Math 6397: Mathematics of Medical Imaging

Math 6397 -- Mathematics of Medical Imaging
SPRING 2015

	Instructor: Demetrio Labate OFFICE: PGH 694 EMAIL ADDRESS: dlabate@math.uh.edu HOMEPAGE: http://www.math.uh.edu/~dlabate When and Where MEETING TIME: Mon, Wed, Fri 12-1, MEETING PLACE: AH 301 OFFICE HOURS: Mon, Wed 11-12 (or by appointment) Course Description: At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data. This course provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most imaging modalities in current use, including Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). In the process, we covers many important mathematical concepts and techniques from Fourier analysis, integral geometry, sampling theory and noise analysis. Textbook: Introduction to the Mathematics of Medical Imaging, by C. L. Epstein, Society for Industrial & Applied Mathematics; 2nd edition (September 28, 2007). HOMEWORK: Homework 1: 1.2.4, 1.2.10, 1.2.12, 2.1.5, 2.1.6, 2.2.2 - Due 02/04 - Solution Homework 2: 3.2.1, 3.4.2, 3.4.6, 3.4.9, 3.4.11, 4.2.7 - Due 02/13 - Solution Homework 3: 4.2.14, 4.2.22, 4.2.24, 4.3.11, 4.5.5, 5.1.9 - Due 03/04 - Solution Homework 4: 5.1.11, 6.1.2, 6.1.6, 6.2.3, 6.2.5, 6.2.8 - Due 03/27 - Solution Test 1 with Solution Test 2. Useful code files. Due April 20.

Instructor: Demetrio Labate

dlabate@math.uh.edu

http://www.math.uh.edu/~dlabate

When and Where

Course Description:

At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data. This course provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most imaging modalities in current use, including Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). In the process, we covers many important mathematical concepts and techniques from Fourier analysis, integral geometry, sampling theory and noise analysis.

Textbook:

Introduction to the Mathematics of Medical Imaging, by C. L. Epstein, Society for Industrial & Applied Mathematics; 2nd edition (September 28, 2007).

HOMEWORK:

Solution

Test 1 with Solution
Test 2. Useful code files. Due April 20.

Other useful references (I will use some material from here):

Mathematical methods in image reconstruction, by F Natterer and F Wubbeling, Society for Industrial and Applied Mathematics (December 20, 2001).
Principles And Advanced Methods In Medical Imaging And Image Analysis, by Atam P. Dhawan, H K Huang, Dae-Shik Kim, H. K. Huang, World Scientific Publishing Company (March 17, 2008).

Prerequisites:

Ideal prerequisites are MATH 6320-21. However the course will be so designed that any interested student with a solid background of calculus, linear algebra (MATH 4377), and basic mathematical analysis (MATH 4331) will be able to follow the course.

Course outline:

- Fourier Analysis

- Liner filters and convolution

- Tomography

- Radon and X-ray transforms

- Magnetic Resonance Imaging

- Other Topics in Image Reconstruction

Tests and Exam Dates:

There will be two midterm exams, whose tentative dates are Wed 03/11 and Fri 04/17. There will be a final project consisting in reading a research paper (or possibly a group of closely related papers), writing a 1-2 page report and presenting it in class (15 min). Alternatively, the final project may consist in developing a numerical code based on a paper, writing a 1-2 page report and presenting it in class (15 min). NOTE: The choice of project need to be approved by the instructor.

♦ Here is a list of possible research papers for the final projects. You can also propose a paper to the instructor.

♦You need to submit a report on your paper according to the following instructions. Due date: MON April 27.

Grading:

Grades will be based on homework assignments, counting 40% towards the final grade, on two midterm exams counting 30% towards the final grade, and one final project counting 30%.

The grade will be determined according to a set point scale: 90%-100%: A, 80%-89%: B, 70%-79%: C, 60-69% D; F is less than 60% (+ and - will also be used).