Office Rm. Blocker 614A, Telephone (979)862-3257
E-mail: kuchment AT math DOT tamu DOT edu, Home Page: /~kuchment
Time: TR 2:20 -3:35 pm
Room: Blocker 506A (notice the room change)
Office hours: Tuesdays 4-5 pm, Thursdays 12:30-1:30 pm.
Additional office hours can be arranged by appointment.
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.
I will use a variety of sources (including the instructor's notes
and probably some texts placed on reserve), so there is no
Here are some useful books:
T. Feeman, The mathematics of medical imaging: a beginner's guide, Springer 2009. An undergraduate text about very basic stuff.
P. Kuchment, The Radon transform and medical imaging, SIAM 2014. Graduate level. The closest to the class.
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 Somewhat outdated.
F. Natterer and F. Wuebbeling, Mathematical methods in image reconstruction, SIAM 2001. More or less updates the 1986 book.
S. Helgason, The Radon transform, Birkhauser 1980. A very nice book. Theoretical, directed more towards integral geometry and abstract harmonic analysis than tomography.
S. Helgason, Integral geometry and Radon transform, Springer 2011. Similar in the spirit to the previous book.
P. K. introductory lectures, Berkeley 2009
P. K. Hybrid imaging, Berkeley 2010
P. K. Hybrid imaging, Bangalore 2014
will be based upon class participation.
The standard bunch of warnings:
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.
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