Most of this research was partially supported by the U.S. National Science Foundation, The Humboldt Stiftung, Wenner Gren Stiftelserna, U.S. Air Force, Otto Monsteds Fond, Simons Foundation. Tufts University and other organizations also provided support.

“Any opinions, findings, and conclusions or recommendations expressed in this website are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (or other funding agencies).”

For detailed information, please see my resume (pdf).

Edited Books

3.  Integral geometry and tomography Co-editor, Eric Grinberg, Contemporary Mathematics, Vol. 113, Amer. Math. Soc, Providence , RI , 1990.
4. Tomography, Impedance Imaging, and Integral Geometry, Lecture Notes in Applied Math., Vol. 30, Chief editor.
5. Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis, Contemporary Math., Vol. 251, Co-editors Marvin Knopp (Number Theory), Shif Berhanu and Gerardo Mendoza (PDE), and Eric Grinberg
6. Radon Transforms and Tomography, Contemporary Math., Vol. 278, Chief editor. Co-editors Leon Ehrenpreis, Adel Faridani, Fulton Gonzalez, and Eric Grinberg
7. The Radon Transform, Inverse Problems, and Tomography, Co-editor Gestur Olafsson, (Proceedings of the 2005 AMS Short Course, Atlanta, GA) Proceedings of Symposia in Applied Math. Vol. 63, 2006.
8. Integral Geometry and Tomography, Co-editor Andrew Markoe, Contemporary Math, vol. 405, 2006.
9. Radon Transforms, Geometry, and Wavelets, Co-editors: Gestur Olafsson (head), Eric Grinberg, David Larson, Palle Jorgensen, Peter Massopust, Boris Rubin, Contemporary Mathematics, Vol 464, 2008.
10. Geometric Analysis and Integral Geometry, Coeditors Jens Christensen and Fulton Gonzalez, Contemporary Mathematics, Vol. 598, 2013.
11. The Proceedings of International Conference on Sensing and Imaging, Chengdu University of Information Technology, Chengdu, Sichuan, China, on June 5-7, 2017, coeditors, Ming Jiang (head editor), Nathan Ida, Alfred Louis. Lecture Notes in Electrical Engineering springer Verlag, 2018.
12. “Recent Developments in Sensing and Imaging,” Special issue of Sensing and Imaging (head editor), Coeditors, Mark Anastasio, Tingting Jiang, Yu Shang, 2018.
13. The Proceedings of International Conference on Sensing and Imaging 2018, Guangxi University, China, October 14-18, head editor, coeditors: Ming Jiang, Nathan Ida, Alfred Louis. Lecture Notes in Electrical Engineering, Vol. 606 Springer Verlag, 2020.
14. Generalized Radon Transforms and Applications in Tomography, special issue of Inverse Problems, coeditor Gaik Ambartsoumian, 2019.
15. Modern Challenges in Imaging, special issue of Inverse Problems, coeditors Bernadette Hahn, Gael Rigaud, 2020 (in progress).

