Home page for Math 584 Mathematics of Medical Imaging Spring
Instructor: Charles L. Epstein
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In the last 50 years have witnessed an ongoing revolution in image
techniques in fields from astrophysics to electron microscopy and most
in medical imaging. In each of these fields one would like to have a
picture of a 2 or 3 dimensional object that cannot be obtained
accessible data is typically some collection of filtered averages. The
of image reconstruction is to build an object out of the averaged data
estimate how close the reconstruction is to the actual object.
we introduce the mathematical techniques used to model measurements and
reconstruct images. In this context we cover some of the basic
mathematical analysis, the Fourier transform, interpolation and
of functions, sampling theory, digital filtering, noise analysis, and
prerequisites are calculus through math 241, basic mathematical analysis, linear algebra as
Coursework: Problem sets,
and/or computational exercises
will be assigned every week, or every other week; in addition each student will be asked
to prepare a presentation for the class on a subject related to
The textbook is Introduction
to the Mathematics of Medical
Imaging, 2nd Edition
by C.L. Epstein. Students should purchase the textbook directly from
Amazon, or SIAM (become a student member of SIAM for free, and get the
discounted member price).
Additional material may be
the following sources:
- *Principles of Computerized Tomographic Imaging by
Avinash C. Kak
and Malcolm Slaney This book is now available online at Kak and Slaney
- *Computerized tomography: The new medical X-ray technology
by L.A. Shepp
and J.B. Kruskal in Amer. Math. Monthly 1978, pages 421-439
- Image reconstruction from Projections by Gabor T.
- Foundations of Medical Imaging by Cho, Jones, Singh
- Intermediate Physics for Medicine and Biology by
Russell K. Hobbie
- Radiological Imaging by Barrett and Swindell
- The Mathematics of Computerized Tomography by Frank
- *Numerical Linear Algebra by Trefethen and Bau
- Foundations of Image Science
by Barrett and Meyers. This is an encyclopedic treatment of
mathematical methods used in imaging.
Out: Inverse Problems and Applications. A collection of
mathematical articles on topics connected to imaging, Gunther Uhlmann,
- Webpage with software and references on the Non-uniform Fast
Fourier Transform (NUFFT).
- The class meets on TTh from 1:30-3:00 in DRL, room 2C2.
- My office hour is 2:30 to 3:30 on Mondays in my office, room 4E7
DRL, tel. 8-8476.
- My email is: firstname.lastname@example.org.
Send e-mail if you have a question, or need to contact me.
- Jinshuo Dong is the grader. His e-mail is email@example.com. His
office hours will be announced, his office 1N1 in
- The first class will be held January 12, 2017 at 1:30.
- Our classroom has been moved to 2C2 in DRL effective 1/17/17.
- We will have project presentations in class on April 25th (the last day of class).
- Problem set 1, due January 31, 2017.
- Problem set 2, due February 14, 2017. You should work through the first 4 MATLAB worksheets: Basics, Linear Algebra, Images, and the Radon Transform. Make sure to do the exercises!
- Problem set 3, due February 28, 2017.
- Problem set 4, due March 28, 2017.
- Problem set 5, due April 11, 2017.
- Problem set 6, due April 25, 2017.
- For the week of 1/16 read Chapter 1, and Section 2.1
- For the weeks of 2/1-12 read Chapter 3.1-3.4
- For the weeks of 2/27-3/ 17 read Chapter 5 and the beginning of Chapter 6
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