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References on Geometric and Microlocal Analysis
4 July 2022
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Integral Geometry and Geometric Tomography
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Analytic microlocal analysis and tomography
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A. Homan and H. Zhou,
Injectivity and stability for a generic class of generalized Radon transforms,
The Journal of Geometric Analysis, 27 (2017), pp.1515–1529,
doi: 10.1007/s12220-016-9729-4.
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P. Stefanov,
Support theorems for the light ray transform on analytic Lorentzian manifolds,
Proceeding of the American Mathematical Society, 145 (2017), pp.1259-1274,
doi: 10.1090/proc/13117.
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E. T. Quinto,
Radon transforms satisfying the Bolker assumption,
pp. 263-270, Proceedings of conference "Seventy-five Years of Radon Transforms",
International Press Co. Ltd., Hong Kong, 1994.
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E. T. Quinto,
Support theorems for the spherical Radon transform on manifolds,
International Mathematics Research Notices, Volume 2006 (2006), article ID 67205,
doi: 10.1155/IMRN/2006/67205.
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Microlocal Artifacts
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L. Borg, J. Frikel, J. S. Jørgensen and E. T. Quinto,
Analyzing reconstruction artifacts from arbitrary incomplete X-ray CT data,
SIAM Journal on Imaging Sciences, 11 (2018), pp.2786--2814,
doi: 10.1137/18M1166833.
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J. K. Choi, H. S. Park, S. Wang, Y. Wang, and J. K. Seo,
Inverse problem in quantitative susceptibility mapping,
SIAM Jornal of Imaging Science, 7 (2014), pp.1669–1689,
doi: 10.1137/140957433.
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H. S. Park, J. K. Choi, and J. K. Seo,
Characterization of metal artifacts in X-ray computed tomography,
Communications on Pure and Applied Mathematics, 70 (2017), pp.2191–2217,
doi: 10.1002/cpa.21680.
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B. Palacios, G. Uhlmann and Y. Wang,
Reducing streaking artifacts in quantitative susceptibility mapping,
SIAM Journal on Imaging Science,
10 (2017), pp.1921--1934,
doi: 10.1137/16M1096475.
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B. Palacios, G. Uhlmann and Y. Wang,
Quantitative analysis of metal artifacts in X-ray tomography,
SIAM Journal on Mathematical Analysis,
50 (2018), pp.4914--4936,
doi: 10.1137/17M1160392.
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Y. Wang and Y. Zou,
Streak artifacts from non-convex metal objects in X-ray tomography,
Pure and Applied Analysis, 3 (2021), pp.295-318,
doi: 10.2140/paa.2021.3.295.
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E. T. Quinto,
An introduction to X-ray tomography and Radon transforms,
"The Radon Transform, Inverse Problems, and Tomography",
Proceedings of Symposia in Applied Mathematics, 63, pp.1--23,
American Mathematical Society, Providence, RI, 2006,
url.
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V. P. Krishnan and E. T. Quinto,
Microlocal analysis in tomography,
Handbook of mathematical methods in imaging. Vol. 1, 2, 3,
pp.847--902, Springer, New York, 2015,
pdf.
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Spiral CT
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A. Katsevich,
Theoretically exact filtered backprojection-type inversion algorithm for spiral CT,
SIAM Journal of Applied Mathematics, 62 (2002), pp.2012–2026,
doi: 10.1137/S0036139901387186.
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A. Katsevich,
Microlocal analysis of an FBP algorithm for truncated spiral cone beam data,
Journal of Fourier Analysis and Applications,
8 (2002), pp.407–425,
doi: 10.1007/s00041-002-0020-7.
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A. Katsevich,
An improved exact filtered backprojection algorithm for spiral computed tomography,
Advances in Applied Mathematics 32 (2004), pp.681–697,
doi: 10.1016/S0196-8858(03)00099-X.
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A. Katsevich,
Stability estimates for helical computer tomography,
Journal of Fourier Analysis and Applications, 11 (2005), pp.85–105,
doi: 10.1007/s00041-004-4013-6.