Articles

17.The dependence of the generalized Radon transform on defining measures, Trans. Amer Math. Soc., 257(1980), 331-346. (pdf)
18. A Radon transform on spheres through the origin in R^n and applications to the Darboux equation, joint with Allan Cormack, Trans. Amer. Math. Soc..  260(1980), 575-581. (pdf).
21. The invertibility of rotation invariant Radon transforms, J. Math.  Anal.  Appl.  91(1983), 510-522. Erratum, J. Math.  Anal.  Appl.  94(1983), 602-603 (pdf).
22. Singular value decompositions and inversion methods for the exterior Radon transform and a spherical transform, J. Math.  Anal.  Appl.  95(1983), 437-448. (pdf).
27. Support theorems for real analytic Radon transforms, coauthor: J. Boman, Duke Math. J. 55(1987), 943-948. (pdf)
28. Tomographic reconstructions from incomplete data–numerical inversion of the exterior Radon transform, Inverse Problems, 4(1988), 867-876. (pdf)
31. The mathematics and physics of radiation dose planning, coauthor Allan Cormack, Contemporary Mathematics 113(1990), 41-55. (pdf)
34. Support theorems for real analytic Radon transforms on line complexes, coauthor: J. Boman, Trans. Amer. Math. Soc. 335(1993), 877-890. (pdf)
35. Real analytic Radon transforms on Rank one symmetric spaces, Proc. Math. Soc. 117(1993), 179-186. (pdf)
36. Pompeiu transforms on geodesic spheres in real analytic manifolds, Israel J. Math., 84(1993), 353-363. (pdf)
37. Singularities of the X-ray transform and limited data tomography in R^2 and R^3, SIAM J. Math. Anal., 24(1993), 1215-1225. (pdf)
38. Support theorems for Radon transforms on higher rank symmetric spaces, coauthor Fulton Gonzalez, Proc. Amer. Math. Soc, 122(1994), 1045-1052. (pdf)
39. 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. (pdf)
40. Radon transforms on curves in the plane, Lecture Notes in Applied Mathematics, 30(1994), 231-244. (pdf)
41. Injectivity sets for a Radon transform and complete systems of radial functions, an announcement, coauthor Mark Agranovsky , International Mathematical Research Notes (Duke J.), 11(1994), 467-473.
42. Injectivity sets for the Radon transform over circles and complete systems of radial functions, coauthor Mark Agranovsky, Journal of Functional Analysis, 139 (1996), 383-414. (pdf).
43.Injectivity of the spherical mean operator and related problems, coauthor Mark Agranovsky, in Complex Analysis, Harmonic Analysis and Applications, editors R. Deville, J. Esterle, V. Petkov, A. Sebbar, A. Yger, Addison Wesley, London (article pdf).
44.Morera Theorems via Microlocal Analysis,  coauthor  Josip  Globevnik,  J.  Geom.   Analysis  6(1996), 20-30 (article pdf)
45. Exterior and Limited Angle Tomography in Non-destructive Evaluation, Inverse Problems, 14 (1998), 339-353. (pdf)
46. A Morera Theorem for spheres through a point in C^n, coauthor Eric Grinberg, R.P. Gilbert, et al., eds. “Recent Developments in Complex Analysis and Computer Algebra,” (1999), 267-275. Kluwer. (pdf)
47. On the non-uniqueness of optimal radiation treatment plans, with Christoph Boergers, Inverse Problems, 15(1999), 1115-1138. (pdf)
48. Two-radius Support Theorems for Spherical Radon transforms on Manifolds, with Yiying Zhou, Contemporary Mathematics, 251(2000), 501-508. (pdf)
49. Local Tomographic Methods in SONAR, with Alfred Louis, in “Surveys on Solution Methods for Inverse Problems” Springer Verlag, 2000. (pdf)
50. Morera theorems for complex manifolds, coauthor Eric Grinberg, Journal of Functional Analysis, 178(2000), 1-22. (pdf)
51. Radon Transforms, Differential Equations, and Microlocal Analysis, Contemporary Mathematics, 278(2001), 57-68. (pdf)
52. Geometry of Stationary Sets for the Wave Equation in R^n, The Case of Finitely Supported Initial Data, with Mark Agranovsky , Duke Math. J. 107(2001), 57-84. (pdf)
53. Geometry of Stationary Sets for the Wave Equation in R^n, The Case of Finitely Supported Initial Data, an Announcement, with Mark Agranovsky , Southwest J. Pure and Appl. Math., 7(1) (2001), 29-37 (electronic journal, (compressed postscript, pdf).
54. Analytic Continuation of Convex Bodies and Funk’s Characterization of the Sphere, with Eric Grinberg, Pacific J. Math. 201(2) (2001), 309-322 (pdf)
55. Stationary Sets for the Wave Equation on crystallographic domains, with Mark Agranovsky, Trans. Amer. Math. Soc., 355(2003), 2439-2451 (pdf).
56. Mean Value Extension Theorems and Microlocal Analysis, Proc. Amer. Math. Soc.,131(2003), 3267-3274 (pdf).
57. Some problems of integral geometry arising in tomography (pdf) (with Peter Kuchment), appendix to The universality of the Radon Transform by Leon Ehrenpreis, Oxford University Press, 2003.
58.On a regularization scheme for linear operators in distribution spaces with an application to the spherical Radon transform, coauthor Thomas Schuster, SIAM J. Appl. Math, 65(2005), 1369-1387(pdf).
