An algorithm for real-time tomography of gas concentrations,using prior information about spatial derivatives |
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| Institution: | 1. Department of Physics, Kuvempu University, Shankaraghatta, Shimoga 577 451, India;2. Inspire Institute Inc., Alexandria, VA, 22303, USA;3. Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India;4. Institute of Mathematical Sciences, C.I.T. Campus, Tharamani, Chennai, 600113, India;5. Department of Physics, Bangalore University, Bangalore 560 056, India;1. Department of Physics, Zhejiang University, Hangzhou 310027, PR China;2. Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Břehová 7, 115 19 Praha 1, Czech Republic;3. Uşak University, Faculty of Art and Sciences, Department of Statistics, Uşak, Turkey;1. Dipartimento di Matematica e Informatica, Università di Cagliari, viale Merello 92, 09123 Cagliari, Italy;2. INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato, Italy;3. Rudjer Bošković Institute, Bijenička cesta 54, 10002 Zagreb, Croatia;1. Linné Flow Centre, KTH Mekanik, Osquars Backe 18, SE-10044 Stockholm, Sweden;2. Nordita, Roslagstullsbacken 23, 106 91 Stockholm, Sweden;3. Chemistry, Materials and Chemical Engineering Department ‘Giulio Natta’, Politecnico di Milano, Milano, Italy |
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| Abstract: | We present a new computed tomography method, the low third derivative (LTD) method, that is particularly suited for reconstructing the spatial distribution of gas concentrations from path-integral data for a small number of optical paths. The method finds a spatial distribution of gas concentrations that (1) has path integrals that agree with measured path integrals, and (2) has a low third spatial derivative in each direction, at every point. The trade-off between (1) and (2) is controlled by an adjustable parameter, which can be set based on analysis of the path-integral data. The method produces a set of linear equations, which can be solved with a single matrix multiplication if the constraint that all concentrations must be positive is ignored; the method is therefore extremely rapid. Analysis of experimental data from thousands of concentration distributions shows that the method works nearly as well as smooth basis function minimization (the best method previously available), yet is about 100 times faster. |
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