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A. Katsevich,
3PI algorithms for helical computer tomography,
Advances in Applied Mathematics 36 (2006), pp.213–250,
doi: 10.1016/j.aam.2006.01.001.
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M. Kapralov and A. Katsevich,
A one-PI algorithm for helical trajectories that violate the convexity condition,
Inverse Problems 22 (2006), pp.2123–2143,
doi: 10.1088/0266-5611/22/6/013.
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A. Katsevich and M. Kapralov,
Filtered backprojection inversion of the cone beam transform for a general class of curves,
SIAM Journal Applied Mathematics, 68 (2007), pp.334–353,
doi: 10.1137/060673187.
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M. Kapralov and A. Katsevich,
A study of 1PI algorithms for a general class of curves,
SIAM Journal Imaging Science, 1 (2008), pp.418–459,
doi: 10.1137/070711888.
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Limied Data
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D. Finch, I.-R. Lan and G. Uhlmann,
Microlocal analysis of the x-ray transform with sources on a curve,
Inside out: inverse problems and applications,
Mathematical Sciences Research Institute Publications,
47 (2003), pp.193--218,
pdf.
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J. Frikel and E. T. Quinto,
Limited Data Problems for the Generalized Radon Transform in Rn,
SIAM Journal on Mathematical Analysis, 48 (2016), pp.2301--2318,
doi: 10.1137/15M1045405.
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C. Mathison,
Sampling in thermoacoustic tomography,
Journal of Inverse and Ill-posed Problems, 28 (2020), pp.881–897,
doi: 10.1515/jiip-2020-0001.
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E. T. Quinto,
Singularities of the X-Ray Transform and Limited Data Tomography in R2 and R3,
SIAM Journal on Mathematical Analysis, 24 (1993), pp.1215--1225,
doi: 10.1137/0524069.
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Integral Geometry related with Rader, Sonar, Seismic Imaging and etc
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J. Christensen, F. Gonzalez and T. Kakehi,
Surjectivity of mean value operators on noncompact symmetric spaces,
Journal of Functional Analysis, 272(9) (2017), pp.3610–3646,
doi: 10.1016/j.jfa.2016.12.022.
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R. Felea, R. Gaburro, A. Greenleaf and C. Nolan,
Microlocal analysis of borehole seismic data,
Inverse Problems and Imaging, May 2022,
doi: 10.3934/ipi.2022026.
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Y. Okada and H. Yamane,
Generalized spherical mean value operators on Euclidean space,
arXiv:2003.10005.
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E. T. Quinto, A. Rieder and T. Schuster,
Local inversion of the sonar transform regularized by the approximate inverse,
Inverse Problems 27(3) (2011), 035006, 18 pp,
doi: 10.1088/0266-5611/27/3/035006.
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B. Rubin,
Higher-rank Radon transforms on constant curvature spaces,
arXiv:2110.04832.
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B. Rubin,
A note on the sonar transform and related Radon transforms,
arXiv:2206.05854
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Tensor Tomography
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S. Gouezel and T. Lefeuvre,
Classical and microlocal analysis of the X-ray transform on Anosov manifolds,
arXiv:1904.12290.
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C. Guillarmou, M. Lassas and L. Tzou,
X-Ray Transform in Asymptotically Conic Spaces,
arXiv:1910.09631.
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M. V. de Hoop, G. Uhlmann and J. Zhai,
Inverting the local geodesic ray transform of higher rank tensors,
Inverse Problems, 35 (2019), 115009,
doi: 10.1088/1361-6420/ab1ace.
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J. Ilmavirta,
On Radon transform on tori,
Journal of Fourier Analysis and Applications,
21, (2015), pp.370-382,
doi: 10.1007/s00041-014-9374-x.
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J. Ilmavirta and G. Uhlmann,
Tensor tomography in periodic slabs,
Journal of Functional Analysis,
275, (2018), pp.288-299,
doi: 10.1016/j.jfa.2018.04.004.
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J. Ilmavirta and K. M\"onkk\"onen,
Unique continuation of the normal operator of the X-ray transform and applications in geophysics,
Inverse Problems,
36, (2020), 045014,
doi: 10.1088/1361-6420/ab6e75.