60. An Introduction to X-ray Tomography and Radon Transforms, Proceedings of Symposia in Applied Mathematics, 63(2006), 1-23 (NOTE: (A.13) on p. 19 is true for local canonical graphs not general canonical relations)(pdf).
61. Remarks on stationary sets for the wave equation, with Mark Agranovsky, Contemporary Mathematics, vol. 405 (2006), 1-17 (pdf).
62. Support theorems for the spherical Radon transform on manifolds, International Mathematical Research Notices, 2006, 1-17 (abstract: pdf), (article: pdf).
63. Local Algorithms in Exterior Tomography, Journal of Computational and Applied Mathematics, 199(2007), 141-148 (pdf).
64. Range descriptions for the spherical mean Radon transform, with M. Agranovsky and P. Kuchment, Journal of Functional Analysis, 248(2007), 344-386 (article: pdf).
65. Local Tomography in Electron Microscopy, with O. Oktem, SIAM J. Applied Math. 68(2008), 1282-1303 (article: pdf).
66. Inversion of the X-ray transform from limited angle parallel beam region of interest data with applications to electron tomography, with O. Oktem, Proc. Appl. Math. and Mech. 7 (2007), 105031-105032 (article: pdf).
67. Local Tomography in 3-D SPECT, with Tania Bakhos and Sohhyun Chung (as undergraduate research students), in Mathematical Methods in Biomedical Imaging and Intensity-Modulated Radiation Therapy (IMRT), Edizioni della Normale (CRM Series # 7), Pisa Italy, 2008.(article: pdf).
68. Helgason’s Support Theorem and Spherical Radon Transforms, Contemporary Mathematics, 464(2008), 249-264 (article: pdf).
69. Electron Lambda Tomography, with Ozan Öktem and Ulf Skoglund, Proc. National Acad. Sci. U.S.A., 106(2009) no. 51 21842-21847 (preprint: pdf).
71.Local Sobolev Estimates of a Function by means of its Radon transform, with Hans Rullgård, Inverse Problems and Imaging 4(2010), 721-734. (article: pdf).
72. Reply to G. Wang and H. Yu: Both Electron Lambda Tomography and Interior Tomography have their uses, with Ozan Öktem and Ulf Skoglund, Proc. Nat. Acad. Sci. USA, 107(2010), E94-E95, (preprint: pdf).
73. Electron Microscope Tomography over Curves, joint with Hans Rullgård, Oberwolfach Reports, 18/2010, 1092-1095 (preprint: pdf).
74. Local Inversion of the Sonar Transform Regularized by the Approximate Inverse, with Andreas Rieder and Thomas Schuster, Inverse Problems. 27(2011) 035006 (18 pages) (pdf). Chosen as one of the Highlights of 2011 by Inverse Problems.
75. The microlocal properties of the Local 3-D SPECT operator, with Raluca Felea, SIAM J. Math. Anal., 43(2011), 1145-1157 (pdf).
76. Microlocal Aspects of Bistatic Synthetic Aperture Radar Imaging, joint with Venkateswaran Krishnan, Inverse Problems and Imaging, 5(2011), 659-674.(pdf)
77.Remembrances of Leon Ehrenpreis (with Daniele Struppa, Hershel Farkas, Takahiro Kawai, Peter Kuchment, Shlomo Sternberg, and Alan Taylor), Notices Amer. Math. Soc., 58(2011), 674-681 (pdf)
78. Microlocal Analysis of Elliptical Radon Transforms with Foci on a Line, joint with Venkateswaran Krishnan and Howard Levinson, The Mathematical Legacy of Leon Ehrenpreis, 1930-2010 (editors Irene Sabadini and Daniele Struppa), Springer Proceedings in Mathematics, 16(2012), 163-182 (pdf).
79. A class of singular Fourier integral operators in synthetic aperture radar imaging, joint with Gaik Ambartsoumian, Raluca Felea, Venkateswaran Krishnan, and Clifford Nolan, Journal of Functional Analysis, 264(2013), 246-269 (pdf).
80. Review of “Integral Geometry and Radon Transforms” by Sigurdur Helgason, with Fulton Gonzalez, Bulletin of the American Mathematical Society, S 0273-0979(2012),01391-5 (pdf).
81. Local Singularity Reconstruction from Integrals over Curves in R^3, with Hans Rullgård, Inverse Problems and Imaging 7(2)(2013), 585-609 (pdf).
82. The Microlocal analysis of the ultrasound operator with circular source and detectors, joint with Gaik Ambartsoumian, Jan Boman, and Venkateswaran Krishnan, Contemporary Mathematics, 598(2013), 45-58 (pdf).
83. Characterization and reduction of artifacts in limited angle tomography, joint with J{\u}rgen Frikel, Inverse Problems, 29(2013) 125007 (pdf). Addendum with reference
85. How to characterize and decrease artifacts in limited angle tomography using microlocal analysis, joint with J{\u}rgen Frikel, IOP Insights, January 7, 2014 http://iopscience.iop.org/0266-5611/labtalk-article/55769
86.Microlocal Analysis and Imaging, a short note in “The Mathematics of the Planet Earth,” with Gaik Ambartsoumian, Raluca Felea, Venky Krishnan, Cliff Nolan, Chapter 7, pages 8-11.Springer, Berlin, New York, 2014.
87. Wavelet methods for a weighted sparsity penalty for region of interest tomography, joint with Esther Klann and Ronny Ramlau, Inverse Problems 31(2015) 025001 (22pp) pdf. New reference
88. Microlocal Analysis in Tomography, joint with Venkateswaran Krishnan, (pdf) in Handbook of Mathematical Methods in Imaging, 2e, Book editor: Otmar Scherzer, 2015.
89. Artifacts in incomplete data tomography with applications to photoacoustic tomography and sonar, joint with J{\u}rgen Frikel, SIAM J. Appl. Math,75(2),(2015) 703–725. (23 pages) ((pdf).
