**Selected Publications of Todd Quinto
(with links)** **and other professional information****.**

*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, Tufts University and other organizations also provided support.*

*"Any opinions, findings, and conclusions or recommendations expressed in this web site 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,

**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 EngineeringSpringer 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. Generalized Radon Transforms and Applications in Tomography, *special issue of

**Articles:**

**15.**The dependence of the generalized Radon transform on defining measures, Trans. Amer Math. Soc., 257(1980), 331-346. (pdf)

**16. **A Radon transform on spheres
through the origin in R^n and applications to the Darboux equation, joint
wiht Allan
Cormack, *Trans. Amer. Math. Soc.*. **260**(1980),
575-581. (pdf).

**19. **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).

**20. **Singular value decompositions
and inversion methods for the exterio Radon transform and a spherical transfrom, *J. Math. Anal. Appl*. **95**(1983), 437-448. (pdf).

**25.** Support theorems for real analytic Radon transforms, coauthor: J. Boman, Duke Math. J. 55(1987), 943-948. (pdf)

**26.** Tomographic reconstructions from incomplete data--numerical inversion of the exterior Radon transform, Inverse Problems, 4(1988), 867-876. (pdf)

**30.** The mathematics and physics of radiation dose planning, coauthor Allan Cormack, Contemporary Mathematics 113(1990), 41-55. (pdf)

**32.** Support theorems for real analytic Radon transforms on line complexes, coauthor: J. Boman, Trans. Amer. Math. Soc. 335(1993), 877-890. (pdf)

**33.** Real analytic Radon transforms on Rank one symmetric spaces, Proc. Math. Soc. 117(1993), 179-186. (pdf)

**34.** Pompeiu transforms on geodesic spheres in real analytic manifolds, Israel J. Math., 84(1993), 353-363. (pdf)

**35. **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)

**36.** Support theorems for Radon transforms on higher rank symmetric spaces, coauthor Fulton Gonzalez, Proc. Amer. Math. Soc, 122(1994), 1045-1052. (pdf)

**37.** 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)

**38.** Radon transforms on curves in the plane, Lecture Notes in Applied Mathematics, 30(1994), 231-244. (pdf)

**39.** Injectivity sets for a Radon transform and complete systems of radial functions, an announcement, coauthor

**40.** Injectivity sets for the Radon transform over circles and complete systems of radial functions, coauthor

**41.**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).

**42.**Morera Theorems via Microlocal Analysis, coauthor Josip Globevnik, J. Geom. Analysis **6**(1996), 20-30 (article pdf)

**43. **Exterior and Limited Angle Tomography in Non-destructive Evaluation, Inverse Problems, 14 (1998), 339-353. (pdf)

**44.** 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)

**45.** On the non-uniqueness of optimal radiation treatment plans, with Christoph Boergers, Inverse Problems, 15(1999), 1115-1138. (pdf)

**46. **Two-radius Support Theorems for Spherical Radon transforms on Manifolds, with Yiying Zhou, Contemporary Mathematics, 251(2000), 501-508. (pdf)

**47.** Local Tomographic Methods in SONAR, with Alfred Louis, in ``Surveys on Solution Methods for Inverse Problems'' Springer Verlag, 2000. (pdf)

**48.** Morera theorems for complex manifolds, coauthor Eric Grinberg, Journal of Functional Analysis, 178(2000), 1-22. (pdf)

**49.** Radon Transforms, Differential Equations, and Microlocal Analysis, Contemporary Mathematics, 278(2001), 57-68. (pdf)

**50. **Geometry of Stationary Sets for the Wave Equation in R^n, The Case of Finitely Supported Initial Data, with

**51.** Geometry of Stationary Sets for the Wave Equation in R^n, The Case of Finitely Supported Initial Data, an Announcement, with

**52. **Analytic Continuation of Convex Bodies and Funk's Characterization of the Sphere, with Eric Grinberg, Pacific J. Math. 201(2) (2001), 309-322 (pdf)

**53.** Stationary Sets for the Wave Equation on crystallographic domains, with Mark Agranovsky, Trans. Amer. Math. Soc., 355(2003), 2439-2451 (pdf).

**54.** Mean Value Extension Theorems and Microlocal Analysis, Proc. Amer. Math. Soc.,131(2003), 3267-3274 (pdf).

**55.** 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.

**56.**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).

**57. **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).

**58.** Remarks on stationary sets for the
wave equation, with Mark Agranovsky, Contemporary
Mathematics, vol. 405 (2006), 1-17 (pdf).

**59.** Support theorems for the spherical Radon transform on manifolds, International Mathematical Research Notices, 2006, 1-17 (abstract: pdf),
(article: pdf).

**60.** Local Algorithms in Exterior Tomography, Journal of Computational and Applied Mathematics, 199(2007), 141-148 (pdf).