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J. Ilmavirta and K. M\"onkk\"onen,
X-ray tomography of one-forms with partial data,
arXiv:2006.05790.
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J. Ilmavirta and F. Monard,
Integral geometry on manifolds with boundary and applications,
"The Radon Transform: The First 100 Years and Beyond" (Ronny Ramlau, Otmar Scherzer, eds.), de Gruyter, 2019,
arXiv:1806.06088.
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J. Rallo,
Fourier analysis of periodic Radon transforms,
Journal of Fourier Analysis and Applications,
26 (2020), Article Number 64,
doi: 10.1007/s00041-020-09775-1.
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V. P. Krishnan and R. K. Mishra,
Microlocal Analysis of a Restricted Ray Transform on Symmetric m-Tensor Fields in Rn,
SIAM Journal on Mathematical Analysis, 50 (2016), pp.6230--6254,
doi: 10.1137/18M1178530.
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F. Monard,
Functional relations, sharp mapping properties and regularization of the X-ray transform on disks of constant curvature,
arXiv:1910.13691.
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G. P. Paternain, M. Salo and G. Uhlmann,
Tensor tomography: Progress and challenges,
Chinese Annales of Mathematics, Series B,
35 (2014), pp.399--428,
doi: 10.1007/s11401-014-0834-z.
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G. P. Paternain, M. Salo and G. Uhlmann,
Invariant distributions, Beurling transforms and tensor tomography in higher dimensions,
Mathematische Annalen,
363 (2015), pp.305--362,
doi: 10.1007/s00208-015-1169-0.
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P. Stefanov, G. Uhlmann, A. Vasy and H. Zhou,
Travel time tomography,
Acta Mathematica Sinica, English Series,
35 (2019), pp.1085--1114,
doi: 10.1007/s10114-019-8338-0.
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P. Stefanov, G. Uhlmann and A. Vasy,
Local and global boundary rigidity and the geodesic X-ray transform in the normal gauge,
Annales of Mathematics,
194 (2021), pp.1--95,
doi: 10.4007/annals.2021.194.1.1.
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Inversion of X-ray transform
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L. Pestov and G. Uhlmann,
On characterization of the range and inversion formulas for the geodesic X-ray transform,
International Mathematics Research Notices, 2004, no. 80, pp.4331–4347,
doi: 10.1155/S1073792804142116.
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V. P. Krishnan,
On the inversion formulas of Pestov and Uhlmann for the geodesic ray transform,
Journal of Inverse and Ill-Posed Problems, 18 (2010), pp.401–408,
doi: 10.1515/jiip.2010.017.
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C. Guillarmou and F. Monard,
Reconstruction formulas for X-ray transforms in negative curvature,
Annles de L'Institut Fourier (Grenoble), 67 (2017), pp.1353–1392,
doi: 10.5802/aif.3112.
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S. Holman and G. Uhlmann,
On the microlocal analysis of the geodesic X-ray transform with conjugate points,
Journal of Differential Geometry, 108 (2018), pp.459-494,
doi: 10.4310/jdg/1519959623.
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Original Papers or Surveys on Basic Ideas
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A. M. Cormack,
Representation of a function by its line integrals, with some radiological applications,
Journal of Applied physics,
34 (1963), pp.2722,
doi: 10.1063/1.1729798.
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A. M. Cormack,
Representation of a function by its line integrals, with some radiological applications. II,
Journal of Applied physics,
35 (1964), pp.2908,
doi: 10.1063/1.1713127.
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P. C. Lauterbur,
Image formation by induced local interactions: Examples employing nuclear magnetic resonance,
Nature,
242 (1973), pp.190--191,
doi: 10.1038/242190a0.
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G. Beylkin,
The inversion problem and applications of the generalized radon transform,
Communications on Pure and Applied Mathematics, 37 (1984), pp.579--599,
doi: 10.1002/cpa.3160370503.
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M. Cheney, D. Isaacson and J. C. Newell,
Electrical impedance tomography,
SIAM Review,
41 (1999), pp.85--101,
doi: 10.1137/S0036144598333613.
