Syllabus for Math 584
The general topics covered are:
Mathematical models and measurement.
- Linear equations and an introduction to function spaces.
Integral transforms: the Fourier transform, the Radon transform, the Abel
Sampling and digitization, interpolation and approximation.
- Nyquist's theorem and basic concepts of signal processing.
Implementing shift invariant filters, fast algorithms.
Imaging modalities and the basic algorithms of image reconstruction in X-ray CT, and MRI.
- Introduction to Probability and Statistics, and the analysis of noise.
- Reconstruction in PET.
- Image analysis.
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