* A paradigm for the characterization of artifacts in tomography, joint with J{\u}rgen Frikel (arXiv), (local pdf).
90. Common Midpoint versus Common Offset Acquisition Geometry in Seismic Imaging, with Raluca Felea, Venkateswaran Krishnan, and Clifford Nolan, Inverse Problems and Imaging, to appear, 2016 (pdf).
91. Limited data problems for the generalized Radon transform in R^n, joint with J{\u}rgen Frikel, SIAM J. Math. Analysis 48(4)(2016), 2301-2318 (arXiv) (local pdf).
92. Detectable singularities from dynamic Radon data, joint with Bernadette Hahn, SIAM J. Imaging Sciences, 9 (3)(2016), 1195-1225 ( arXiv) (local pdf).
93. Simultaneous reconstruction and segmentation with the Mumford-Shah functional for electron tomography, with Li Shen; Shiqiang Wang; Ming Jiang, 38th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC): (2016), Pages: 5909 – 5912, DOI: 10.1109/EMBC.2016.7592073.
94. Artifacts and Visible Singularities in Limited Data Tomography, Journal of Sensing and Imaging (2017) 18: 9. doi:10.1007/s11220-017-0158-7,(local pdf), Springer Version
95. Approximate inverse for the common offset acquisition geometry in 2D seismic imaging, joint with Christine Grathwohl, Peter Kunstmann, and Andreas Rieder, Inverse Problems, 34(1) 2018, 014002.(local pdf)
96. Singular FIOs in SAR Imaging, II: Transmitter and Receiver at Different Speeds, with Gaik Ambartsoumian, Raluca Felea, Venkateswaran Krishnan, and Clifford Nolan, SIAM J. Math. Analysis, 50(2018) 1 591-621.(local pdf) arXiv
97.Simultaneous reconstruction and segmentation with the Mumford-Shah functional for electron tomography, Li Shen, Shiqiang Wang, Eric Todd Quinto, and Ming Jiang, Inverse Problems and Imaging, (2018), 12(6), 1343-1364 doi: 10.3934/ipi.2018056 (local pdf).
98. Analyzing Reconstruction Artifacts from Arbitrary Incomplete X-ray CT Data, L. Borg, J. Frikel, J.S. Jorgensen, E.T. Quinto, SIAM Journal on Imaging Sciences, 11(4), 2786–2814 Oct. 2018. (29 pages) SIAM version, local pdf, arXiv
99. Microlocal Analysis of imaging operators for effective common offset seismic reconstruction, Christine Grathwohl, Peer Kunstmann, Eric Todd Quinto, and Andreas Rieder, Inverse Problems, 34(11)2018 114001 (24 pages) pdf .
101. Generalized Radon Transforms and Applications in Tomography, G. Ambartsoumian and E.T. Quinto, Inverse Problems 36(2)(2020)(preface to special issue) 020301, M pdf .
102. Microlocal Analysis of a Compton tomography problem, James Webber and Eric Todd Quinto, SIAM Journal on Imaging Sciences, 13(2)(2020), 746-774 local pdf arXiv .
103. Microlocal properties of dynamic Fourier integral operators, Bernadette Hahn and Melina Kienle Garrido, and Eric Todd Quinto, accepted book chapter, Time-dependent Problems in Imaging and Parameter Identification, editors Barbara Kaltenbacher, Thomas Schuster, Anne Wald, Springer Nature, Switzerland, 2020.  local pdf .
104. A joint reconstruction and lambda tomography regularization technique for energy-resolved X-ray imaging, James Webber, Eric Todd Quinto, Eric L. Miller, arXiv , local pdf, Inverse Problems 36 (2020) 074002 (32pp).
105. Imaging with the elliptic Radon transform in 3D from an analytical and numerical perspective, Christine Grathwohl, Peter Kunstmann, Eric Todd Quinto, and Andreas Rieder, SIAM J. Imaging Sciences, 13(4)(2020), 2250-2280 (local pdf)
106. Microlocal analysis of generalized Radon transforms from scattering tomography, James Webber, Eric Todd Quinto SIAM J. Imaging Sci., 14(3)(2021), 976-1003  arXiv , local pdf .
107. Limited-Data Tomography, chapter in Computed Tomography: Algorithms, Insight and Just Enough Theory, editors Per Christian Hansen, Jakob Sauer Jørgensen, William R. B. Lionheart pages 125-154 of xvii + 337 pages, ISBN: 978-1-611976-66-3, 2021, local preprint.
108. Seismic imaging with generalized Radon transforms:  stability under the Bolker condition, Peer Christian Kunstmann, Eric Todd Quinto, and Andreas Rieder, submitted 2021, local preprint.
109. Microlocal properties of seven-dimensional lemon and apple Radon transforms with applications in Compton scattering tomography, James Webber and Eric Todd Quinto, to appear Inverse Problems, 2022, local preprint.
110. What can you see with Computed Tomography? Per Christian Hansen, Jakob Sauer Jørgensen, William R.B. Lionheart, and Eric Todd Quinto, (From the SIAM Bookshelf) SIAM News, 55(7)(2022), 10-11 local preprint.
111. Ellipsoidal and hyperbolic Radon transforms; microlocal properties and injectivity, James Webber, Sean Holman, and Eric Todd Quinto, Journal of Functional Analysis, to appear, 2023. Local preprint.
112. Forward to Special Issue of Inverse Problems on Modern Challenges in Imaging, Bernadette N. Hahn, Eric Todd Quinto, and Gaël Rigaud, Inverse Problems, 39 (2023), 030401 DOI 10.1088/1361-6420/acb569. Local preprint.

