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Syllabus of Math 664, Section 601

Seminar in Applied Mathematics: Mathematics of medical imaging, Fall 2015

Instructor Peter Kuchment

Office Rm. Blocker 614A, Telephone (979)862-3257

E-mail: kuchment AT math DOT tamu DOT edu, Home Page: /~kuchment


Mathematics behind medical imaging (e.g., well known CAT scan, MRI, Ultrasound, and many others) is very diverse and beautiful. In spite of the title, industrial, geophysics, and homeland security applications will also be touched upon.
I will cover the basics of Radon and related transforms arising in imaging, their relations to radiative transport and wave equations, mathematics of various types of classical, as well as newly being developed tomographic methods.
The background suggested is basics of Real, Complex, and Functional analysis, elements of Fourier series and transforms (albeit a write-up will be provided) are highly desirable. Elements of PDEs would not hurt as well.

Recommended literature

I will use a variety of sources (including the instructor's notes and probably some texts placed on reserve), so there is no textbook required.
Here are some useful books:

  1. T. Feeman, The mathematics of medical imaging: a beginner's guide, Springer 2009. An undergraduate text about very basic stuff.

  2. P. Kuchment, The Radon transform and medical imaging, SIAM 2014. Graduate level. The closest to the class.

  3. F. Natterer, The mathematics of computerized tomography, Wiley 1986. Reprinted by SIAM in 2001. The classical excellent source. Rather terse writing, but rewarding reading. Somewhat outdated.

  4. F. Natterer and F. Wuebbeling, Mathematical methods in image reconstruction, SIAM 2001. More or less updates the 1986 book.

  5. S. Helgason, The Radon transform, Birkhauser 1980. A very nice book. Theoretical, directed more towards integral geometry and abstract harmonic analysis than tomography.

  6. S. Helgason, Integral geometry and Radon transform, Springer 2011. Similar in the spirit to the previous book.

Video lectures by the instructor (the links also contain lectures by other experts on related topics)


will be based upon class participation.

The standard bunch of warnings:

Class Announcements, E-Mail Policy and Communications:

Class announcements will be posted on my homepage and in most important cases e-mailed to your NEO accounts (it is your responsibility to check your NEO accounts daily).
E-mail (kuchment AT math DOT tamu DOT edu) is the preferred way of contacting me. When writing to me, please include your full name and "Math 664". Use your NEO e-mail account to send me e-mails.

Students with Disabilities:

The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Services for Students with Disabilities (Cain Hall, Room B118, or call 845-1637).

Copyright policy:

All printed materials disseminated in class or on the web are protected by Copyright laws. One xerox copy (or download from the web) is allowed for personal use. Multiple copies or sale of any of these materials is strictly prohibited.

Scholastic dishonesty:

Copying work done by others, either in class or out of class, looking on other student?s papers during exams or quizzes, having possession of unapproved information in your calculator/computer/phone, etc., and/or having someone else do your work for you are all acts of scholastic dishonesty. These acts, and other acts that can be classified as scholastic dishonesty, will be prosecuted to the full extent allowed by University policy. In this class, collaboration on graded assignments, either in class or out of class, is forbidden unless permission to do so is granted by the instructor. For more information on university policy regarding scholastic dishonesty, see University Student Rules at
"An Aggie does not lie, cheat, steal, or tolerate those who do." Visit and follow the rules of the Aggie Honor Code.


This syllabus is subject to change at the instructor's discretion

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Last revised April 23rd, 2015