Citation: William R. B. Lionheart. Histogram tomography[J]. Mathematics in Engineering, 2020, 2(1): 55-74. doi: 10.3934/mine.2020004
[1] | Natterer F (2001) The Mathematics of Computerized Tomography, Philadelphia: Society for Industrial and Applied Mathematics. |
[2] | Sales M, Strobl M, Shinohara T, et al. (2018) Three dimensional polarimetric neutron tomography of magnetic fields. Sci Rep 8: 2214. |
[3] | Desai NM, Lionheart WRB, Sales M, et al. (2019) Polarimetric neutron tomography of magnetic fields: Uniqueness of solution and reconstruction. Inverse Probl DOI: https://doi.org/10.1088/1361-6420/ab44e0. |
[4] | An X, Kraetschmer T, Takami K, et al. (2011) Validation of temperature imaging by H_{2}O absorption spectroscopy using hyperspectral tomography in controlled experiments. Appl Opt 50: A29-A37. |
[5] | Ma L, Li X, Sanders S, et al. (2013) 50-kHz-rate 2D imaging of temperature and H_{2}O concentration at the exhaust plane of a J85 engine using hyperspectral tomography. Opt Express 21: 1152-1162. doi: 10.1364/OE.21.001152 |
[6] | Andersson F (2005) The Doppler moment transform in Doppler tomography. Inverse Probl 21: 1249. |
[7] | Sharafutdinov VA (1994) Integral Geometry of Tensor Fields, Walter de Gruyter. |
[8] | Lionheart WRB, Withers PJ (2015) Diffraction tomography of strain. Inverse Probl 31: 045005. |
[9] | Boman J, Sharafutdinov V (2018) Stability estimates in tensor tomography. Inverse Probl Imaging 12: 1245-1262. doi: 10.3934/ipi.2018052 |
[10] | Bogachev VI (2007) Measure Theory, Berlin: Springer Science & Business Media. |
[11] | Akhiezer NI (1965) The Classical Moment Problem: And Some Related Questions in Analysis, Edinburgh: Oliver & Boyd. |
[12] | Gardner RJ, McMullen P (1980) On Hammer's X-Ray Problem. J Lond Math Soc 2: 171-175. |
[13] | Gardner RJ, Gritzmann P (1997) Discrete tomography: Determination of finite sets by X-rays. T Am Math Soc 349: 2271-2295. |
[14] | Gardner RJ, Kiderlen M (2007) A solution to Hammer's X-ray reconstruction problem. Adv Math 214: 323-343. doi: 10.1016/j.aim.2007.02.005 |
[15] | Gardner RJ (2006) Geometric Tomography, 2 Eds., Cambridge University Press. |
[16] | Faridani A, Ritman EL, Smith KT (1992) Local tomography. SIAM J Appl Math 52: 459-484. |
[17] | Herman GT, Kuba A (2012) Discrete Tomography: Foundations, Algorithms, and Applications, Springer Science & Business Media. |
[18] | Batenburg KJ, Sijbers J (2011) DART: A practical reconstruction algorithm for discrete tomography. IEEE T Image Process 20: 2542-2553. |
[19] | Bentz C, Costa MC, De Werra D, et al. (2008) On a graph coloring problem arising from discrete tomography. Networks 51: 256-267. |
[20] | Schuster T (2008) 20 years of imaging in vector field tomography: A review, In: Math. Methods in Biomedical Imaging and Intensity-Modulated Radiation Therapy (IMRT). Ser. Publications of the Scuola Normale Superiore, 7: 389-424. |
[21] | Sparr G, Strahlen K, Lindstrom K, et al. (1995) Doppler tomography for vector fields. Inverse Probl 11: 1051. |
[22] | Kravtsov YA (1968) "Quasi-isotropic" approximation of geometrical optics. Dokl Akad Nauk SSSR 183: 74-76. |
[23] | Aben H, Errapart A, Ainola L, et al. (2005) Photoelastic tomography for residual stress measurement in glass. Opt Eng 44: 093601. |
[24] | Tomlinson RA, Yang H, Szotten D, et al. (2006) The design and commissioning of a novel tomographic polariscope, In: SEM Annual Conf. and Exposition on Experimental and Applied Mechanics, 1141-1147. |
[25] | Lionheart W, Sharafutdinov V (2009) Reconstruction algorithm for the linearized polarization tomography problem with incomplete data. Contemp Math 14: 137. |
[26] | Johnstone D, van Helvoort A, Midgley P (2017) Nanoscale strain tomography by scanning precession electron diffraction. Microsc Microanal 23: 1710-1711. |
[27] | Woracek R, Santisteban J, Fedrigo A, et al. (2018) Diffraction in neutron imaging-A review, In: Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 878: 141-158. |
[28] | Georgievskii D (2016) Generalized compatibility equations for tensors of high ranks in multidimensional continuum mechanics. Russ J Math Phys 23: 475-483. |
[29] | Sklar M (1959) Fonctions de répartition à n dimensions et leurs marges. Publ Inst Statist Univ Paris 8: 229-231. |
[30] | Nelsen RB (2007) An Introduction to Copulas, Springer Science & Business Media. |
[31] | Santisteban JR, Edwards L, Fitzpatrick ME, et al. (2002) Strain imaging by Bragg edge neutron transmission, In: Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 481: 765-768. |
[32] | Abbey B, Zhang SY, Vorster WJJ, et al. (2009) Feasibility study of neutron strain tomography. Procedia Eng 1: 185-188. |
[33] | Knops RJ, Payne LE (1971) Modern Uniqueness Theorems in Three-Dimensional Elastostatics, In: Uniqueness Theorems in Linear Elasticity, Berlin: Springer, 32-60. |
[34] | Gregg AWT, Hendriks JN, Wensrich CM, et al. (2017) Tomographic reconstruction of residual strain in axisymmetric systems from Bragg-edge neutron imaging. Mech Res Commun 85: 96-103. |
[35] | Wensrich CM, Hendriks JN, Gregg A, et al. (2016) Bragg-edge neutron transmission strain tomography for in situ loadings, In: Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 383: 52-58. |
[36] | Hendriks JN, Gregg AWT, Wensrich CM, et al. (2017) Bragg-edge elastic strain tomography for in situ systems from energy-resolved neutron transmission imaging. Phys Rev Mater 1: 053802. |
[37] | Desai NM, Lionheart WRB (2016) An explicit reconstruction algorithm for the transverse ray transform of a second rank tensor field from three axis data. Inverse Probl 32: 115009. |