Medical Image Science: Mathematical and Conceptual Foundations
(Medical Physics/Biomedical Engineering 573)
Instructors: Diego Hernando, PhD, and Sean Fain, PhD
Offered: Fall Semester
This course covers the mathematical fundamentals required for medical imaging science. Prof. Hernando covers fundamentals of signal analysis with an emphasis on Fourier transforms in one and multiple dimensions. Additional topics include noise in imaging and image reconstruction. This is a hands-on course with a combination of theoretical foundations (on the white board) and computational exercises (using a language such as Python or Matlab) on real and simulated datasets. Mathematical concepts are presented in the context of real-world clinical and research challenges.
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Materials for the first half of Med Physics/BME 573
Lecture 0: Introduction / Jupyter notebook
Lecture 1: Signals in 1D and N-D / Jupyter notebook
Lecture 2: LSI systems in 1D / Jupyter notebook
Lecture 3: LSI systems in N-D / Jupyter notebook
Lecture 4: The Fourier transform / Jupyter notebook
Lecture 5: Properties of the Fourier transform / Jupyter notebook
Lecture 6: Fourier transforms in N-D / Jupyter notebook
Lecture 7: Properties of the Fourier transform in N-D / Jupyter notebook / Extra notebook
Lecture 8: Sampling in 1D / Jupyter notebook
Lecture 9: Sampling in N-D / Jupyter notebook
Lecture 10: Recap of LSI, Fourier, and sampling / Jupyter notebook
Lecture 11: DFT and FFT / Jupyter notebook
Lecture 12: DFT in multiple dimensions / Jupyter notebook
Lecture 13: Properties of the DFT / Jupyter notebook
Lecture 14: DFT and convolution / Jupyter notebook
Lecture 15: DFT and image reconstruction / Jupyter notebook
Lecture 16: Limitations of the DFT. STFT. / Jupyter notebook
Lecture 17: Intro to wavelets / Jupyter notebook
Imaging in Medicine: Applications
(Medical Physics/Biomedical Engineering 574)
Instructors: Diego Hernando, PhD, and Sean Fain, PhD
Offered: Spring Semester
This course covers topics in medical imaging and image processing, including image reconstruction, registration, and segmentation. These topics provide a deeper understanding of medical imaging systems, and are important for both the characterization of existing systems and for the development of novel imaging techniques. Prof. Hernando covers optimization problems and techniques, which have general applications in imaging and byond, as well image reconstruction. This course will combine a theoretical framework with computational examples and exercises.