Syllabus for Math 584
The general topics covered are:
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Mathematical models and measurement.
- Linear equations and an introduction to function spaces.
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Integral transforms: the Fourier transform, the Radon transform, the Abel
transform, convolution.
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Sampling and digitization, interpolation and approximation.
- Nyquist's theorem and basic concepts of signal processing.
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Implementing shift invariant filters.
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Imaging hardware and the basic algorithms of image reconstruction.
- Analysis of systematic artifacts.
- Introduction to probability and statistics
- Analysis of noise in tomography.
Assignments will be due on 9/26, 10/10, 10/26, 11/7, 11/21 and 12/7.
Student presentations will be given in the evening during the last week
of class. We will have one and possibly two field trips, held outside
class hours.
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