Course Outline
Overview
The course starts with an introduction to multidimensional Fourier transforms. It then goes into four different types of imaging systems. Each of these sections is two weeks. The first week is a description of the physics and geometry of a typical system that uses that imaging mechanism. The second week examines a specific signal processing problem that arises with that modality. Matlab experiments will involve implementing these algorithms on real and simulated data.
Outline
Section 0: Multidimensional Fourier Transforms
Week 1 - Introduction to the course - Review of 1D Fourier transforms - Introduction to Multidimensional Fourier Transforms
Week 2 - 2D and 3D Fourier Transforms - Sampling in multiple dimensions
Section 1: Backprojection Imaging Systems
Week 3 - Physics and geometry of X-Ray CT - Description of PET and SPECT
Week 4 - Backprojection reconstruction algorithms and geometries - Matlab: Implement either convolution backprojection, or Fourier interpolation reconstruction
Section 2: Fourier Encoding Systems
Week 5 - Physics and geometry of MRI systems
Week 6 - Reconstruction of MRI images - Either Fourier interpolation or reconstruction from partial data - Matlab: Implement partial k-space reconstruction using MR data
Section 3: Beam Forming Imaging Systems
Week 7 - Physics of ultrasound imaging systems - Common imaging geometries
Week 8 - Beam forming with ultrasound transducer arrays - Dynamic focus on transmit and receive - Matlab: Implement dynamic focus on receive using ultrasound data.