References on Geometric and Microlocal Analysis

• Integral Geometry and Geometric Tomography
  
  
  • Original Papers or Surveys on Basic Ideas
    • 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.
    • 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.
    • P. C. Lauterbur, Image formation by induced local interactions: Examples employing nuclear magnetic resonance, Nature, 242 (1973), pp.190--191, doi: 10.1038/242190a0.
    • 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.
    • M. Cheney, D. Isaacson and J. C. Newell, Electrical impedance tomography, SIAM Review, 41 (1999), pp.85--101, doi: 10.1137/S0036144598333613.
    • L. Borcea, Electrical impedance tomography, Inverse Problems, 18 (2002), pp.R99--R136, doi: 10.1088/0266-5611/18/6/201.
    
    
  • Some Books on Integral Geometry and Geometric Tomography
    • R. J. Gardner, "Geometric Tomograhy" Second Edition, Encyclopedia of Mathematics and its Applications, 58, Cambridge University Press, 1995, 2006, url.
    • S. Helgason, "Integral Geometry and Radon Transforms", Springer, 2011, doi: 10.1007/978-1-4419-6055-9.
    • P. Kuchment, "The Radon Transform and Medical Imaging", CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, 2014, doi: 10.1137/1.9781611973297.
    • F. Natterer and F. Wübbeling, "Mathematical Methods in Image Reconstruction", SIAM monographs on mathematical modeling and computation, SIAM, 2001, doi: 10.1137/1.9780898718324.
    • 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.
    • V. Palamodov, "Reconstructive Integral Geometry", Springer, 2004, url.
    • V. Palamodov, "Reconstruction from Integral Data", Chapman and Hall/CRC, 2016, url.
    • 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.
    • 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.
    • O. Scherzer eds, "Handbook of Mathematical methods in Imaging", Springer, 2015, url, contents.
    • V. A. Sharafutdinov, "Integral Geometry of Tensor Fields", Inverse and Ill-Posed Problems Series, 1, De Gruyter, 1994, doi: 10.1515/978311090009.
    
    
  • Some Papers on Integral Geometry and Geometric Tomography
    • R. G. Novikov, An inversion formula for the attenuated X-ray transformation, Arkiv för Matematik, 40 (2002), pp.145--167, doi: 10.1007/BF02384507.
    • V. P. Palamodov, A uniform reconstruction formula in integral geometry, Inverse Problems, 28 (2012), 065014, doi: 10.1088/0266-5611/28/6/065014.
    • 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.
    
    
  • Microlocal Artifacts
    • 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.
    • 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.
    • 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.
    • 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.
    • Y. Wang and Y. Zhou, Streak artifacts from non-convex metal objects in X-ray tomography, arXiv:2002.12210.
    
    
  • Limied Data and Sampling Problems
    • 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.
    • 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.
    • P. Stefanov, Semiclassical sampling and discretization of certain linear inverse problems, arXiv:1811.01240.
    • 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.
    
    
  • Tensor Tomography
    • S. Gouezel and T. Lefeuvre, Classical and microlocal analysis of the X-ray transform on Anosov manifolds, arXiv:1904.12290.
    • C. Guillarmou, M. Lassas and L. Tzou, X-Ray Transform in Asymptotically Conic Spaces, arXiv:1910.09631.
    • 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.
    • 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.
    • 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.
    • 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.
    • J. Ilmavirta and K. M\"onkk\"onen, X-ray tomography of one-forms with partial data, arXiv:2006.05790.
    • 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.
    • J. Rallo, Fourier analysis of periodic Radon transforms, arXiv:1909.00495.
    • 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.
    • F. Monard, Functional relations, sharp mapping properties and regularization of the X-ray transform on disks of constant curvature, arXiv:1910.13691.
    • 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.
    • 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.
    • 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.
    
    
  • Various Tomography
    • P. Kuchment and L. Kunyansky, Mathematics of thermoacoustic tomography, European Journal of Applied Mathematics, 19 (2008), pp.191--224, doi: 10.1017/S0956792508007353.
    • 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.
    
    
  • Linear Algebra and Data Science
    • G. Strang, "Linear Algebra and Learning from Data", Wellesley Publishers, 2018, support page.
    • G. Strang, MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018, YouTube Playlist.
    • 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.
    • 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.
    • 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.
    • 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.
    • Jin Keun Seo, Talk in One World IMAGINE seminars, April 29 2020, YouTube Playlist.
    • Jin Keun Seo et al, Deep Learning-Based Solvability of Underdetermined Inverse Problems in Medical Imaging, arXiv:2001.01432.
    
    
  • Geometry of Convex Bodies
    • A. Koldobsky, "Fourier Analysis in Convex Geometry", SURV 116, American Mathematical Society, 2005, url.


• Geometric and Microlocal Analysis except for Tomography
  
  
  • Boutet de Monvel's Calculus and Index Theory
    • 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.
    • 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.
  
  
  • Semiclassical Analysis and Complex Geometry
    • 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.
    • O. Rouby, J. Sjöstrand and S. V. Ngoc, Analytic Bergman operators in the semiclassical limit, arXiv:1808.00199.
    • H. Hezari and H. Xu, On a property of Bergman kernels when the Kähler potential is analytic, arXiv:1912.11478.
    • A. Deleporte, M. Hitrik and J. Sjöstrand, A direct approach to the analytic Bergman projection, arXiv:2004.14606.
    • 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.
  
  
  • Analysis on Generalized Heisenberg Groups
    • A. Kable, On certain conformally invariant systems of differential equations, New York Journal of Mathematics, 19 (2013), pp.189--251, url.
    • 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.
  
  
  • Analysis on the Poincaré Disk
    • S. Zelditch, Pseudodifferential analysis on hyperbolic surfaces, J. Funct. Anal., 68 (1986), pp.72-105, doi: 10.1016/0022-1236(86)90058-3.
    • 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.


• Some Topics in Applied Mathematics
  
  
  • 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.
  
  
  • Mobile Communication
    • 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.