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, fast algorithms.
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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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