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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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Muñoz, E., Barrientos, L., Bernabeu, J., Borja-Lloret, M., Llosa, G., Ros, A., et al. (2020). A spectral reconstruction algorithm for two-plane Compton cameras. Phys. Med. Biol., 65(2), 025011–17pp.
Abstract: One factor limiting the current applicability extent of hadron therapy is the lack of a reliable method for real time treatment monitoring. The use of Compton imaging systems as monitors requires the correct reconstruction of the distribution of prompt gamma productions during patient irradiation. In order to extract the maximum information from all the measurable events, we implemented a spectral reconstruction method that assigns to all events a probability of being either partial or total energy depositions. The method, implemented in a list-mode maximum likelihood expectation maximization algorithm, generates a four dimensional image in the joint spatial-spectral domain, in which the voxels containing the emission positions and energies are obtained. The analytical model used for the system response function is also employed to derive an analytical expression for the sensitivity, which is calculated via Monte Carlo integration. The performance of the method is evaluated through reconstruction of various experimental and simulated sources with different spatial and energy distributions. The results show that the proposed method can recover the spectral and spatial information simultaneously, but only under the assumption of ideal measurements. The analysis of the Monte Carlo simulations has led to the identification of two important degradation sources: the mispositioning of the gamma interaction point and the missing energy recorded in the interaction. Both factors are related to the high energy transferred to the recoil electrons, which can travel far from the interaction point and even escape the detector. These effects prevent the direct application of the current method in more realistic scenarios. Nevertheless, experimental point-like sources have been accurately reconstructed and the spatial distributions and spectral emission of complex simulated phantoms can be identified.
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Roser, J., Muñoz, E., Barrientos, L., Barrio, J., Bernabeu, J., Borja-Lloret, M., et al. (2020). Image reconstruction for a multi-layer Compton telescope: an analytical model for three interaction events. Phys. Med. Biol., 65(14), 145005–17pp.
Abstract: Compton Cameras are electronically collimated photon imagers suitable for sub-MeV to few MeV gamma-ray detection. Such features are desirable to enablein vivorange verification in hadron therapy, through the detection of secondary Prompt Gammas. A major concern with this technique is the poor image quality obtained when the incoming gamma-ray energy is unknown. Compton Cameras with more than two detector planes (multi-layer Compton Cameras) have been proposed as a solution, given that these devices incorporate more signal sequences of interactions to the conventional two interaction events. In particular, three interaction events convey more spectral information as they allow inferring directly the incident gamma-ray energy. A three-layer Compton Telescope based on continuous Lanthanum (III) Bromide crystals coupled to Silicon Photomultipliers is being developed at the IRIS group of IFIC-Valencia. In a previous work we proposed a spectral reconstruction algorithm for two interaction events based on an analytical model for the formation of the signal. To fully exploit the capabilities of our prototype, we present here an extension of the model for three interaction events. Analytical expressions of the sensitivity and the System Matrix are derived and validated against Monte Carlo simulations. Implemented in a List Mode Maximum Likelihood Expectation Maximization algorithm, the proposed model allows us to obtain four-dimensional (energy and position) images by using exclusively three interaction events. We are able to recover the correct spectrum and spatial distribution of gamma-ray sources when ideal data are employed. However, the uncertainties associated to experimental measurements result in a degradation when real data from complex structures are employed. Incorrect estimation of the incident gamma-ray interaction positions, and missing deposited energy associated with escaping secondaries, have been identified as the causes of such degradation by means of a detailed Monte Carlo study. As expected, our current experimental resolution and efficiency to three interaction events prevents us from correctly recovering complex structures of radioactive sources. However, given the better spectral information conveyed by three interaction events, we expect an improvement of the image quality of conventional Compton imaging when including such events. In this regard, future development includes the incorporation of the model assessed in this work to the two interaction events model in order to allow using simultaneously two and three interaction events in the image reconstruction.
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Ros Garcia, A., Barrio, J., Etxebeste, A., Garcia-Lopez, J., Jimenez-Ramos, M. C., Lacasta, C., et al. (2020). MACACO II test-beam with high energy photons. Phys. Med. Biol., 65(24), 245027–12pp.
Abstract: The IRIS group at IFIC Valencia is developing a three-layer Compton camera for treatment monitoring in proton therapy. The system is composed of three detector planes, each made of a LaBr3<i monolithic crystal coupled to a SiPM array. Having obtained successful results with the first prototype (MACACO) that demonstrated the feasibility of the proposed technology, a second prototype (MACACO II) with improved performance has been developed, and is the subject of this work. The new system has an enhanced detector energy resolution which translates into a higher spatial resolution of the telescope. The image reconstruction method has also been improved with an accurate model of the sensitivity matrix. The device has been tested with high energy photons at the National Accelerator Centre (CNA, Seville). The tests involved a proton beam of 18 MeV impinging on a graphite target, to produce 4.4 MeV photons. Data were taken at different system positions of the telescope with the first detector at 65 and 160 mm from the target, and at different beam intensities. The measurements allowed successful reconstruction of the photon emission distribution at two target positions separated by 5 mm in different telescope configurations. This result was obtained both with data recorded in the first and second telescope planes (two interaction events) and, for the first time in beam experiments, with data recorded in the three planes (three interaction events).
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Roser, J., Barrientos, L., Bernabeu, J., Borja-Lloret, M., Muñoz, E., Ros, A., et al. (2022). Joint image reconstruction algorithm in Compton cameras. Phys. Med. Biol., 67(15), 155009–15pp.
Abstract: Objective. To demonstrate the benefits of using an joint image reconstruction algorithm based on the List Mode Maximum Likelihood Expectation Maximization that combines events measured in different channels of information of a Compton camera. Approach. Both simulations and experimental data are employed to show the algorithm performance. Main results. The obtained joint images present improved image quality and yield better estimates of displacements of high-energy gamma-ray emitting sources. The algorithm also provides images that are more stable than any individual channel against the noisy convergence that characterizes Maximum Likelihood based algorithms. Significance. The joint reconstruction algorithm can improve the quality and robustness of Compton camera images. It also has high versatility, as it can be easily adapted to any Compton camera geometry. It is thus expected to represent an important step in the optimization of Compton camera imaging.
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