**61. **Range descriptions for the spherical mean Radon transform, with M. Agranovsky and P. Kuchment, Journal of Functional Analysis, 248(2007), 344-386 (article: pdf).

**62. **Local Tomography in Electron Microscopy, with O. Oktem, SIAM J. Applied Math. 68(2008), 1282-1303 (article: pdf).

**63. **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).

**64.** 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).

**65. **Helgason's Support Theorem and Spherical Radon Transforms, Contemporary Mathematics, 464(2008), 249-264 (article: pdf).

**66.** Electron Lambda Tomography, with Ozan Öktem and Ulf Skoglund, Proc. National Acad. Sci. U.S.A., 106(2009) no. 51 21842-21847 (preprint: pdf).

**67.**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).

**68.** 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).

**69. **Electron Microscope Tomography over Curves, joint with Hans Rullgård, Oberwolfach Reports, 18/2010, 1092-1095 (preprint: pdf).

**70. **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.

**71. **The microlocal properties of the Local 3-D
SPECT operator, with Raluca Felea, SIAM J. Math. Anal., 43(2011), 1145-1157 (pdf).

**72. **Microlocal Aspects of Bistatic Synthetic
Aperture Radar Imaging, joint with Venkateswaran Krishnan,
Inverse Problems and Imaging, 5(2011),
659-674.(pdf)

**73.**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)

**74.** 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).

**75. **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).

**76.** 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).

**77. **Local Singularity Reconstruction from
Integrals over Curves in R^3, with Hans Rullgård, *Inverse Problems and Imaging 7(2)(2013), 585-609 * (pdf).

**78. **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).

**79. **Characterization and reduction of
artifacts in limited angle tomography, joint with
J{\u}rgen Frikel, Inverse Problems, 29(2013) 125007 (pdf). Addendum with reference

**80.** 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

**81.**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.

**82. **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

**83. **Microlocal Analysis in Tomography, joint with
Venkateswaran Krishnan, (pdf) in *Handbook of
Mathematical Methods in Imaging, 2e, *Book editor: Otmar Scherzer, 2015.

**84. **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) (copy on arXiv), (local pdf).

*** **A paradigm for the characterization of artifacts in tomography, joint with J{\u}rgen Frikel (copy on arXiv), (local pdf).

**85. **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).

**86. **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 (copy on arXiv) (local pdf).

**87. **Detectable singularities from dynamic Radon data, joint with Bernadette Hahn, SIAM J.
Imaging Sciences, 9 (3)(2016), 1195-1225 (copy on arXiv) (local pdf).

**88. **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.

**89. **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

**90.** 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)

**91. **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

**92.**Simultaneous reconstruction and segmentation with
the Mumford-Shah functional for electron tomography, with Li Shen;
Shiqiang Wang; Ming Jiang, Inverse Problems and Imaging, (2018), 12(6), 1343-1364 doi: 10.3934/ipi.2018056 (local pdf).

**93. ** Analyzing Reconstruction
Artifacts from Arbitrary Incomplete X-ray CT Data, with L. Borg, J.
Frikel, J.S. Jorgensen, SIAM Journal on Imaging Sciences, 11(4),
2786–2814 Oct. 2018. (29 pages)
SIAM version,
local pdf, arXiv

**94. ** Microlocal Analysis of imaging operators for
effective common offset seismic reconstruction, joint authors
Christine Grathwohl, Peer Kunstmann, and Andreas Rieder, Inverse
Problems, to appear, 2018, pdf .

**95. ** Microlocal Analysis of a Compton tomography problem,
joint author James Webber, submitted 2019,
local pdf, arXiv .

Over 160 Research Lectures in the US, China, Europe, India, Israel, and Japan

Current Conferences and Minisymposia Organized click here.

Editor:

Inverse Problems (Editor
in chief: Simon Arridge)

Journal of Fourier Analysis and Applications
(Editor-in-Chief: Hans Feichtinger)

Journal of Inverse and Ill-Posed Problems (editor-in-Chief: Sergey Kabanikhin)

SIAM
Journal of Imaging Science (Editor in Chief: Michael Elad)
2007-2017

Referee for numerous journals.

Recent and Current Research Support:

National Science Foundation Grant DMS-1712207, Tomography and microlocal analysis, 2017-2020

My research has been supported by the NSF, NIH, or Air Force continuously
since 1982.

Industrial Collaborations:

Scientific Advisor Board, Mobius Imaging.

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 Oktem

**Consultant for medical and industrial companies, including Perceptics, Inc., Sidec, Stockholm, and Visualization Technology, Inc.
**

Current and Recent Department and University Responsibilities:

Faculty Research Awards Committee, 2017-

Tufts Community Appeal Board, 2017-

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

Home

Last modified by Todd Quinto on 8/14/2018