Over 175 Research Lectures in the US, Austria, China, Denmark, Finland, France, Germany, India, Israel, Italy, Japan, Switzerland, Sweden, and the United Kingdom

Current Conferences and Minisymposia Organized, see here.

Editor

Referee for numerous journals.

Recent and Current Research Support

  • Simons Collaboration Grant 708556, Tomography and Microlocal Analysis, 2020-2025
  • National Science Foundation Grant DMS-1712207, Tomography and microlocal analysis, 2017-2022
  • My research has been supported by the NSF, NIH, or Air Force continuously since 1982.

Industrial Collaborations

  • Scientific Advisor Board, Mobius Imaging until 2017
  • Member BLL, formerly Scientific Advisory Board, Breakaway Imaging, now a Medtronic company (O-arm surgical imaging system).
  • Patents pending for electron microscopy reconstruction algorithm with Ozan Öktem
  • Consultant for medical and industrial companies, including Perceptics, Inc., Sidec, Stockholm, and Visualization Technology, Inc.

Current and Recent Department and University Responsibilities

  • Department Honors Committee, head 2022-23
  • Department Diversity Equity and Inclusion Committee head 2020-2021
  • Department Outreach Committee, head/co-head 2017-2020
  • Faculty Research Awards Committee, 2017-18
  • Tufts Community Appeal Board, 2017-19
  • Tenure and Promotion Committee 2014-16
  • Department Curriculum Committee Head, 2010-2012, 2014-15
  • Academic Review Board, 2006-2011
  • Interim Department Head 2007-2008
  • Leonard Carmichael Society faculty staff board member 2003-
  • Educational Policy Committee, 2000-2004, 2009-2012
  • Cohead 2000-2002, 2003-4
  • Phi Beta Kappa Executive Committee 1986-
    • President 1987-1990
  • Department Hiring Committees
  • Department Academic Honors