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L. Borcea,
Electrical impedance tomography,
Inverse Problems,
18 (2002), pp.R99--R136,
doi: 10.1088/0266-5611/18/6/201.
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Some Papers on Integral Geometry and Geometric Tomography
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C. L. Epstein,
Introduction to magnetic resonance imaging for mathematicians,
Annales de l'institut Fourier (Grenoble), 54 (2004), pp.1697--1716,
doi: 10.5802/aif.2063.
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T. Kaasalainen,
M. Ekholm,
T. Siiskonen,
and
M. Kortesniemi,
Dental cone beam CT: An updated review,
European Journal of Medical Physics, 88 (2021), pp.193--217,
doi: 10.1016/j.ejmp.2021.07.007.
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P. Kuchment and L. Kunyansky,
Mathematics of thermoacoustic tomography,
European Journal of Applied Mathematics,
19 (2008), pp.191--224,
doi: 10.1017/S0956792508007353.
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P. Kuchment and L. Kunyansky,
Mathematics of Photoacoustic and Thermoacoustic Tomography,
Handbook of mathematical methods in imaging. Vol. 1, 2, 3,
pp.1117--1167, Springer, New York, 2015,
arXiv:0912.2022.
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R. G. Novikov,
An inversion formula for the attenuated X-ray transformation,
Arkiv för Matematik, 40 (2002), pp.145--167,
doi: 10.1007/BF02384507.
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V. P. Palamodov,
A uniform reconstruction formula in integral geometry,
Inverse Problems, 28 (2012), 065014,
doi: 10.1088/0266-5611/28/6/065014.
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B. Rubin,
Overdetermined Transforms in Integral Geometry,
Complex Analysis and Dynamical Systems VI: Part 1: PDE, Differential Geometry, Radon Transform, pp.291--313,
Contemporary Mathematics, 653, American Mathematical Society, 2015,
doi: 10.1090/conm/653.
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E. C. Tarabusi and M. A. Picardello,
Radon transform in hyperbolic spaces and their discrete counterparts,
Complex Analysis and Operator Theory, 15 (2021), article number 13,
doi: 10.1007/s11785-020-01055-6.
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G. Varoquaux and V. Cheplygina
Machine learning for medical imaging: methodological failures and recommendations for the future,
npj Digital Medicine, 5(48) (2022),
doi: 10.1038/s41746-022-00592-y.
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Some Books on Integral Geometry and Geometric Tomography
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C. L. Epstein,
"Introduction to the mathematics of medical imaging, Second edition",
SIAM, 2008,
doi: 10.1137/9780898717792.
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R. J. Gardner,
"Geometric Tomograhy" Second Edition,
Encyclopedia of Mathematics and its Applications,
58,
Cambridge University Press, 1995, 2006,
url.
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S. Helgason, "Integral Geometry and Radon Transforms",
Springer, 2011,
doi: 10.1007/978-1-4419-6055-9.
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P. Kuchment,
"The Radon Transform and Medical Imaging",
CBMS-NSF Regional Conference Series in Applied Mathematics,
SIAM, 2014,
doi: 10.1137/1.9781611973297.
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F. Natterer,
"The Mathematics of Computerized Tomography",
SIAM, 2001,
doi: 10.1137/1.9780898719284.
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F. Natterer and F. Wübbeling,
"Mathematical Methods in Image Reconstruction",
SIAM monographs on mathematical modeling and computation,
SIAM, 2001,
doi: 10.1137/1.9780898718324.
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G. Olafsson and E. T. Quinto eds,
"The Radon Transform, Inverse Problems, and Tomography",
Proceedings of Symposia in Applied Mathematics, 63,
American Mathematical Society, Providence, RI, 2006,
url.
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V. Palamodov, "Reconstructive Integral Geometry",
Springer, 2004,
url.
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V. Palamodov, "Reconstruction from Integral Data",
Chapman and Hall/CRC, 2016,
url.
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R. Ramlau and O. Scherzer eds,
"The Radon Transform - The First 100 Years and Beyond",
Radon Series on Computational and Applied Mathematics 22,
de Gruyter, 2019,
url.
