination in continuous scintillation crystals. This method is based, on one hand, in the correlation between the scintillation light distribution width in monolithic crystals and the DOI, and, on the other hand, on a small modification of the widely applied charge dividing circuits (CDR). In this work we present a new system calibration that includes the DOI information, and also the development of the correction equations that relates the LOR without and with DOI information. We report the results obtained for different measurements along the transaxial field of view (FOV) and the image quality enhancement achieved specially at the edge of the FOV.
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