Research Themes for the Mathematical Sciences: IMAGINGCo-listings: CAAM 498, MATH 498, STAT 498 (1-3cr)CAAM 698, MATH 698, STAT 698 (1-3cr)Meets: Mondays, 4-6 PM in Duncan Hall 1070 |
Instructors:
Dennis Cox (STAT) email: dcox@rice.edu Homepage: http://statistics.rice.edu/FacultyDisplayHttpRequest.aspx?FID=268
Robert Hardt (MATH) email: hardt@rice.edu Homepage: http://math.rice.edu/~hardt/
William Symes(CAAM) email: symes@rice.edu Homepage: http://www.trip.caam.rice.edu/
Description:
Imaging and image processing are critical components of many scientific and engineering disciplines. Seismic imaging produces the most detailed structural maps of the earth's interior available to geoscientists, both for industrial applications (oil exploration) and for academic investigations of deep earth structure. Modern medicine relies on a myriad of imaging technologies, including X-ray computed tomography (CT), magnetic resonance imaging (MRI), ultrasonic imaging, positron emission tomography (PET), optical imaging, and electrical impedance tomography. Materials scientists and mechanical engineers use ultrasonic, eddy current, and other imaging techniques to idenfity fractures and other flaws in manufactured objects such as reactor vessels and turbine blades. All of these technologies are undergoing rapid development.
At the same time, mathematicians, statisticians, and signal processing engineers have made great strides in understanding some of the cross-cutting issues in image processing, such as object recognition and registration, image de-noising and de-blurring, and in the basic process of reconstructing images from measurable data of various sorts. Scientific and technological needs continue to motivate new mathematics, and the new mathematics continues to be used to improve the performance of practical imaging methods.
This course will be an introduction to some of these applications and their underlying mathematical theories. The format will involve several outside speakers(*) who will be scientists or mathematicians specializing in various imaging problems. The three instructors will endeavor to give introductory mathematical material that provides both preparation for some of these invited lectures as well as suitable discussions inspired by the lectures.
Students who register for the full 3 credits will be required to do a small project that will involve some presentation later in the semester.
The first meeting on Monday August 25 will involve a description of the operation of the course as well as some short overview talks by the three instructors. There also will be a poster and course representatives at the VIGRE Poster Presentation, Wednesday, August 27 4-5:30pm in the Brochstein Pavilion.
(*) List of Confirmed Guest Speakers so far:
Schedule of Talks:
August 25. Description and Organization: D. Cox, R. Hardt, W. Symes
September 8. Introduction to Medical Imaging: D. Cox
September 15. CANCELLED due to Hurricane Ike
September 22. Seeing Through Rock: The Mathematics of Reflection Seismology, William Symes
September 29. A Very Short Introduction to Fourier Analysis on Groups and Representation Theory, Robert Hardt
October 6. Luc Bidaut
October 13. Mid-Semester Break
October 20. Jacek Turski
October 27. Robert Azencott
November 3. William Symes, Reflection Seismology
November 10. Yunmei Chen, Medical Imaging Analysis
November 17. Robert Hardt, Some Remarks on Total Variation and Imaging
November 24. Dennis Cox, Some Statistical Methods for Image Analysis
December 1. Lecture cancelled
Happy Holidays!
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Updated December 1, 2008
