References on Geometric Tomography and Related Topics

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References on Geometric and Microlocal Analysis

4 July 2022

Integral Geometry and Geometric Tomography

Analytic microlocal analysis and tomography
- 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.
- 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.
- 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.
- 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.
Microlocal Artifacts
- 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. 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
Spiral CT
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
Limied Data
- 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.
- 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.
- C. Mathison, Sampling in thermoacoustic tomography, Journal of Inverse and Ill-posed Problems, 28 (2020), pp.881–897, doi: 10.1515/jiip-2020-0001.
- 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.
Integral Geometry related with Rader, Sonar, Seismic Imaging and etc
- 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.
- 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.
- Y. Okada and H. Yamane, Generalized spherical mean value operators on Euclidean space, arXiv:2003.10005.
- 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.
- B. Rubin, Higher-rank Radon transforms on constant curvature spaces, arXiv:2110.04832.
- B. Rubin, A note on the sonar transform and related Radon transforms, arXiv:2206.05854
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, Journal of Fourier Analysis and Applications, 26 (2020), Article Number 64, doi: 10.1007/s00041-020-09775-1.
- 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.
- 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.
Inversion of X-ray transform
- 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.
- 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.
- 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.
- 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.
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 Papers on Integral Geometry and Geometric Tomography
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
Some Books on Integral Geometry and Geometric Tomography
- C. L. Epstein, "Introduction to the mathematics of medical imaging, Second edition", SIAM, 2008, doi: 10.1137/9780898717792.
- 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, "The Mathematics of Computerized Tomography", SIAM, 2001, doi: 10.1137/1.9780898719284.
- 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.

Mathematics of Data Science / Computational Science

Computer Program
- K. Kim, 3D Cone beam CT (CBCT) projection backprojection FDK, iterative reconstruction Matlab examples, MATLAB Central File Exchange, Retrieved March 8, 2021, url.
Calculus and Linear Algebra
- 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.
- 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 .
- 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.
Sampling and Visualization
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- P. Stefanov and S. Tindel, Sampling linear inverse problems with noise, arXiv:2011.13489.
- F. Monard and P. Stefanov, Sampling the X-ray transform on simple surfaces, arXiv:2110.05761.
- L. Bétermin, M. Faulhuber and S. Steinerberger A variational principle for Gaussian lattice sums, arXiv:2110.06008, 1W-MINDS, 10 March 2022.
Machine Learning
- H. Andrade-Loarca, G. Kutyniok, O. Öktem and P. Petersen, Deep microlocal reconstruction for limited-angle tomography, arXiv:2108.05732.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
Geometric Data Analysis
- Parvaneh Joharinad and Jürgen Jost, Geometry of data arXiv:2203.07208.
- Raul Rabadan and Andrew J. Blumberg, "Topological Data Analysis for Genomics and Evolution", Cambridge University Press, 2019, doi: 10.1017/9781316671665.
Computational Science
- 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.

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
- Applications of Fourier Analysis on the Euclidean Space
  - 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.
- 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.