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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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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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Soriano, A., Gonzalez, A., Orero, A., Moliner, L., Carles, M., Sanchez, F., et al. (2011). Attenuation correction without transmission scan for the MAMMI breast PET. Nucl. Instrum. Methods Phys. Res. A, 648, S75–S78.
Abstract: Whole-body Positron Emission Tomography (PET) scanners are required in order to span large Fields of View (FOV). Therefore, reaching the sensitivity and spatial resolution required for early stage breast tumor detection is not straightforward. MAMMI is a dedicated breast PET scanner with a ring geometry designed to provide PET images with a spatial resolution as high as 1.5 mm, being able to detect small breast tumors ( < 1 cm). The patient lays down in prone position during the scan, thus making possible to image the whole breast, up to regions close to the base of the pectoral without the requirement of breast compression. Attenuation correction (AC) for PET data improves the image quality and the quantitative accuracy of radioactivity distribution determination. In dedicated, high resolution breast cancer scanners, this correction would enhance the proper diagnosis in early disease stages. In whole-body PET scanners, AC is usually taken into account with the use of transmission scans, either by external radioactive rod sources or by Computed Tomography (CT). This considerably increases the radiation dose administered to the patient and time needed for the exploration. In this work we propose a method for breast shape identification by means of PET image segmentation. The breast shape identification will be used for the determination of the AC. For the case of a specific breast PET scanner the procedure we propose should provide AC similar to that obtained by transmission scans as we take advantage of the breast anatomical simplicity. Experimental validation of the proposed approach with a dedicated breast PET prototype is also presented. The main advantage of this method is an important dose reduction since the transmission scan is not required.
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