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B. Rubin, "Introduction to Radon Transforms, With Elements of Fractional Calculus and Harmonic Analysis",
Encyclopedia of Mathematics and its Applications,
160,
Cambridge University Press, 2015,
url.
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O. Scherzer eds,
"Handbook of Mathematical methods in Imaging",
Springer, 2015,
url,
contents.
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V. A. Sharafutdinov,
"Integral Geometry of Tensor Fields",
Inverse and Ill-Posed Problems Series, 1,
De Gruyter, 1994,
doi: 10.1515/978311090009.
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Mathematics of Data Science / Computational Science
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Computer Program
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K. Kim,
3D Cone beam CT (CBCT) projection backprojection FDK, iterative reconstruction Matlab examples,
MATLAB Central File Exchange,
Retrieved March 8, 2021,
url.
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Calculus and Linear Algebra
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G. Strang,
"Linear Algebra and Learning from Data",
Wellesley Publishers, 2018,
support page.
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G. Strang,
MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018,
YouTube Playlist.
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C. Eckart and G. Young,
The approximation of one matrix by another of lower rank,
Psychometrika, 1 (1936), pp.211–218,
doi: 10.1007/BF02288367.
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M. Udell and A. Townsend,
Why are big data matrices approximately low rank?,
SIAM Journal on Mathematics of Data Science, 1, (2019), pp.144-160,
doi: 10.1137/18M1183480
.
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T. Y. Hou, Z. Li and Z. Zhang,
Analysis of asymptotic escape of strict saddle sets in manifold optimization,
SIAM Journal on Mathematics of Data Science, 2, (2020), pp.840-871,
doi: 10.1137/19M129437X.
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Sampling and Visualization
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H. Andrade-Loarca, G. Kutyniok, O. Öktem, and P. C. Petersen,
Extraction of digital wavefront sets using applied harmonic analysis and deep neural network,
SIAM Journal on Imaging Sciences, 12 (2019), pp.1936--1966,
doi: 10.1137/19M1237594.
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T. A. Bubba,
G. Kutyniok,
M. Lassas,
M. Marz,
W. Samek,
S. Siltanen
and
V. Srinivasan,
Learning the invisible: a hybrid deep learning-shearlet framework for limited angle computed tomography,
Inverse Problems, 35 (2019), 064002,
doi: 10.1088/1361-6420/ab10ca.
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C. L. Epstein,
How well does the finite Fourier transform approximate the Fourier transform? ,
Communications on Pure and Applied Mathematics, 58 (2005), pp.1421--1435,
doi: 10.1002/cpa.20064.
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H. Andrade-Loarca, G. Kutyniok and O. Öktem
Shearlets as feature extractor for semantic edge detection: the model-based and data-driven realm,
Proceedings of the Royal Society A: Mathematical, Phisical and Engineering Science,
25 November 2020,
doi: 10.1098/rspa.2019.0841.
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G. Kutyniok and D. Labate,
Resolution of the wavefront set using continuous shearlets,
Transactions of the American Mathematical Society,
361 (2009), pp.2719--2754,
doi: 10.1090/S0002-9947-08-04700-4.
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P. Grohs,
Continuous shearlet frames and resolution of the wavefront set,
Monatshefte für Mathematik, 164 (2011), pp.393--426,
doi: 10.1007/s00605-010-0264-2.
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B. Han, S. Paul and N. K. Shukla,
Microlocal analysis and characterization of Sobolev wavefront sets using shearlets,
Constructive Approximation, (2021),
doi: 10.1007/s00365-021-09529-2.
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P. Stefanov,
Semiclassical sampling and discretization of certain linear inverse problems,
SIAM Journal on Mathematical Analysis, 52 (2020), pp.5554–5597,
doi: 10.1137/19M123868X.
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P. Stefanov and S. Tindel,
Sampling linear inverse problems with noise,
arXiv:2011.13489.
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F. Monard and P. Stefanov,
Sampling the X-ray transform on simple surfaces,
arXiv:2110.05761.
