Lectures: M W 2:00 - 3:15 in ECG 335
Recitation: F 1:40 - 3:30 in ECG 335
Professor: Svetlana Roudenko

• Office: PSA 629
• Office Phone: 695-3791
• Office Hours:
  • by appointment
• E-mail: svetlana@math.asu.edu
• Webpage: http://math.asu.edu/~svetlana/Fall2008.html

Graduate TA : Cristi Guevara
Office: PSA 327
Office hours: Monday 1-1:50pm (preliminary) or by appointment
E-mail: guevara@mathpost.asu.edu
Undergraduate TA : Steven Troxler
Office: PSA 16
Office hours: Wednesday 1-1:50pm (preliminary) or by appointment
E-mail: Steven.Troxler@asu.edu

Text: Introduction to the Mathematics of Medical Imaging (2th edition!) by Charles L. Epstein.

Supplementary Texts: (available in Science Library for 3 day loan)
1. An Introduction to the Principles of Medical Imaging by Chris Guy and Dominic ffytche
2. Fourier Analysis: An Introduction by Elias Stein and Rami Shakarchi
3. Principles of Magnetic Resonance Imaging: A Signal Processing Perspective by Zhi-Pei Liang and Paul Lauterbur

Extra Material:
1. Lecture Notes (will be available on class webpage as we cover the material)
2. "The Basics of MRI" -- MRI online textbook by Dr. Joseph P. Hornak
3. Paul Lauterbur "Image Formation by Induced Local Interactions: Examples Employing Nuclear Magnetic Resonance , Nature 242 (1973), 190-191 html link

Attendance:
Students are expected to attend lectures on Mondays and Wednesdays and are encouraged to participate in discussions and work on projects on Fridays.

Special features of this class:
* We have a graduate and undergraduate TAs to help students with learning the material. Please, discuss any concerns, suggestions, remarks about the material/class/topics/projects with any of the TAs or/and with the instructor.
* We will have a `field trip' on Friday 09/05 to the research MRI Lab at St.Joseph hospital in downtown Phoenix. Details on time and direction will follow soon.
* There will be at least 2 guest lectures by experts on Medical Imaging: Mark your calendars:

• October 1 - "Intro to MRI" presentation
• November 3 - "Modern methods in MRI" presentation

Lecture Notes:
Lecture Notes will be available on http://math.asu.edu/~svetlana/Fall2008lectures.html .
Tentative Topics:

• Review of Linear Algebra
• Metrics, Norms, Inner Products
• Discrete Fourier Transfrom
• Convergence and Completeness
• Basics of Lp theory
• Fourier series
• Convolution and Intro to Distributions
• Fourier Transform (extention to L^2 and tempered distributions)
• Basics of Sampling Theory
• Theory of the Radon Transform
• Basics of CT
• Reconstruction in CT: filtered back-projection
• Basics of MRI: Physics of MR, Magnetization, Relaxation, RF and Gradient Fields, Excitations, Slice Selection, Phase and Frequency Encoding, Bloch equation, 3D Imaging, 2D Projection Reconstruction, 2D FT reconstruction
• More topics in MRI: Reconstruction in MRI: rectilinear sampling and gridding, Contrast Adjustment (T1 and T2 weighting), Fast Imaging Methods, Modern Techniques
• Applications of Probability

Projects:
A preliminary list of projects can be found at http://math.asu.edu/~svetlana/Fall2008projects.html .
Each Friday will contain the discussion of the material lectured on Monday and Wednesday and work on projects.
Tentative List of Projects:

• Linear Algebra
• Convergence and Completeness
• FFT project (MATLAB)
• Function spaces and sets of measure zero
• Convolution and basics of distributions
• Basics of the Fourier transform
• Fourier Transform on L^2
• Sampling
• Invertion of the Radon Transform
• The Bloch Equation in MRI
• Excitation in MRI
• Slice selection in MRI
• FT reconstruction of MRI data (MATLAB)
• CT reconstruction

Evaluation: by projects
This means that we will usually start working on projects on Friday and if not finished, they should be finished at home (if there are any questions, see any of the TAs) and then turned in on the following Wednesday in class. Special projects (like MATLAB assignments or more research oriented) will have special deadlines.