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L. Bétermin, M. Faulhuber and S. Steinerberger
A variational principle for Gaussian lattice sums,
arXiv:2110.06008,
1W-MINDS, 10 March 2022.
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Machine Learning
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H. Andrade-Loarca,
G. Kutyniok,
O. Öktem
and
P. Petersen,
Deep microlocal reconstruction for limited-angle tomography,
arXiv:2108.05732.
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T. A. Bubba,
M. Galinier,
M. Lassas,
M. Prato,
L. Ratti
and
S. Siltanen,
Deep neural networks for inverse problems with pseudodifferential operators: an application to limited-angle tomography,
SIAM Journal of Imaging Science, 14 (2021), pp.470-505,
doi: 10.1137/20M1343075.
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J. Feliu-Fabà, Y. Fan and L. Ying,
Meta-learning pseudo-differential operators with deep neural networks,
Journal of Computational Physics,
408, (2020), 109309, 18 pages,
doi: 10.1016/j.jcp.2020.109309.
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C. Fefferman, S. Ivanov, Y. Kulylev, M. Lassas and H. Narayanan,
Reconstruction of a Riemannian manifolds I: The geometric Whitney problem,
Foundations of Computational Mathematics, 20, (2020), pp.1035-1133,
doi: 10.1007/s10208-019-09439-7.
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C. Fefferman, S. Ivanov, M. Lassas J. Lu and H. Narayanan,
Reconstruction of a Riemannian manifolds II: Inverse problems for Riemannian manifolds with partial distance data,
arXiv:2111.14528.
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C. Fefferman, S. Ivanov, M. Lassas and H. Narayanan,
Reconstruction of a Riemannian manifold from noisy intrinsic distances,
SIAM Journal on Mathematics of Data Science, 2, (2020), pp.770-808,
doi: 10.1137/19M126829X.
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Thomas Hofmann, Bernhard Schölkopf and Alexander J. Smola,
Kernel methods in machine learning,
Annals of Statistics, 36 (2008), pp.1171-1220,
doi: 10.1214/009053607000000677.
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Chang Min Hyun,
Seong Hyeon Baek,
Mingyu Lee,
Sung Min Lee
and
Jin Keun Seo,
Deep Learning-Based Solvability of Underdetermined Inverse Problems in Medical Imaging, Medical Image Analysis, 69 (2021), 101967,
doi: 10.1016/j.media.2021.101967.
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Hyoung Suk Park,
Jin Keun Seo,
Chang Min Hyun,
Sung Min Lee,
and
Kiwan Jeon,
A fidelity-embedded learning for metal artifact reduction in dental CBCT,
Medical Physics, 18 May 2022,
doi: 10.1002/mp.15720.
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Gunther Uhlmann and Yiran Wang,
Convolutional neural networks in phase space and inverse problems,
SIAM Journal on Applied Mathematics, 80(6) (2020), pp.2560–2585,
doi: 10.1137/19M1294484.
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Geometric Data Analysis
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Parvaneh Joharinad and Jürgen Jost,
Geometry of data
arXiv:2203.07208.
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Raul Rabadan and Andrew J. Blumberg,
"Topological Data Analysis for Genomics and Evolution",
Cambridge University Press, 2019,
doi: 10.1017/9781316671665.
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Computational Science
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L. A. Peletier and J. Gabrielsson,
Impact of mathematical pharmacology on practice and theory: four case studies,
Journal of Pharmacokinetics and Pharmacodynamics,
45 (2018), pp.3-21,
doi: 10.1007/s10928-017-9539-8.
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Geometric and Microlocal Analysis except for Tomography
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Boutet de Monvel's Calculus and Index Theory
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E. Schrohe,
A short introduction to Boutet de Monvel's calculus,
Operator Theory: Advances and Applications,
125, pp.85-116, Springer, 2001,
doi: 10.1007/978-3-0348-8253-8_3,
pdf.
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V. Nazaikinskii, B.-W. Schulze and B. Sternin,
"The Localization Problem in Index Theory of Elliptic Operators",
Pseudo=Differential Operators, 10, Birkhäuser, 2014,
doi: 10.1007/978-3-0348-0510-0.
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Semiclassical Analysis and Complex Geometry
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H. Hezari and Z. Lu and H. Xu,
Off-diagonal Asymptotic Properties of Bergman Kernels Associated to Analytic Kähler Potentials,
International Mathematics Research Notices,
Volume 2020, Issue 8 (2020), pp. 2241–2286,
doi: 10.1093/imrn/rny081.
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O. Rouby, J. Sjöstrand and S. V. Ngoc,
Analytic Bergman operators in the semiclassical limit,
arXiv:1808.00199.
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H. Hezari and H. Xu,
On a property of Bergman kernels when the Kähler potential is analytic,
arXiv:1912.11478.
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A. Deleporte, M. Hitrik and J. Sjöstrand,
A direct approach to the analytic Bergman projection,
arXiv:2004.14606.
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X. Ma and G. Marinescu,
Berezin Toeplitz quantization on Kähler manifolds,
Journal für die reine und angewandte Mathematik,
662 (2012), pp.1--56,
doi: 10.1515/CRELLE.2011.133.
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Analysis on Generalized Heisenberg Groups
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A. Kable,
On certain conformally invariant systems of differential equations,
New York Journal of Mathematics,
19 (2013), pp.189--251,
url.
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A. Kable,
On certain conformally invariant systems of differential equations II,
Tsukuba Journal of Mathematics,
39 (2015), pp.39--81,
doi:10.21099/tkbjm/1438951817.
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Analysis on the Poincaré Disk
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S. Zelditch,
Pseudodifferential analysis on hyperbolic surfaces,
J. Funct. Anal., 68 (1986), pp.72-105,
doi: 10.1016/0022-1236(86)90058-3.
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W. Bauer and L. A. Coburn,
Heat flow, weighted Bergman spaces, and real analytic Lipschitz approximation,
J. Reine Angew. Math., 703 (2015), pp.225-246,
doi: 10.1515/crelle-2015-0016.
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Some Topics in Applied Mathematics
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Applications of Fourier Analysis on the Euclidean Space
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Paolo Boggiatto, Carmen Fernández, Antonio Galbis, Alessandro Oliaro
"Wigner transform and quasicrystals",
arXiv:2106.09364.
-
T. Strohmer,
Pseudodifferential operators and Banach algebras in mobile communications,
Applied and Computational Harmonic Analysis,
20 (2006), pp.237--249,
doi: 10.1016/j.acha.2005.06.003.
In this paper, mobile communication is formulated in terms of pseudodifferential operators of order zero, and some finite dimensional approximation is proposed.
-
A. Koldobsky,
"Fourier Analysis in Convex Geometry",
SURV 116,
American Mathematical Society, 2005,
url.
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Shannon's Celebrating Papers:
-
C. E. Shannon,
A mathematical theory of communication,
the Bell System Technical Journal,
27(3) (1948), pp.379-423,
doi: 10.1002/j.1538-7305.1948.tb01338.x,
pdf.
-
C. E. Shannon,
A mathematical theory of communication,
the Bell System Technical Journal,
27(4) (1948), pp.623-656,
doi: 10.1002/j.1538-7305.1948.tb00917.x.
-
C. E. Shannon,
Communication in the presence of noise,
Proceedings of the Institute of Radio Engineers,
37(1) (1949), pp.10-21,
doi: 10.1109/JRPROC.1949.232969,
pdf.
-
Compressive Sampling
-
E. J. Candes, J. K. Romberg and T. Tao,
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,
IEEE Transactions on Information Theory,
52 (2006), pp.489--509,
doi: 10.1109/TIT.2005.862083,
pdf.
-
E. J. Candes, J. K. Romberg and T. Tao,
Stable signal recovery from incomplete and inaccurate measurements,
Communications on Pure and Applied Mathematics,
59 (2006), pp.1207--1233,
doi: 10.1002/cpa.20124,
pdf.
-
E. J. Candes and T. Tao,
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?,
IEEE Transactions on Information Theory,
52 (2006), pp.5406--5425,
doi: 10.1109/TIT.2006.885507,
pdf.